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. 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.”įinally, there’s an intangible quality to Escher’s work that some critics have described as an interest in exploring infinity. 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: These works and others present the viewer with a visual chicken/egg dilemma: Where does it all start and end? I like that.įifth, 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. Relativity, above, depicts such infinite loops, as does the work Drawing Hands:Īnd this one that depicts lizards crawling to life/becoming tessellations: Miraculously, Escher makes the work cohere no matter what viewing perspective we try to bring to it:įourth, 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. 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. You can see impossible constructions depicted in Escher’s famous “Relativity” piece that depicts people simultaneously ascending and descending stairs in an infinite loop. 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. Or in this piece, Day and Night, a whole landscape shifting: In his woodcut Sky and Water, for example, we see birds becoming fish/fish becoming birds. These transformations appear most clearly in Escher’s tessellation pieces. Second, Escher depicted in his work transformation/transmutations where we see one shape becoming another. We see tessellations in Escher works such as these: Honeycombs and interlocking pavement tiles are examples of tessellations. Tessellations, by the way, are the composite result of geometric shapes that are repeated without overlaps or gaps. ( 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. Let’s take a look.įirst, 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. 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). 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. “Are you really sure that a floor can’t also be a ceiling?” “My work is a game, a very serious game.”
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