What are "they" thinking? Well, it depends a lot on who "they" are. Work, family, health, relationships, dreams, desires, irritations, even out and out hatreds, you name it. All that stuff swimming through our heads in different measures all day -- and some times all night -- long. I'll go out on a limb here and posit that for most of us, there's not a lot of math going on in there. Sure, there's the one percent of the one percent...of the one percent (that's one ten thousandth of a percent for those of you keeping track) who spend their days immersed in or using numbers: the mathematicians, statisticians and physicists, the "quants" and "data architects" that all kinds of businesses are now employing to make sense of the steady flow of behavioral data we are now all leaving in our wake as we walk the world. But, in my experience there's another group out there thinking about math, at least from time to time, and that's the artists, well, at least some of them.
I was thinking about this the other day, after spending a little time with the artist James Drake, whose new work "Anatomy of Drawing and Space (Brain Trash)" (or more precisely, a subset of this) is now hanging at the Lannan Foundation in Santa Fe, NM after a well-received showing a the San Diego Museum of Contemporary Art. "Brain Trash" is the result of a two-year project in which Drake pushed himself to draw every day. The images are rendered in a variety of different media on large rectangular pieces of drawing paper and then organized into huge wall-sized mosaics labeled as "Chapters".
The images that Drake produces are -- like our thoughts -- all over the place. This is Drake's "brain trash". It's figurative and abstract, dense and spare, light and dark (both visually and in subject matter). Yours would probably look different, but some themes might feel familiar. There are images but there is also text. And there is also math.
Math? Yes, there is really math. And I don't mean straight lines and shapes that hint at math (although, this is math!) or even some free floating Jasper Johns-like numbers scattered here and there. I mean "real" math -- formulas and symbols that you would at least recognize as mathematical, even if you couldn't attach any meaning to them. Some of them were written down by the Nobel Laureate (and Santa Fe Institute Professor) Murray Gell-Mann, related to particle physics and quantum mechanics and serve as ingredients in several of Drake's drawings. But there are also Drake's own reproductions of the basic wave equation of quantum mechanics, first written by (and named for) the physicist and Nobel Laureate Erwin Schrödinger, as well as a wonderful and witty symbolic mathematical-textual representation of the famous "Schrödinger's cat" paradox, both dead and alive (or neither dead nor alive) used to evoke the mysteries inherent in the phenomenology of light, that in some contexts appears as a wave, but in others as a particle.
Gell-Mann's hand in the work reflects his place in Drake's thoughts. Drake had many a conversation with Gell-Mann, curious about the science and mathematics of the world, hoping to enhance his own self-study with some explanations of complexity science, particle physics, and quantum mechanics from one of the great physicists of our age. Drake is fascinated by mathematics and science and there is math in Drake's brain trash.
The equations among the drawings point up the visual connections between drawings and mathematical representations -- two forms of mark making that can be beautiful in the own rights as well as powerful and expressive media. Schrödinger's cat has always been something of a paradox, but it's an interpretation of the equation, which in and of itself represents no paradox at all. In this case, the math works where words fail us. The same could be said for many a great drawing.
For Drake the math-art connection is even deeper than this. It's not just in the products. It's also in the process. These are two creative activities that share a wrestling with ideas, each beholden to its own kind of internal logic. As I look back over my own notebooks, I get a sense of the "brain trash" of a mathematician -- the proportions of the various kinds of images might differ, but much of the content feels the same. Marks on a paper, manifesting a private and public language that I'm using to make sense of the world, both inside and out.