Art and math converged at Bookcourt in Brooklyn, during a public conversation between painter Simon Dinnerstein and mathematician Paul Lockhart.
Lockhart is author of the newly-published Measurement, a compact, conversational volume that presents math as an art form and invites readers to set aside fear and try it themselves. Dinnerstein is a painter whose most famous work, “The Fulbright Triptych,” painted between 1971 and 1974, is the subject of The Suspension of Time. The book consists of essays about the huge and richly detailed painting; the pieces are written by an eclectic group of contributors, from novelist Jhumpa Lahiri to actor John Turturro.
Lockhart and Dinnerstein met 13 years ago when Lockhart, now a math teacher at Saint Ann’s School, enrolled in Dinnerstein’s painting class; Lockhart continued to study painting and drawing for eight years. At the bookstore event the two took turns posing questions to each other (in a manner that Dinnerstein likened to the movie My Dinner With Andre. Below, some of the back-and-forth.
Dinnerstein: Paul, how did you come to mathematics?
Lockhart: From the age of 12 or 13, math was my comic book inside my schoolbook. Math was my escape. To me it was all about rebellion, and it still is. To me math is the most rebellious thing you can possibly do. One thing I love about it is that it is utterly noncommercial. It has no value at all. As an idealist what more could you want than math? It’s not even here. It’s way, way, far away.
My grandfather was actually a mathematician before becoming a drunk. In his later years when I was 6, 7 or 8 we’d sit together with several glasses of scotch and do math. So from a pretty early age I knew about the existence of this abstract study of patterns. And it always spoke to me. A big event that I recall was my father going on an errand. He was a clinical psychologist and he had to go to a technical bookstore and he dragged me along. I ended up in the math section of this technical bookstore. Kaboom! There are other people in the world like me.
ON KNOWING WHEN YOU’RE DONE
Lockhart: How do you know when you’re done? I know when I solve a problem―I know it when I see it. But what does it mean to finish a painting? That’s something I never was able to do. Every painting I’ve ever done was unfinished because time was up or we got a new model or I got sick of it. Is this ["The Fulbright Triptych"] done in your eyes? And if so why?
Dinnerstein: This painting took three years to paint. I was living in Germany and I had a Fulbright grant. I was doing printmaking and I was carving a plate on this table (he points to the table in the painting) and I was sitting on this chair (the chair he’s sitting on in the painting). I moved back in the chair and looked at the landscape out the window and at the table, and I thought, “Wow, this would make an incredible painting.” About half the pictures in the middle were up and some of the tools were there. So I ordered this [center] panel. I drew everything in that middle panel with a rapidograph pen—no studies. I would never work like that now.
When we came back to New York, all of this was drawn. The people who owned the home in Germany let me take the radiator and the table-top with me. The crate was enormous! I started working on it, and I didn’t really think about how difficult this would be to do—not just to do it, but do it on a high level and carry it off. I continued working on it, and it was a point where I didn’t have any financial resources to keep going, and I happened to meet a gallery dealer who bought the painting from me before it was finished—he paid me by the month to work on it. And at the end of three years, it seemed to me that I had said what I had to say. And it seemed that was the right time. It was finished.
Lockhart: It was finished because you no longer had any need to work on it?
Dinnerstein: If I kept working on it, it would be diminishing returns. I would be overworking it.
Lockhart: Wow! That’s the opposite of the way that I work. Because for me, it comes in a huge flash. Most of the time when you’re doing mathematics you’re in this doldrum place and then—BANG!—it’s good. I don’t even need to work out the details because every fiber of my being sees it’s going to work. I’ll write it up later. Now I can get some sleep.
ON ART CRITICISM
Lockhart: I’ve been reading Simon’s book. I’ve been reading a lot of art criticism, which, to be perfectly frank, I’ve always, my whole life, believed was complete bullshit…But I have to say I had a really good time, actually, and I would like to try to do it myself right now. I’m going to do art criticism!
Well, Simon…what you have here is a triptych. And there’s a long history of, I’m going to say, Northern European Gothic Altarpiece Art, (snort) which has to do with triptychs. The only thing you’re missing here is baby Simone’s arm in a benedictory pose. (Simone is Dinnerstein’s daughter, pictured in the painting.) You know what I’m talking about— these Netherland-ish things: You’ve got mother and baby Jesus in the middle, then you’ve got Saint So-and-So and maybe scenes from the annunciation on the wings.
