Abstraction, not just mathematics, has its place in science as it does in art
The Obvious, Last
In science, we distance reality by representing it, in molecular models or mathematical equations. There is risk in that distancing, but also tremendous power—for instance, the calculus, along with a mathematical technique called perturbation theory, allows us to calculate the path of a Mars lander to a few meters.
The representations of science are both iconic and symbolic—they look like the thing and they are arbitrary. The lines in the ball-and-stick model of a molecule do give one a rough idea of the relative microscopic distances; the atom labels are just a convention. The representations are then manipulated on paper, on computer screens and in our minds with all the conventions of art—and that includes abstract art. So we focus in a cubist way on one part of a molecule, distorting it, and we indicate forces with Klee arrows. And when we need to represent essences, to focus in on what matters, we simplify, often in the way artists did in the beginning of abstract art in the 20th century.
Consider the problem of representing the essential backbone of proteins—biopolymers whose chains are sometimes helical, or sometimes stretched out with a pleated appearance. Its similarities and differences from protein to protein must be perceived. In the early 1980s Jane Richardson of Duke University invented a “ribbon” representation that is based on the reality of molecular structure obtained from experiment (above right). The ribbon representation, an abstraction I would say, was a genial idea. First done by hand, now computerized, this way of seeing has shaped the way we imagine proteins in our mind’s eye.
Abstraction, both through equations and simplified representations of molecular structure, is an essential mechanism of science. But analogies to abstract art and music also enter in other ways—in the opposition to the natural, in playful and purposeful pursuit of essences, in the way time and chance are given their due. In science and art both, we create and discover meaning.
I am grateful to Bruce Ganem for discussions.
- Hoffmann, R., and P. Laszlo. 1991. Representation in chemistry. Angewandte Chemie International Edition 30:1–16.
- Gooding, M. 2001. Abstract Art. London: Tate Publishing.