Arcadia: Act 1, Scene 4 Summary & Analysis

Back in the present day, Hannah and Valentine are looking at Thomasina’s old math textbook. Hannah reads Thomasina’s note about how she’s discovered a “method whereby all the forms of nature must give up their numerical secrets and draw themselves by number alone.” Thomasina, harking back to Fermat’s note about his proof, explains that the margin is too small for her to write out her equations.

Valentine explains Thomasina’s meaning, looking at both the textbook and Thomasina’s notebook, where she’s written more details and graphs. He tells Hannah that Thomasina was using iteration, a mathematical technique based on feedback, in order to describe a pattern. Valentine uses iteration to study grouse, but the technique has only been around for twenty years, and Thomasina’s use of it is mysterious. Valentine compares math’s progress in the 20th century as resembling the leap from classical, representative art to wildly imaginative modern art. Yet “the freaky stuff is turning out to be the mathematics of the natural world.”

Hannah asks for more details about how Valentine’s work relates to Thomasina’s. Valentine explains that he’s trying to find the mathematical algorithm that describes patterns in the grouse population, whereas Thomasina’s work started with an algorithm. Valentine bemoans all the “noise” in the grouse data from the Sidley Park game books. It’s hard to pick out what the pattern might be. Hannah persists in trying to figure out if Thomasina had really hit on something important. Valentine is reluctant to see her work as anything more than random doodling, but he acknowledges that her iterated algorithm is a way of using math to represent nature—not the shapes of animals, but the shapes of populations and other complicated systems.

Hannah asks if Valentine might be able to draw the apple leaf using iteration. Valentine explains that iteration could roughly show you the shape of the leaf, by showing the general pattern within which randomness may occur. Valentine’s personality shifts to genuinely enthusiastic, even poetic, as he talks about how nature is governed by both “the unpredictable and the predetermined,” and ultimately the future can’t be predicted, because tiny changes can have a huge impact. Hannah and Valentine listen to Gus play the piano in the other room, and Valentine explains that, though Gus hasn’t talked since he was five, he seems to know more about the garden than their mother.

Bernard enters, thrilled to have discovered a note about “The Couch of Eros” penciled into Byron’s satirical poem “English Bards and Scotch Reviewers” (which Lady Croom mentioned in Scene 3). Bernard sees this as proof of his hypothesized Byron-Chater connection. Hannah mentions that she’s discovered a letter that notes that Brice and Mrs. Chater married in 1810, presumably after Chater’s death. Bernard reiterates his idea: Byron killed Chater in a duel over Mrs. Chater’s honor. He is entirely certain and plans to write a paper, but Hannah still isn’t convinced, as Bernard hasn’t found direct evidence for the duel.

Valentine cuts in to mention that he knows that Byron stayed at Sidley Park in 1809 because of the game books. Bernard, stunned, exits in search of the books. Gus enters, and Valentine prepares to leave. Hannah, still focused on Thomasina’s iterations, asks why no one did that kind of work until the 20th century. Valentine explains that it’s because iteration is so time-intensive that it’s only practical on calculators. Otherwise, you’d need a lifetime of repetitive work, and “you’d have to be insane.”