A Beautiful Mind
Only in an M.C. Escher drawing does the impossible look so possible. Never-ending staircases, worlds within worlds, and transforming shapes are all naturally occurring themes in the visual abstractions of Escher’s mind. Midway through his career, these bizarre representations captured the hearts and minds of the scientific communities which, in turn, catapulted him to world-wide success. Escher’s works employ highly complex examples of geometrical and scientific ideas such as symmetry, tessellation, and self-reference combined with everyday objects and scenes. The result is a fascinating journey into the unreal and a feast of inspiration for scientific world.
After careful examination of Escher’s work, one would never guess that he was a high school drop-out. However, this native of the Netherlands is an exemplary exception like so many other famous high school drop-outs. In 1919 at the age of 21, M.C. Escher attended the Haarlem School for Architecture and Decorative Arts. Here, under the guidance of a graphics instructor, Escher’s extraordinary talent for drawing and woodcutting was discovered and developed. After these formative years, Escher traveled extensively throughout Europe, particularly in Italy. Escher became well known in Europe during this time for his remarkable lithographs of the Mediterranean coast and other landscapes. It wasn’t until a second trip to Spain’s Alhambra in 1936 that M.C. Escher’s focus shifted inward from the real world to his surreal imagination.
The Alhambra is an ancient Moorish palace in the city of Granada, Spain. Its walls are covered in a startling array of colorful geometric tiling that Escher described himself as “the richest source of inspiration that I have ever tapped.” Almost every expanse is covered completely in tiles in the shape of triangles, squares, rectangles and other regular forms that do not overlap or leave any gaps. This technique is known as tessellation, and it became Escher’s primary artistic device. Today, tessellation has found its way into the field of computer graphics, where it is used extensively for rendering three-dimensional environments. Still, back in the 1940s, Escher knew that shapes alone did not hold significant artistic value. Therefore, he often experimented by distorting regular shapes into everyday subjects such as birds, fish and turtles to give his work life. Escher’s obsession with tessellation is most notable in his masterpieces Metamorphosis I, II, and III.
Around this time, Escher’s popularity in the world was growing exponentially. The public found his artwork striking and fresh, while the scientific community found it intellectually exciting. Scientists raved over his work as their ideas crept into the subconscious of his designs. Crystallographers, mathematicians, and physicists all began to share in Escher’s passion for theoretical phenomena such as multi-dimensional symmetry, hyperbolic space, non-Euclidean geometry, and spatial paradoxes. In his Circle Limit III and IV, Escher offers a glimpse into an infinite world of hyperbolic space where squares and rectangles can’t exist. He also sketched creatures walking on a one-sided, single-edged lattice, scientifically known as a Möbius Strip. Perhaps more famously, Escher defied spatial logic with his lithograph of staircases that don’t go up or down. This paradoxical effect was duplicated in Waterfall where water falls and then “descends” back to the top in a perpetual motion machine type manner.
Escher also explored self-reference with his lithographs Drawing Hands and Print Gallery, which play with the idea of consciousness and self-awareness. Drawing Hands depicts two hands emerging from the paper, each drawing the other. Print Gallery features a man inside a shop along a dock looking at a print of just the same image. This visual trick is known as the Droste effect for its popular usage on a Dutch chocolate maker’s cocoa box. Both of these works involve self-reference, which is a popular topic in mathematics, philosophy, and computers. Pulitzer Prize winning author Douglas R. Hofstadter posited Escher’s works as so important to the theory behind the field of artificial intelligence that they formed the foundation for his seminal work Gödel, Escher, Bach: An Eternal Golden Braid.
Escher died in 1972, but his work continues to influence modern art and pop-culture. Contemporary television shows such as the Simpsons, Futurama, and The Family Guy have featured Escher-like paradoxes as gags. Sci-fi movies and novels have also explored the curious worlds of Escher’s work, specifically Relativity. Even video games such as Sonic the Hedgehog include visual references to Escher’s lithographs. However, the real value of Escher’s legacy is not his role as a pop-culture icon. Much like his many lithographs, Maurits Cornelis Escher’s true legacy is his work’s ability to inspire scientific minds, challenge assumptions, and spur other new ideas.
Lenstra Jr., H.W., and B. de Smit, eds. "Artful Mathematics: The Heritage of M.C. Escher." Notices of the AMS 50.4 (2003): 446-456.