Maurits Cornelis Escher, who was born in Holland in 1898, till this day is one of the world’s most famous graphic artists. His art is enjoyed by millions of people all over the world. The youngest son of a civil engineer spent most of his childhood in Arnhem. Targeting to be an architect, he enrolled in the School for Architecture and Decorative Arts in Haarlem where he received his first instruction in drawing, by F.W. Van Der Haagen, who helped him to develop his graphic skill by teaching in the technique of the linoleum cut (an engraving and printing technique derived from woodcutting). He created visual riddles, playing with the pictorially logical and the visually impossible. He was instructed in the graphic techniques by S. Jessurun de Mesquita, whose sturdy personality drastically influenced Escher’s further development, as a graphic artist.
Apart from being a graphic artist, Maurits illustrated books, designed tapestries, postage stamps and murals.
According to his official website (www.mcescher.com); after finishing school, he traveled extensively through Italy, where he met his wife Jetta Umiker, whom he married in 1924. They settled in Rome, where they lived until 1935. During these eleven years, Escher would travel each year throughout Italy, drawing and sketching for the various prints he would make when he returned home.
Among his greatest admirers were mathematicians, who recognized in his work an extraordinary visualization of mathematical principles as mentioned in the Mathematical Art of Escher’s website (http://www.mathacademy.com/pr/minitext/escher/index.asp). What is even more amazing is that Escher had no formal mathematics training past secondary school. As his work developed, he drew great inspiration from the mathematical ideas he read about, often working directly from structures in plane and projective geometry, and eventually capturing the essence of non-Euclidean geometries. He was also fascinated with illogicality and “impossible” figures, and used an idea of Roger Penrose’s (highly regarded for his work in mathematical physics. He is also a recreational mathematician and controversial philosopher) to develop many fascinating works of art. Thus, for the student of mathematics, Escher’s work encompasses two broad areas: the geometry of space, and what we may call the logic of space.
Regular divisions of a plane, “tessellations,” are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. Typically, the shapes making up a tessellation are polygons or similar regular shapes, such as the square tiles often used on floors. Escher, however, was fascinated by every kind of tessellation – regular and irregular – and took special delight in what he called “metamorphoses,” in which the shapes changed and interacted with each other, and sometimes even broke free of the plane itself. His interest began in 1936, when he traveled to Spain and viewed the tile patterns used in the Alhambra. He spent many days sketching the tilings, and later claimed that this “was the richest source of inspiration that I have ever tapped.”
The regular solids, known as polyhedra, held a special fascination for Escher. He made them the subject of many of his works and included them as secondary elements in a great many more. There are only five polyhedra with exactly similar polygonal faces, and they are called the Platonic solids: the tetrahedron, with four triangular faces; the cube, with six square faces; the octahedron, with eight triangular faces; the dodecahedron, with twelve pentagonal faces; and the icosahedron, with twenty triangular faces.
The creation of a woodcut is slow, handmade work, and Escher never created large editions. Every print requires careful inking of the woodblock, and the paper has to be positioned and rubbed with great care to get the ink to lay on the paper just right, and no mechanized machinery is used. Making ten woodcut prints is tough work, and an addition of one hundred is monumental undertaking.
It is for this reason that prints are among the great art treasures of the twentieth century. The print you own is an original Escher in every sense of the word, and it is the only type of work he created… he did not produce any drawings or paintings except in preparation of making his prints. “I am a graphic artist, heart and soul,” he said.
Among the most important of Escher’s works from a mathematical point of view are those dealing with the nature of space itself. His woodcut Three Intersecting Planes is a good place to begin a review of these works, for it exemplifies the artist’s concern with the dimensionality of space, and with the mind’s ability to discern three-dimensionality in a two-dimensional representation. Escher often exploited this latter feature to achieve astonishing visual effects. Escher’s art involves its relationship to the fields of information science and artificial intelligence. This aspect of his work has been largely overlooked in previous studies, but the case for its importance to these fields was forcefully made by Douglas R. Hofstadter in his 1980 Pulitzer Prize winning book, Gödel, Escher, Bach: An Eternal Golden Braid.
By the “logic” of space we mean those spatial relations among physical objects which are necessary, and which when violated result in visual paradoxes, sometimes called optical illusions. All artists are concerned with the logic of space, and many have explored its rules quite deliberately. Picasso, for instance.
Escher understood that the geometry of space determines its logic, and likewise the logic of space often determines its geometry. One of the features of the logic of space which he often applied is the play of light and shadow on concave and convex objects. In the lithograph Cube with Ribbons, the bumps on the bands are our visual clue to how they are intertwined with the cube. However, if we believe our eyes, then we cannot believe the ribbons!
By introducing unusual vanishing points and forcing elements of a composition to obey them, Escher was able to render scenes in which the “up/down” and “left/right” orientations of its elements shift, depending on how your eye takes it in. in his perspective study for High and Low, the artist has placed five vanishing points: top left and right, bottom left and right, and center.
My final consideration of Escher’s art involves its relationship to the fields of information science and artificial intelligence. This aspect of his work has been largely overlooked in previous studies. A central concept which Escher captured is that of self reference, which many believe lies near the heart of the enigma of consciousness – and the brains ability to process information in a way that no other computer has come close to mimicking it successfully. The lithograph Drawing Hands and the woodcut Fish and Scales each captures this idea in a different way. In the former the self-reference is more functional; one might rather call it self-resemblance. In this way the woodcut describes not only fish but all organisms, for although we are not built, at least physically, from small copies of ourselves, in an information-theoretic sense we are indeed built in such a way, for every cell of our bodies carries the complete information describing the entire creature, in the form of DNA.
People repeatedly confuse the word ‘print’ with things that are copies or reproductions. A reproduction is a drawing or painting that is photographed and made copies of. This is completely different than carving a hard woodblock by hand, carefully inking it, and making a print from that same block. So printing is not reproducing, you are not reproducing anything, not copying anything, and so every print you make is an original.
By the way, following Escher’s death in 1972 all of his woodblocks were cancelled in the state museum of Holland by drilling holes through them so they could not be printed again, since Escher was meticulous to only create his own small editions. There are no large Escher editions, and all of his prints are rare woodcuts and lithographs. Lithographs are also handmade prints with a more complicated technique and too complex to get into. Escher’s prints of “Reptiles” and “Waterfall” are lithographs, which look more like pencil drawings, where as “Day & Night” and “Sky & Water” are woodcuts with flat areas of ink printed from woodblocks.
