“Order is repetition of units. Chaos is multiplicity without rhythm.”
“My work is a game, a very serious game.”
“Are you really sure that a floor can’t also be a ceiling?”
– M.C. Escher
I’ve long been curious about M.C. Escher’s (1898-1972) drawings and woodcuts because of their precision, their order and symmetry, their use of repetition and optical illusions, and the way they seem to point towards what could be called the infinite. Lately I’ve been thinking about what these qualities in Escher’s art have to offer those of us working in music (whether making it or writing about it). Let’s take a look.
First, Escher incorporated tessellations into his work, a technique he picked up in his study of tile mosaics while visiting Alhambra, a Moorish palace in Spain in the early 1920s. (Which reminds me of an article on the advanced geometry of 12-century Islamic art.) Seeing the tile mosaics inspired Escher to use geometric grids as the basis for his art as a way of gaining precision. Tessellations, by the way, are the composite result of geometric shapes that are repeated without overlaps or gaps. Honeycombs and interlocking pavement tiles are examples of tessellations. We see tessellations in Escher works such as these:
Second, Escher depicted in his work transformation/transmutations where we see one shape becoming another. These transformations appear most clearly in Escher’s tessellation pieces. In his woodcut Sky and Water, for example, we see birds becoming fish/fish becoming birds.
Or in this piece, Day and Night, a whole landscape shifting:
Third, Escher was fascinated by so-called “impossible constructions” or visual illusions such as the Necker cube and the Penrose triangle that take advantage of quirks of perception and perspective. You can see impossible constructions depicted in Escher’s famous “Relativity” piece that depicts people simultaneously ascending and descending stairs in an infinite loop. Are the figures moving up or down, sideways this way or that way? I like to rotate this piece onto its different sides to see how it holds up. Miraculously, Escher makes the work cohere no matter what viewing perspective we try to bring to it:
Fourth, and speaking of infinite loops, Escher’s works illustrate the idea of recursiveness—that is, something feeding back upon itself in a never-ending cycle. Relativity, above, depicts such infinite loops, as does the work Drawing Hands:
And this one that depicts lizards crawling to life/becoming tessellations:
These works and others present the viewer with a visual chicken/egg dilemma: Where does it all start and end? I like that.
Fifth, it’s been said that Escher’s art demonstrated an “intuitive” understanding of mathematical order and symmetry and perhaps this is the reason why his works are so pleasing to look at? What’s remarkable is that this intuitive understanding was so accurate that in the late 1950s the Canadian mathematician H.S.M. Coxeter said of Escher’s hyperbolic tessellations (regular tilings of a hyperbolic plane): “Escher got it absolutely right to the millimeter.” Here is his Circle Limit III:
This notion of Escher’s intuitive mathematical understanding reminds me of a quote from the philosopher-mathematician Gottfried Lebniz (1646-1716) that always made intuitive sense to me: “Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.”
Finally, there’s an intangible quality to Escher’s work that some critics have described as an interest in exploring infinity. The repetition, the tessellations depicting nature’s transformations and evolution, the impossible constructions playing with our perceptions, the infinite loops feeding back upon themselves—all of these characteristics of Escher’s art suggest an artist trying to represent that which can’t be represented, a reality beyond, a time-space outside our everyday experience of space-time. You even see it in tiny details, like when Escher draws a reflection of himself. In his work The Eye, for example, the reflection is twofold: there’s the mirror-image close up of his face where we see the folds around his eye, and there’s also that next level reflection deep in his eye’s pupil where we see Escher post-Escher–he’s already a corpse! It’s these kinds of little details that suggest that Escher was always somehow thinking beyond the Now even as he had intricate, and serious fun (“My work is a game, a very serious game”) constructing its beguiling representations:
For me, Escher’s work has musical resonances and looking at his pieces reminds me of the work of various composers, especially that of the American minimalists such as Steve Reich and Philip Glass. Over the years I’ve spent much time thinking through their work (you can read more about their work here; and you can view a Ventrilo-Dialogue with Reich here). Escher’s tessellations remind me of minimalist music that is similarly built out of small repeating units of sound strung together to make long rhythmic tapestries. (Now that I think of it, a lot of electronic dance music fits this bill as well.) Escher’s transformations/transmutations remind me of how minimalist music changes over time through subtle additive or subtractive procedures—adding or taking away a note here and there to transform one motive into another before our ears. (Ditto for electronic dance music.) And Escher’s impossible constructions remind me of minimal music’s perceptual artifacts—where as a listener you’re not sure if you’re listening to three groups of four beats or four groups of three beats, for example. Like Escher’s Relativity, a piece like Reich’s Drumming allows the listener to hear both perspectives at once. As for recursiveness, a lot of classic minimal music really does have an endless quality about it: a sense that it could, and just might, go on forever—or at least long enough for the listener to stop worrying about where it’s “going.” (It’s not going anywhere, just being something for a time.) Finally, to return to Escher’s intuitive understanding of math: Aren’t composers kinds of mathematicians too in that in one way or another they’re concerned with numbers and quantity, structure, space, and change? Like Escher, most composers frame what they do not in clinical terms (“I spend a lot of time exploring e-minor…” or “I do most of my compositional work in 5/4 time…”) but in intuitive and emotional terms (“In this song I was trying to capture the sadness of my break-up with a girlfriend…”) And isn’t music a good example of a kind of equation in sound that presents not an argument or a “proof” but rather shares the results of a procedure, solving itself and bringing us along for the ride?