I'm a big fan of WNYC's public radio show Radiolab, wherein "Big questions are investigated, tinkered with, and encouraged to grow" in a manner most interestingly. Topics range from linguistics to animal behavior to mathematical theory to what happens when you sleep, and it always manages to be fascinating, if sometimes a little conceptually scattered. Robert Krulwich, one of the show's two hosts, maintains an occasional blog on NPR's website that follows a similar exploratory arc, and the latest entry was a great one (read it here).
He covers the work of two people: Vi Hart's funny, inventive videos about "doodling" and mathematics, and a lengthly essay by Paul Lockhart about the (many) problems with mathematics education. I really, really recommend watching the video and reading the essay in full.
Lockhart's essay is damning, interesting, and a great read. There are some problems - for one, he lacks a sophisticated understanding of what visual art is when he compares it to music and mathematics, but to be fair he hasn't had the post-post-modern conceptual perspective (or indoctrination) that most of us contemporary artists have. Now that art can exist solely in the realm of "ideas," it can be a concept, an action, a performance. (I know this isn't really new to anyone familiar with, say, Jackson Pollock, but every so often I'm amazed by how revolutionary and far-seeing these ideas were in the 50s and 60s. We take it for granted now that we aren't all stuck painting placid landscapes trying to get into the Paris Conservatory.) Art, like pure mathematics, need not be confined to the physical world. The best art never has been. Like Lockhart points out, Michelangelo had other things on his mind than decorating when he envisioned the Sistine Chapel ceiling.
His critique of math educators and the "institution" of learning is absolutely scathing. I'm not sure how I would feel if I were a math teacher and read this. (Or any teacher. He's pretty harsh on the idea of pedagogy overall.) All the same, I think he has some great points to make about the need to approach mathematics with the same creativity, playfulness, and inventive problem-solving we use to explore music, art, poetry, and the other arts.
While I read, I realized that many of my own artistic and intellectual heroes - Leonardo da Vinci, Leon Battista Alberti, James Audubon, Archimedes - approached mathematical or logistical problems with a creativity we reserve now for artmaking. Having a teacher take this tack with me might have avoided the complete mathematical paralysis I have as an adult. I can hardly approach math beyond simple arithmetic, although I don't really care about that (you don't think I use trig when I'm engraving, do you?). Instead, I wish that I had been encouraged to think about mathematical problems the way he describes, by formulating my own proofs through creative thinking, trial and error, rebuttal, discussion.
There is sort of a tie-in here, finally. Working with Deanna over the past year and doing a lot of free-form, responsive, automatic drawing (or "doodling," a word we both hate) has really put my educational background in perspective. Sometimes I feel really conflicted about what having a BFA means, particularly from an established school with a great reputation, like, ahem, Carnegie Mellon. In the end, I feel like I learned what I was supposed to from art school - how to see, how to think, how to create. Your pencil, and what comes out of it, is not really as important as what's happening between your ears and behind your eyes. Yet, getting an education in art is always sort of walking a tightrope over a sea of institutionalized technique, and some schools fall into it, even the best ones. For years, that technique was what I thought I wanted - that I couldn't be a real artist until I learned perspective, or anatomy, or how to use oil paint properly. CMU is a rarity in art schools in that it really stresses a conceptual vocabulary in its art students, to the admitted sacrifice of technical facility in some traditional areas.
Frankly, at this point I couldn't care less about whether I can draw a proper vanishing point to create perfect bricks in two-point perspective. I still hate oil paint. I'm pretty good at anatomy. But in the end, those are tools. They're not your vision. It's harder to be original and creative and exploratory, to make mistakes and search in the dark, but that's what real art - and math - is. As a person and artist who's always craved structure, rules, and predictability, it is a particular challenge to remind myself that the people goofing off in class with their own amazing projects are sometimes the visionaries on the way to greatness. It's a challenge to maintain spontaneity and creativity and free thinking. I try, though.
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