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Robert L. Devaney
Department of Mathematics
Boston University
Boston, MA 02215
Introduction
Tom Stoppard's hilarious new play, Arcadia, offers
teachers of both mathematics and the humanities the opportunity to join
forces in a unique and rewarding way. The play features not one but two
mathematicians, and the mathematical ideas they are involved with form one
of the main subthemes of the play. In particular, such contemporary topics
as chaos and fractals form an integral part of the plot, and even Fermat's
Last Theorem and the Second Law of Thermodynamics play important roles.
The play is set in two time periods, the early nineteenth century and
the present, in the same room in an English Estate, Sidley Park. As the
play opens, we meet Thomasina, a young thirteen year old girl who
struggles with her algebra and geometry under the watchful eye of her
tutor, Septimus Hodge. But Thomasina is not your typical mathematics
student; as becomes clear as the play unfolds, she is a prodigy who not
only questions the very foundations of her mathematical subjects, but also
sets about to change the direction of countless centuries of mathematical
thought. In the process, she invents "Thomasina's geometry of
irregular forms" (aka fractal geometry), discovers the second law of
thermodynamics, and lays the foundation for what is now called chaos
theory.
In the modern period, we meet Valentine, a contemporary mathematician
who is attempting to understand the rise and fall of grouse populations
using iteration. As luck would have it, Valentine is heir to Sidley Park
and part of his inheritance is a complete set of game books that go back
to Thomasina's time. These books detail the precise number of grouse shot
at the estate each year. Gradually, he becomes aware of some of the old
mysteries surrounding Sidley Park, including Thomasina's discoveries, and
this sets the stage for a unique series of scenes that hop back and forth
between the nineteenth century and the present. Mathematics is not the
only theme of this play, of course, but the ideas of regular versus
irregular geometry or chaos versus order seem to pervade all of the other
events occurring at Sidley Park. We are thrust into a debate about
emerging British landscape styles featuring the orderly classical style
versus the irregular, ``picturesque'' style. Valentine's fianc\'ee Hannah
Jarvis methodically proceeds to uncover Sidley Park's secrets, in stark
contrast to her nemesis, Bernard Nightingale, who jumps from one theory to
another with reckless abandon. Indeed, the entire play pits the
rationalism of Newton against the romanticism of Byron.
Thomasina's Geometry of
Irregular Forms (Next Section)
(Return to Arcadia index)
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