JOURNAL
(Photo to the right, taken by Aimee Zaring in Santorini)

Art + Math = Beauty/Truth?
March 10, 2008

In the last couplet of “Ode on a Grecian Urn,” John Keats writes these enduring words: “‘Beauty is truth, truth beauty,’--that is all/Ye know on earth, and all ye need to know.”

In January, I attended the celebrated Key West Literary Seminar. One of the talks I found most illuminating was a Q & A session with Janna Levin, author and assistant professor of Astrophysics at Columbia University's Barnard College. During the session, Levin discussed beauty and truth, particularly in relation to mathematics. She mentioned that if a publisher of a scientific journal was deciding between two papers, both presenting mathematical theories equally well conceived and articulated, the publisher would tend to select the paper presenting the more beautiful theory.

This prompted a discussion about what is considered beautiful in mathematics. Levin explained that it tends to mirror what most people find beautiful in great art--simplicity, symmetry, and unity. In a March, 2007 interview for the science magazine Seed, Levin further expounds: “in science, we really hold on to beauty and elegance as the goal because, for reasons that I think nobody fully understands, it's a good criterion for distinguishing what's right from what's wrong. And if something is beautiful and elegant, it's probably right.”

Scientists have long pursued theories because they are more beautiful, even if these theories can not, at the time, be proven. Take the Polish astronomer Copernicus. He sought a more beautiful, simple, and systematic theory of the order of the universe than the one Ptolemy proposed, which upheld Earth as the center of the universe. He could never prove his theory in his lifetime, but he shook up the scientific world enough to prompt more rigorous investigation, and the works of Galileo and Kepler later helped further his theory that Earth revolves around the sun.

But why should beauty be a good criterion for developing our ideas about the universe?
And how reliable is beauty in pointing us to Truth?

In her thought-provoking debut novel, A Madman Dreams of Turing Machines, Levin, through an intricate weaving of fact and fiction, explores the interior lives and works of two geniuses, the great logician Kurt Gödel and the father of the modern computer, Alan Turing.

In a scene from A Madman, Gödel argues with his fellow members of the famed Vienna Circle: “Mathematics is perfect. But it is not complete. To see some truths you must stand outside and look in.”

One of Gödel’s great contributions to the field of mathematics was his incompleteness theorem. Gödel proved that in a formal system there exists at least one undecidable statement--one that can’t be proven true or false. Even if we know the statement is true, the system can’t prove it and is therefore incomplete. In other words, there are limits to what we can ever know. As Gödel tells the Circle: “There are some truths that can never be proven.”

Unlike Gödel, who believed in the transmigration of the soul and even attempted to construct an ontological proof for the existence of God, Turing was a pragmatist and viewed humans as biological machines. In an interview with Public Radio’s Speaking of Faith host Krista Tippett, Levin explained that Turing found meaning and order through mathematics--something he could never find through religion. Turing became freer and happier after fully embracing a materialist/naturalist worldview. In a sympathetically written scene in A Madman, Levin portrays Turing’s loss of faith as not dark and bleak but rather hopeful, indeed “beautiful.”

Admittedly, my knee-jerk response to Turing’s rejection of God is one of deep sympathy and sadness. But doesn’t the divine manifest itself in countless and often surprising ways? Can not the laws and rules behind mathematics and science also bring us toward the divine, toward Truth? Einstein believed if you studied the laws behind the universe, you could also better understand God’s rules, the way God thought.

But science can only take us so far. Mathematician and social critic Bertrand Russell wrote in Portraits from Memory, “I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But . . . after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.”

The problem with Turing and Gödel, as Levin points out in her Speaking of Faith interview, was that both men adhered so closely to logic that they became confused and lost, their rigid theories leading them further away from revelation, from what could possibly be true.

In Bridges to Infinity: the Human Side of Mathematics, physicist Michael Guillen describes one of the implications of Gödel’s theorems: “the only possible way of avowing an unprovable truth, mathematical or otherwise, is to accept it as an article of faith.” It seems then that both the arts and the sciences are subject to faith.

We will never know if Keats was proclaiming a universal truth in the last lines of “Ode on a Grecian Urn.” But the fact that art and mathematics both seem to uphold beauty as a standard for Truth, or at least as a guidepost in the pursuit of it, should tell us something. We can’t help but see in beauty something of the transcendent. In Beauty: The Invisible Embrace, John O’Donohue writes, “the Beautiful offers us an invitation to order, coherence, and unity. When those needs are met, the soul feels at home in the world.” But as O’Donohue also reminds us, “Beauty is not to be captured or controlled for there is something intrinsically elusive in its nature. . . . The glimpse, the touch of beauty is enough to quicken our hearts with the longing for the divine.”