Journey to Infinity

M.C. Escher (1898-1972) has been described as the quintessential “anti-artist,” a title that is appropriate on multiple levels. Despite being active when the great Modernist coteries and manifestos were coming into fruition, Escher gravitated more towards mathematicians and generally stuck to more formalist techniques to craft his work. This is not to say his work was unoriginal or lackluster—in fact, his depictions of complex concepts such as relativity, infinity, and paradox verges on Surrealist aesthetics but without the same concern for dream-states. His artistic medium was similarly uncommon.

As a graphic artist, Escher’s oeuvre is primarily woodcuts, lithographs, mezzotints, and other intaglio and relief prints. Or perhaps it can attributed to his conservative attitude towards avant-garde and mainstream artists alike. Nevertheless, Escher’s interdisciplinary approach helped create a dialogue between art, science, and mathematics, and his “impossible geometries” are both a stunning technical feat and an innovative execution of optical illusion that remains unmatched.

Escher’s attention to perceptive, angular details, and evocative tonal contrasts is evident even in his earliest landscape work. Castrovalva (1930) exemplifies his surrealistic adaptation of the countryside, utilizing dark shading and precise inking to ensure a textural evocation that is simultaneously grotesque and sublime.

During his travels across Europe, Escher would begin to experiment with “scratch drawings,” where he would lay down lithographic ink on paper and scratch the surface to explore the limits of saturation and shading.

But it was his exposure in 1934 to the Moorish tiles of the Alhambra in Granada, Spain, that would trigger a fascination for mathematical design. One particular area is tessellations, what Escher called the “regular division of the plane.” Frustrated by the limits of flat surfaces, he describes the process as such: “a plane, which should be considered limitless on all sides, can be filled with or divided into similar geometric figures that border each other on all sides without leaving any empty spaces. This can be carried on to infinity according to a limited number of systems.” As evident in Regular Division of the Plane III (1957-1958), Escher fills the paper with geometric rigor, creating a visual portrayal of infinity through his patterning. Not only was this impressively accurate mathematically, but it proved to be an intriguing scientific exploration of crystallography and fractalization through aesthetics.

Even without a formal education in math, Escher was inspired by the work done by mathematicians. After displaying his work for the International Congress of Mathematicians in 1954, he made contacts with critical figures in the field such as H.S.M. Coxeter and Roger Penrose. Both were awed by Escher’s Relativity (1953), especially its paradoxical points of view and playful, mind-bending perspective.

In this piece Escher showcases his expertise in the traditional laws of perspective; however, instead of having one vanishing point, he has three. The space of the room is thus indeterminable, constantly shifting with the viewer. It was this work that coaxed Penrose to send his impossible tribar to Escher, which would inspire contradictory pieces regarding perception such as Waterfall (1961).

Escher’s contrast of diagonal and vertical lines through the bridge and waterfall not only replicate the Penrose Triangle, but it fixes them in a real-time optical infinity. This creates an existential looping for the viewer. The tops of the two towers further speak to Escher’s fascination with Platonic solids, topping them with stellated polyhedron (in other words, regular solids whose flat faces have been replaced by pyramids). Coxeter’s work on hyperbolic space and non-Euclidean symmetry was also particularly inspiring for Escher, resulting in more complex interpretations of the infinite plane as seen in Circle Limit III (1959) and Circle Limit IV (Heaven and Hell) (1960).

In summary, M.C. Escher has exposed the fine line between the two- and three-dimensional, developed a unique bridging between art and mathematics to a degree unseen since the Renaissance, and has allowed us to view the impossible.