Sunday, January 17, 2010

Robert Motherwell on Math and Abstraction

Continuing a thread on quotes about math and art, I found these from Robert Motherwell:
"I have often quoted Alfred North Whitehead in what I think is one of the crucial statements on abstraction, that 'the higher the degree of abstraction, the lower the degree of complexity.' In that sense, mathematical formulae are (ironically) by nature of a lower degree of complexity than a painted surface with three lines, even if it's an Einsteinian equation."
"Advanced mathematicians say that when there are two mathematical solutions to the same problem that are equally valid, mathematicians will often reject one of the two solutions as less beautiful than the other. Even in something seemingly as cool and remote as mathematics, there is an element of the aesthetic involved."
Both of these quotes are from a lecture Motherwell gave on 2/7/1970, at St. Paul’s School, Concord, New Hampshire. I picked them up from The Writings of Robert Motherwell, edited by Dore Ashton with Joan Banach, 2007, Berkeley, CA: University of California Press, p. 250 ; from the article, "On the Humanism of Abstraction, the Artist Speaks", 1970, Robert Motherwell at St. Paul's School, exhibition catalogue, and reprinted in Tracks: A Journal of Artist Writings, vol. 1, no. 1, 1974.

I purposely selected these quotes for their reference to math, but the article they come from is not much about math. The quotes are out of context, and I recommend reading the entire selection, if not the book. Nevertheless, I take exception to the idea that a math formula is less complex than a painted surface with three lines. Applied mathematics, being the language we use to describe natural concepts (as in e=mc2), is not necessarily abstract. The formulas of pure mathematics are often as not the language of a larger process or proof, so though abstract are still complex. Sometimes three lines are equally as complex &/or abstract as a formula, as in three lines making a right triangle and the formula, a2+b2=c2.

Here's a gratuitous design, Samurai.

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