In the struggle between emotion and reason in Arcadia, Hannah Jarvis acts as the voice of reason. Hannah is the academic, feminist researcher who prides herself on thorough and well-thought research and sacrifices human contact for it. Hannah, like Thomasina's description of Queen Elizabeth, is able to separate sex from intellectual power and, in her case, push sex from view. Hannah resists carnal knowledge with effort: she doesn't like the idea of having her picture taken or submitting to a kiss, she refuses Valentine's idea of calling her his fiancée, and she scorns Gus's flirtation. Most of all, Hannah rejects Bernard's proposal that Lord Byron would have been silly enough to kill someone out of love.
It seems that Hannah did, at one point, know love but has decided to pursue better things ("I don't know a worse bargain. Available sex against not being allowed to fart in bed"). Hannah's rejection of love or knowledge of love has left her unaware of her own self. It appears as though she has deluded herself into academic sterility. Bernard tells Hannah that, if she understood herself a little better, she wouldn't have written her first book about Caroline Lamb, a romantic "waffle." When Hannah storms into Bernard's lecture and interrupts his speech about Lord Byron killing someone for love, Chloe turns psychologist for Hannah and politely asks her if she has been deeply wounded in the past.
Hannah cannot, however, reject the love of the shy Gus. The mute boy and mystery of the modern Croom household is able to crack Hannah, he is able to get her to dance with her. Gus's genius qualities, much like Thomasina before him, make him not only mentally like the subject of Hannah's studies, but give him an intuitive sense of history. As a silent messenger and connection to the past of Sidley Park, Gus gives Hannah the apple Septimus will eat and whose leaf Thomasina will describe. Gus also dresses Augustus in Regency wear, finds the foundation for the destroyed outbuilding, reveals the identity of the Sidley Park Hermit and asks Hannah for a much needed dance and embrace. Hannah accepts Gus's invitation for unknown reasons, but possibly his relevance and help with her own research play into the mix and certainly a real need for carnal embrace.
Thomasina is the girl genius of epic proportions. Thomasina intuitively knows the second law of thermodynamics and can refute determinism based on her ideas. Thomasina is a typical thirteen and then sixteen-year-old girl, except for the fact that she is unusually privileged and is given unusual educational opportunities. Although Lady Croom tells Thomasina that she must wed before she is overeducated, Lady Croom seems unconcerned at the intensity of her child's work until Thomasina nears the age of seventeen.
Thomasina is clearly driven not only by academic zeal but also by a desire for sexual knowledge. In the first scene, during her lesson with Septimus, Thomasina asks Septimus to tell her what a "carnal embrace" is. From the first pages of the book, Stoppard makes clear a duel purpose within Thomasina's character—to discover the rules of life and love while also working out the rules of mathematics. Thomasina's approach, including both carnal and academic knowledge, leads her to great success because she understands the principles of heat. Heat, which becomes equated with sexual knowledge, is the key to Thomasina's theory. Specifically articulated by Chloe, Thomasina's modern day counterpart, Thomasina's theory holds that sex messes up the Newtonian Universe because it is completely random.
Thomasina is ironically engulfed in the flame that she once seemed to understand better than anyone. Her tragic death, at the eve of her womanhood, drives Septimus to spend his lifetime tragically attempting to prove Thomasina's hypothesis. The final waltz that Thomasina and Septimus share at the end of play reveals a necessary urgency for sexual knowledge between all people. While the two talk about the end of the Earth, it seems Thomasina knows her end will be near. There is an understanding between tutor and student in the conclusion of the play; Thomasina and Septimus both understand the limits of and the ultimately unfulfilling nature of academic knowledge. Septimus and Thomasina dance and embrace to revel in the mystery they will never solve.
Bernard, the modern and foppish academic, reveals the danger of allowing present motivations to leap ahead of historic truths. Bernard's theory, that Lord Byron killed Mr. Chater in a lover's duel, is the product of his lust for fame and recognition. The evidence that Bernard puts together seems sketchy at best and the result of his theory and publication of his results is clear from the outset. Bernard never brings the platonic, third letter on stage, and it remains unclear how Byron got a hold of Septimus's book. Nevertheless, Bernard can't restrain himself. Undoubtedly reflecting Stoppard's own commentary on academic eagerness, Bernard ignores Hannah's objections to his theory in favor of quick fame. Bernard has little interest in the Croom family besides an opportunity to bring him recognition.
But Bernard, despite his mistakes, is essential to Hannah finding the identity of the hermit. While seducing Chloe in the library stacks, Bernard notices "something between her legs," a contemporary account of the hermit's identity that describes the hermit's turtle, Plautus. This is Bernard at his best, his sole constructive contribution into the Croom mystery.
Bernard is one character who is not aided by his sexual knowledge, despite his discovery while supposedly having sex (the modern day account of the hermit). Bernard's forthright proposal to Hannah and seduction of Chloe do no more than win him a loyal teenage fan. Bernard does, however, seem to know a bit more than Hannah because of his supposed knowledge. Bernard tells Hannah that she wouldn't have written a book about Caroline Lamb if she had known herself better. Yet, it remains unclear why Bernard didn't know himself better than to publish his results about Lord Byron before having more concrete proof of the theory. It is evident that neither academic nor canal knowledge alone will do.