At the time I was attracted to pure science — physics — where you could speculate and be creative. It’s equivalent to being an artist. If you get the chance, and the cards fall right, there’s no difference. The intellectual play and spirit are the same.
— David Byrne (interviewed by Timothy Leary), 2000
I’ve commented more than once here on the myth of the Mad Scientist: contrary to popular belief, there are no easy shortcuts to scientific greatness. It’s true that some of our creative processes are subconscious, that we sometimes come up with ideas on vacation or after a good night’s sleep. No one, however, becomes a great scientist by just sleeping a lot. Our subconscious faculties only become engaged after we’ve studied the problem and thought about it extensively, often to the point of exhaustion. They don’t kick in every time, and when they do, their input is not even always useful. (I’ve woken up many times with shiny new ideas that did not hold up on inspection.) Excitement, inspiration and quality vacationing can make it easier to put in the sustained, disciplined work of constructing correct and complete mathematical arguments, but does not replace it. As for the relation to actual mental illness, I’ve linked before to a relevant interview with John Nash.
I didn’t get any disagreement on that from math and science types. We understand well enough how the creative process works. We know that being all fired up to prove the Riemann hypothesis is different from actually doing it. Imagine my surprise, then, when I attended a discussion on art and science in the “Philosopher’s Cafe” series a few weeks ago. Scientists and mathematicians came in good numbers, and many of them professed exactly the same kind of misconceptions about art that they would dismiss outright with regard to science. Art, if you believe them, is all about feelings. When a work of art evokes strong emotions, we assume that the artist was overwhelmed accordingly at the moment of creation, leaving no room for intellectual mediation or for calculated, deliberate activity. In other words, the artist experiences an intense feeling, whips himself into a state of rapture, and bang, a painting or whatever materializes in front of him in a puff of magic dust. The Mad Artist swipes his cape and takes a bow, in all his fictional glory.
I’m a research mathematician of some renown. (The regulars here know that, but I’ll say it explicitly anyway, for those who might find this post via links and google searches.) I’m also an amateur photographer (see my Google+ page for samples), and I’ve been attracted to visual arts all my life in some way or other. I’m finding in my own practice that the creative processes in art and in mathematics are often more similar than it might first appear, and I’ve had plenty of confirmation of that from both sides of the aisle. This post is about that, with emphasis on the mathy and sciencey side of art. (Time permitting, there will also be a follow-up post in the converse direction.)
This is not a post about “mathematical art.” Honestly, I have little interest in most of it. I write research papers about fractals, but I find neither mathematical insight nor artistic value in the rainbow-coloured pictures of fractals usually found at math art exhibitions. Don’t even think about sending me links to math rap songs, either. I don’t need art to talk to me about mathematics. I want it to speak to me as art, on its own merits, with no special bonus points for math themes or content.
I’m interested in the less obvious but more organic similarities on the level of the creative process. I’m hardly the first to observe them. Just last year, I attended an artist talk where a painter spoke of his work in terms of “solving the mathematical equation.” Yet, it was plainly in evidence in that discussion a few weeks ago that too many scientists think of art as a softer, lower grade kind of creative endeavour where the concepts of logical thinking and problem solving are pretty much unknown. In that regard, here are a few points to consider.
I’ll be talking mostly about photography, and to some extent about painting, because that’s what I know best. If you think it’s different in other arts, I’ll refer you to Ursula Le Guin’s excellent description of a physicist’s creative process in The Disposessed; I can’t find a link now, but I recall reading somewhere that it was based on her own experiences with writing. If you think that it’s just me thinking that way, that’s very easy to check. There are many artists out there who have blogs, public Facebook or Google+ pages. They might post pictures of work in progress, talk about their influences, recount how a particular piece came about. They might be using different, less “scientific” language, but you will still find a good deal of premeditation, problem solving and analytic thought in what many of them do. And if you tell me that not all art is that great… well, yeah. Not every math paper is a towering pinnacle of intellectual achievement, either. We all do what we can.