Abstraction, not just mathematics, has its place in science as it does in art
Abstraction in Art
It is not easy to define abstraction. Is the incised design in a 3,500-year-old Japanese Jomon jar (below) abstract art? Are the colored shapes of pre-Colombian Huari textiles abstract? Yes and no. Their imaginative power over us derives from form, color, texture, juxtaposition—all certainly elements of abstraction. Although we may not be privy to the layers of meaning from different cultures that are implicit in these objects, they do not appear to have been made in willed opposition to representation.
Although abstract art has been with us for only about 100 years, sometimes it seems that there are more abstract-art movements than there are scientific “-ologies.” The list begins with cubism, and will not end with postmodern painting. Recognizing that there are degrees of the abstract, my perception of the essence of this artistic direction involves several factors.
First of all, abstraction is oppositional, wanting to be seen as alternative to such ideals as naturalistic representation and the figurative. I will not say “alternative to reality,” for (to paraphrase Magritte) the two-dimensional surface of the most photorealist painting still is not its subject. Not unexpectedly, much theory of the abstract disclaims a definition by opposition. Art desires a broader conception of what stirs the imagination.
Abstraction is also reductive. By that I mean that abstract art often takes some element of the artistic universe and explores all the tensions that it can get out of that element. Mondrian’s squares create visual jazz, Rothko’s broad color swaths can evoke joy or destructive tension. And Calder’s mobiles move, ever so slowly, around inner peace. The element abstracted may be a force, as in Elizabeth Murray’s works that break out from a shaped canvas.
Here is a spirited early statement on abstraction by one of its founders, Kazimir Malevich. In his From Cubism to Futurism to Suprematism: The New Realism in Painting, published in 1915, he writes: “I have destroyed the ring of the horizon and left the circle of things … in which the artist and the forms of nature are confined … [The new art] moves to its own goal—creation.“ Like all reductive philosophies, abstraction from time to time lays claim to “purity.” Such a claim is risky, as one might reflect where else in history such claims have been made, and for what purpose.
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