May 22, 2009
In Tom Stoppard's play Arcadia, which switches between the early 18th century and modern times in the same English country estate, contemporary mathematician-biologist Valentine Coverly discovers ancestor Thomasina Coverly's mathematical notebooks.
Young Thomasina had written that she had "found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone." She continued, "This margin being too mean for my purpose, the reader must look elsewhere for the New Geometry of Irregular Forms discovered by Thomasina Coverly."
The young girl's algorithm generates what we now call fractals, a key to understanding the repeating patterns of a fern leaf, the self-similar swirls of clouds, the vagaries of weather, and even fluctuations in the stock market. In the play, Thomasina's insight leads her to question Newtonian determinism—something that actually happened more than a century later with the development of nonlinear dynamics and chaos theory.
On the evening of May 18, 2009, the MAA's Carriage House Conference Center was the venue for a lively, illuminating discussion of the mathematics underlying Arcadia and the intricacies of mounting such a production. The MAA and the American Mathematical Society organized the gathering in conjunction with the Folger Theatre's production of Stoppard's play (running through June 21, 2009) in Washington, D.C.
From left to right, Michele Osherow, Erin Weaver, and Manil Suri.
Folger Dramaturg Michele Osherow, cast member Erin Weaver—playing the role of young genius Thomasina—and Production Mathematics Consultant Manil Suri (University of Maryland Baltimore County) eagerly held forth on the challenges and joys of representing mathematicians—and mathematics—on the theatrical stage.
Tom Stoppard's "most human" play, Osherow observed, weaves exciting mathematical discoveries with romance, architecture, nature, and love of life.
One challenge, according to mathematician-novelist Suri, is to tackle the perception of a connection between mathematics and mathematicians' emotional turmoil, as exemplified by protagonists in math-based plays and films such as Proof and A Beautiful Mind. Thomasina serves as an appealing counterexample to the usual stereotypes of mathematical genius.
Suri's multimedia examples of iterations and fractals and Weaver's readings from Stoppard's play, however, set the matter straight. Mathematics is beauty and its adherents help us to see surprising links, striking patterns, and self-symmetry everywhere—even when we, like Weaver, don't understand all the mathematical fine points.
Weaver worked hard to understand the part of Thomasina, and she spent months delving into many aspects of the role, including the mathematics. She found ways to express Thomasina's genius in physical terms to create a convincing portrayal. Even if members of the audience don't catch the mathematical nuances, they can still appreciate the character's unique qualities.
"The maths isn't difficult," fictional character Valentine says, perusing Thomasina's notebook. "It's what you did at school. You have some x-and-y equation. Any value of x gives you a value for y. . . . What [Thomasina's] doing is, every time she works out a value of y, she's using that as her next value of x. And so on. Like a feedback. She's feeding the solution back into the equation, and then solving it again. Iteration, you see."
Such passages reveal how well Stoppard understood the basics of the mathematics that he used and could then go on to express the ideas in fresh ways accessible to a wide audience.
In the play, Valentine apparently revels in the new mathematics. "The unpredictable and the predetermined unfold together to make everything the way it is," he declares. "It's how nature creates itself, on every scale, the snowflake and the snowstorm."
"It makes me so happy," he adds. "To be at the beginning again, knowing almost nothing. . . . The future is disorder. . . . It's the best possible time to be alive, when almost everything you thought you knew is wrong."
By delving into new ideas, the interplay of hypothesis and evidence, and the role of human character in discovery, Arcadia also puts to rest the impression that mathematics hasn't changed since Euclid's time. Mathematics evolves, and it has the power to alter the way we think about the world around us. The play brings mathematics to "the ordinary-sized stuff which is our lives, the things people write poetry about—clouds—daffodils—waterfalls—and what happens in a cup of coffee when the cream goes in."
Conclusion: "Stoppard is a genius," said rising star Erin Weaver. Go see the play! —H. Waldman
Listen to part one of the discussion.