Escher's space

This quote comes from 'Escher on Escher: Exploring the infinite', a publication that was compiled after Escher's death using his extensive notes for a series of lectures that he was to hold in the United States in 1964. Escher never got to present these lectures, because he had to undergo unexpected surgery while visiting relatives in Canada prior to his departure to the US. Conscientious and practical as he was, Escher had already prepared the notes and lists of slides before he departed for Canada.

I have included the three slides of Concave and convex, the litho from 1955, next to each other with some white space in between.

The white spaces emphasize the confusing central section. In his inimitable style, Escher often hides a clue in a print that is difficult to decipher. This time, the clue is in the ensign in the right-hand part. I tend to look at it as a concave figure that is bordered along its diagonal bottom and top by a spiraling band of square and diamond planes. Yet when I view it from another angle, I see diagonal cubes that are stacked on top of each other like staggered brickwork. While writing this I found myself looking up and down at the ensign on my computer monitor, until, suddenly, they turned into elongated shoe boxes! In the process, the three grey square planes became the front of the long ‘boxes’, each with a white top and a dark left side. It's as though my eyes ‘flipped’ first, before the image that I was viewing. My brain appears to perceive other things, possibly due to the angle at which I'm viewing? Seeing is therefore not always observing. This sounds like something straight out of a Chinese fortune cookie and yet, with Escher, it is all too often true. Furthermore, he deliberately hides that wisdom in a work of art!

Is Convex and concave an exception? The answer is short and to the point: no. Convex and concave is in fact a product of a development that began very early on (1928) in the career of M.C. Escher. In it, he connects rooms that in reality couldn't possibly be linked up. Incidentally, this technique for dealing with space on a flat surface was frequently deployed by 20th century visual artists. There is however a difference between Escher's stance on how to combine the possible with the impossible within a work of art, and that of most other artists such as cubists and expressionists, not to mention surrealists, who also combined possible and impossible spaces. In these three movements (cubism, expressionism, surrealism), this multiple world view often give rise to unrest and chaos.

In contrast to the exponents of other 20th century European art movements, Escher's combinations are premised on clarity and structure. After the Second World War Escher starts receiving increasingly enthusiastic responses from scientists, including mathematicians, crystallographers and geologists, and his prints become increasingly influenced by the information they imparted. The Canadian and British mathematicians Donald Coxeter and Roger Penrose, as well as the Dutch mathematicians Professor Schouten and Bruno Ernst (Hans de Rijk) shared ideas that challenged and inspired Escher to incorporate them in his prints. Mathematicians were amazed at how a lay person was capable of, as Doris Schattschneider once said to me: “finding a recognisable form for completely abstract formulas.”

Escher's older half-brother Berend had been an important ally of Escher since 1937. A specialist in crystallography, Berend identified with Maurits' visual experiments. From the considerable scientific literature donated by his brother, Mauk gleaned visual information for his tessellation studies that he could apply to his work. The brothers had for some time been planning to work on a book together, with Maurits creating prints that would illustrate Berend's theories. Unfortunately this plan never materialised.

Escher was extremely fastidious; the content of a print was paramount. He remains an artist first and foremost, who had accidentally ventured into the world of science. He was not always enamoured with the information or plans presented to him by the scientific community. Shortly after the first visits from Hans de Rijk, Escher wrote the following to his son Arthur:

Below is a series of prints that illustrate how, since 1928, Escher starts to deploy ever more ingenious ways to combine multiple world views within a single work of art. As always, this is a matter of interpretation. It all begins with Bonifacio and Castrovalva.

In these prints, Escher manages to link up the foreground (plants) to the background (horizon) in an utterly intuitive and believable way. In Covered alley in Atrani (1931) and in Ravello, Porta Maria dell’Ospidale (1932) he combines different spaces in an entirely different way.

In Atrani, he brings together three different perspectives from a real-life situation. We are sitting on a staircase, looking at the covered intersection in front of us. Matters are confused because the left-hand staircase goes up and the right-hand staircase goes down, creating two escape routes within the work. Because we are sitting a few rungs above both stairs, we can also feel a space behind us. The second situation from Ravello is less complicated: at the end of a Gothic-style rib vault we can see two passageways.

In Metamorphosis I, he depicts the transition of the realistically depicted small town of Atrani via geometrically rigid patterns into a tessellation. The outlines of the different geometric figures connect seamlessly to create a freestanding Oriental figure. This last part is a tessellation.

In the two prints Marseille and Still life and street from 1936 and 1937 respectively, Escher's combinations of foreground and background become even more extreme than in the first two of this series (Bonifacio and Castrovalva).

In Other world and Up and down, both from 1947, everything is turned on its head. With his imagination partly fired up by his old school building in Arnhem, Escher effortlessly combines three and two different rooms respectively in an utterly credible way. In our heads, everything whizzes back-and-forth and is turned upside-down, topsy-turvy and inside-out.

The school building in Arnhem was also the inspiration for the impossible spatial combinations from House of stairs and Relativity, from 1951 and 1953.