You’ve done something really interesting. That is, you’ve shoved the holy family out of the middle section―all that’s left is the halo, which is this copper plate. And what it says to me is, this is an altar to art itself. Art is more important than these simians that you’ve shoved to the side. This (indicating the copper plate in the painting) is the only round thing in this picture. Everything else is a set of rectangles. There’s rationality all over the place except here. It’s an egg, even! And, do you know what I noticed just this morning? It’s off center. Ooooh! So, it’s as if to say, in this world of rationality, art is irrational—it’s an egg, it’s a golden egg containing God knows what, but whatever it does contain, it’s off-center. How interesting is that?
So, what I wanted to ask you is: You started with three pieces of wood with nothing on them, and you came up with this whole thing. When you’re working, do you hear art criticism in your head? And if you do, how on earth can you keep that noise out so that you can do art?
And, how was my art criticism, by the way?
Dinnerstein (shrugging): Ah…interesting?
Lockhart: Yeah, OK, you’re saying: “We’ll be looking at your math in a little while.”
Dinnerstein: The point that Paul makes about the art criticism may or may not pertain to my book because the idea in the book was to have an anthology of writing in which the people who wrote were not necessarily art critics.
But the point Paul makes about this painting is actually interesting. In the book, a number of people have written about how work separated this family. I didn’t think of it this way. I thought of the bookends—of myself on one side and Renee and Simone, my daughter, on the other side—as pulling you out to the periphery. The person who bought this painting —before it was complete—told me in no uncertain terms that he would prefer to buy the middle of the painting and that I should not do the ends. I had to argue, with a whole lot of money in front of me… that I wanted to do those two end pieces. And I hope that you (talking to the audience) would take the time to go see this painting. You can think of it without the ends—just the middle— or you can think of it the way it actually exists. And there is some point to arguing even a crazy idea and getting your way.
WHERE DO THESE BOOKS COME FROM?
Dinnerstein: Paul, what is the origin of Measurement?
Lockhart: It goes back to a 1997 winter storm that had me in a cabin, trapped. Luckily I’m a mathematician, so being trapped in a cabin with nothing to do is not a problem. I had been kvetching and complaining about math and school…and then I was like, well, put your money where you mouth is. What would your math book be? So, I took out a yellow pad and made a stab at it. And I hated it and I ripped it up. I made six stabs at my math book before I said, “Oh, yeah—honesty! I’m just going to be honest. I’m just going to talk on paper.”
…But I can’t talk about the origins before explaining a little bit about what math is—because that was my motivation.
The first thing to understand about math is, it’s the study of patterns. What that necessarily entails is the construction in one’s mind of a place capable of housing abstract patterns. In particular, if we’re going to talk about say, shapes, which is a big theme in the book, we have to understand that we’re not talking about things in this world, we’re talking about perfected things.
And this is where what Simon and what I do has something in common, which is reality as a jumping-off point.
This isn’t reality here. (Referring to a drawing of a circle.) This is a subjective take on reality. So, when I talk about something like a circle, it’s absolutely crucial that you understand that there aren’t any. There aren’t any circles. They don’t exist. Circle is a cognitive, linguistic concept. It’s too beautiful and perfect to take place in this vale of tears of complicated complex ugliness. One can make models. One can get out a pair of scissors and make a real circle. You build models and the models are mathematical and the models sit still and it’s calm and its perfect. That makes it something you can have knowledge about. That’s really interesting to me.
Dinnerstein: This book exists because I have a very large art book collection—maybe fifteen hundred or two thousand books. I have 12 or 15 books on one painting, and I’ve always been fascinated by those 12 or 15 books. Those books would be the equivalent of perhaps reading a novel. I felt that this painting would lend itself to that treatment because the painting has a lot of themes and a lot of ways to enter. You could enter the painting from the landscape, you could enter the painting from the two people, you could enter it from the plate, from the tools, from the process…. It turns out a publisher [Milkweed Editions] was very interested in this, and the different writers were chosen to present different points of view.
At the time I did the painting it was the very beginning of my work as an artist. So, to some degree this is a different analogy than Paul, who wrote a book based on years and years of thinking about mathematics. If I’d been smart enough when I started this, I wouldn’t have done it. It takes a certain amount of stupidity and awe to think that you can do this.
[Before she began her essay], Jhumpa Lahiri wanted to go see this painting in person, so we drove to Penn State University [which owns the painting]. She must have looked at this painting for two or three hours without moving away. And I spoke about it, she asked questions. When we left the museum, she said, I know you haven’t seen this in about 10 years. What did you think, having seen this now? I said, you know, the first thing I thought was, I couldn’t believe I did this. It seemed like the best that I could be times 100.
“The Fulbright Triptych”—which is 14 feet across and more than six feet high—is now on display at the German Consulate General, 871 United Nations Plaza, at 49th Street, Manhattan.