|Ivars Peterson's MathTrek|
February 3, 1997
Those words are spoken by Thomasina Coverly, a mathematically precocious teen-ager of the early nineteenth century. She's a character in Arcadia, a recent play written by Tom Stoppard, and the words represent her response to a remark by her tutor Septimus Hodge, who was defending classical geometry.
"Geometry, Hobbes assures us in the Leviathan, is the only science God has been pleased to bestow on mankind," Septimus had said.
Thomasina, however, was deeply engaged in discovering by trial and error her own geometry. In her notebook, she later playfully writes: "I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone."
Then she slyly adds, "This margin being too mean for my purpose, the reader must look elsewhere for the New Geometry of Irregular Forms discovered by Thomasina Coverly."
Fractal ferns as generated by Thomasina's algorithm.
It's unusual to find mathematics in a play, and even more unusual to find it at such a sophisticated level in a witty, fast-paced, popular romp. When I saw Arcadia a few weeks ago at the Arena Stage in Washington, D.C., where it played to a full house, the three hours of the production sped by amazingly quickly.|
Amid the laughs and dramatic surprises, there was little time to savor the nuances of the mathematics and to ponder the deep questions about the nature of scientific discovery that the play raises. So, I found it helpful to obtain a copy of the text of the play and to read Stoppard's inventive descriptions of fractal geometry, iterated function systems, chaos, and much else -- as presented by characters in his play.
It's Valentine who tries to explain iteration, algorithm, and chaos to Hanna Jarvis, a best-selling author and garden historian who is visiting the estate to do research for a new book.
"The maths isn't difficult," he insists. "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."
Valentine clearly revels in this 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 joyfully. "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."
Stoppard's play delves into the unsettling experience of new ideas, the interplay of hypothesis and evidence, and the role of human character in discovery. Heavy stuff, yet the conversation remains sprightly and amusing and the characters engaging and befuddled in very human ways.
Arcadia serves as a handy antidote to the impression many people have that mathematics hasn't changed much since Euclid's time and generally putters along in inscrutable increments. Mathematics does evolve, and it has the power to reorganize the way we think about the world around us.
The play also 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."
The mathematics in Arcadia hasn't gone unnoticed among mathematicians. A New York production of the play was reviewed in the Notices of the American Mathematical Society. Robert L. Devaney of Boston University has an informative website describing and animating some of the mathematical ideas lurking in the background of Stoppard's play.
The play "offers teachers of mathematics and the humanities the opportunity to join forces in a unique and rewarding way," Devaney notes.
Local theater companies have already mounted productions of Arcadia at several colleges and in some communities. The play is well worth seeing, when you get the chance. Until then, reading Stoppard's text provides its own delights.
Copyright © 1996 by Ivars Peterson.
Jackson, Allyn. 1995. Love and the second law of thermodynamics: Tom Stoppard's Arcadia. Notices of the American Mathematical Society 42(November):1284-1287.
Peterson, Ivars. 1987. Packing it in. Science News 131(May 2):283-285.
Stoppard, Tom. 1993. Arcadia. London: Faber and Faber.
Robert Devaney's site, "Chaos, Fractals, and Arcadia," is at http://math.bu.edu/DYSYS/arcadia/.
The fractal fern images were created by Philip Hodge.
Comments are welcome. Please send messages to Ivars Peterson at firstname.lastname@example.org.