Enlightenment vs. Romanticism
By setting much of Arcadia in 1809, Stoppard pits two opposing historical epochs against each other: Enlightenment and Romanticism. The eighteenth century age of Enlightenment stressed orderly, rational thought, and conformity to accepted rules and forms, and looked to the Classical Greeks and Romans as models of simplicity, proportion, and restrained emotion in culture, art, and literature. Romanticism of the early nineteenth century was a deliberate revolt against Enlightenment ideals. Romantic philosophers and artists experimented with literary forms and stressed individuality, freedom, and the wildness of nature in their work.

The characters in Arcadia, in both the past and present scenes, represent both kinds of thought. Lady Croom wants to preserve her classically-inspired gardens where, "The slopes are green and gentle. The trees are companionably grouped at intervals that show them to advantage. The rill is a serpentine ribbon unwound from the lake peaceably contained by meadows on which the right amount of sheep are tastefully arranged.’’ Her adversary in taste is the landscape architect Richard Noakes (hired by the unseen Lord Croom), who is prepared to tear down the neatly manicured shrubbery and carefully groomed hillsides and convert Sidley Park into a Gothic wilderness, complete with a waterfall, gloomy forest, and picturesque hermitage. He defends himself, saying simply, ‘‘It is the modern style.’’

The battle fought between Lady Croom and Noakes over the condition of Sidley Park's gardens is reflected in some of the play's less tangible ideas as well. In the contemporary scenes, Bernard Nightingale and Valentine Coverly line up on each side of the debate between intellect and emotion. Bernard is acting on instinct and emotion, pursuing the unlikely theory that Lord Byron left England in 1809 because he killed a minor poet in a duel. He persists in his notion, even in the face of evidence to the contrary, because of "Gut instinct. The part of you which doesn't reason. The certainty for which there is no back-reference.’’

Valentine, on the other hand, is a graduate student at Oxford, studying chaos theory, and trying to find a pattern in the rise and fall of numbers in his family's centuries-old hunting books. To him, Bernard's interests are trivial. ‘‘The questions you're asking don't matter, you see,’’ he tells the arrogant professor,"It's like arguing who got there first with the calculus. The English say Newton, the Germans say Leibnitz. But it doesn't matter. Personalities. What matters is the calculus. Scientific progress. Knowledge.’’

In the end, each combatant learns a lesson about the other's viewpoint. Bernard rushes ahead to publish and promote his theory before learning all the facts and is publicly embarrassed to discover he was completely wrong. A little more analysis and a little less gut instinct would have served him well. For his part, Valentine must admit to the existence of genius, a human impulse that surpasses science, when he works his way through Thomasina's lesson book and finds she perceived a theory for chaos long before scientists knew one existed. Genius
A genius is someone with natural talents, possessing exceptional intelligence or creative ability. Their powers of perception may be broad and encompass many areas of study and craft, or they may be gifted in a very particular area, such as writing, math, or communications. A couple characters in Arcadia are referred to as geniuses while others are trying desperately to gain that status. Others doubt the existence of genius in the same way they don't believe in fate or God.

Thomasina Coverly is probably a genius. At thirteen, she is seeking proof for Fermat's Last Theorem and trying to devise a numeric formula that will describe the shape of a leaf. She perceives things others do not and can match wits with anyone at Sidley Park. When she asks Septimus, her tutor, if she is more clever than her elders, he admits: "Yes. Much.’’ For his part, Septimus believes genius is a primal ability, existing somewhere in all human beings of every age. When Thomasina laments the loss of the historic library at Alexandria, Septimus reassures her, "You should no more grieve for the rest [of the lost Greek tragedies] than for a buckle lost from your first shoe, or for your lesson book which will be lost when you are old. We shed as we pick up, like travelers who must carry everything in their arms, and what we let fall will be picked up by those behind.’’ Lost plays, mathematical theories, and creative inventions will all be discovered again by geniuses of the future, who will appear, Septimus believes.

Thomasina's counterpart in the present day is Gus Coverly. Like the ancient prophets, ironically struck blind by the gods in order to "see" the future, fifteen-year old Gus is a genius who can't speak and shies away from most human contact. The nature of his ability is not as apparent as Thomasina's, though he is described as someone with great powers of intuition, capable of guessing the needs of others. He found the ruined foundations of the estate's boathouse for his mother, after experts spent months searching; and he provides Hannah with her most important clue: a sketch of Septimus Hodge, the Sidley Park hermit, and his pet tortoise, Plautus.

Valentine doubts the nature of genius when it reaches beyond what he feels are ordinary limitations. After studying Thomasina's lesson books with Hannah and considering the stacks of algebraic illustrations left behind by the Sidley Park hermit, he still can't bring himself to believe someone could have imagined such a theory years before the existence of calculators. ‘‘There's an order things happen in,’’ he insists, ‘‘You can't open the door until there's a house.’’ Hannah has a unique definition for genius. To her, genius can be found not only in extraordinary abilities but in the rigorous pursuit of knowledge. ‘‘It's wanting to know that makes us matter,’’ she stresses to Valentine, ‘‘Otherwise we're going out the way we came in.''