2 - Chaos, Fractals, and Tom Stoppard's Arcadia

Summary

Tom Stoppard's wonderful 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. 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 mathematical biologist 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.