This compromise is forged carefully. The champion of intellectual knowledge is Hannah Jarvis, who, as the scholar of modern day Sidley Park, wrote her first novel about injustice inflicted on Lady Caroline Lamb by Lord Byron through the couple's relationship. Hannah's purpose at Sidley Park is to write a book that essentially criticizes romanticism and heralds classicism. Hannah believes that the life of the hermit of Sidley Park, the "genius of the place" but also "an idiot in the landscape" is an apt metaphor for the downfall of romanticism. Hannah refuses to believe that Lord Byron would kill Ezra Chater because of "gut instinct." Hannah may be right about Lord Byron and Ezra Chater, but what she does not know is that Septimus Hodge, the hermit of Sidley Park, fell into the hermitage for an arguably romantic reason. Septimus escaped into the hermitage out of lost love, destined and determined to finally prove Thomasina's theory, not because of false knowledge or wasted work. Septimus, like Thomasina, is unable to solve the proof because he lacks the proper technology and, even in a life's work, cannot finish the problem. Hannah rejects sexual knowledge in all forms; she won't be photographed or submit to a kiss, she refuses Valentine, and brushes off Gus's flirtation. It seems that Hannah, at one time, knew love, "Chaps sometimes wanted to marry me," but she has turned away, "I don't know a worse bargain. Available sex against not being allowed to fart in bed."

Mrs. Chater, the subject of the Chater principle, has the greatest amount of carnal knowledge. Although she remains unseen, the "Chater" as she's called, seduces Septimus, Lord Byron, Captain Brice, and her husband. She is the infamous woman who demonstrates the random and unexpected nature of carnal knowledge and "bodies in heat." The Chater has, as expected, no known academic ties or pursuits mentioned in the play.

While the play progresses toward Thomasina's fiery end in one story and toward the solution of her diagram in the other, there is an unexpected urgency toward sexual knowledge. As Valentine explains Thomasina's discovery to Hanna, Thomasina begs Septimus for a waltz and kiss before her seventeenth birthday. The knowledge that both stories come to—the irreversible end of life—leads the characters to find what is finally the most important and vital sort of knowledge. As Septimus suggests, the "improved Newtonian Universe" will die and grow cold, as Valentine interjects, "the heat goes into the mix." Thomasina asks once again for a dance. The knowledge each has found is cold and does not lead to heat, which is the final essential ingredient to life. The compromise is the realization, the knowledge of what knowledge will bring and cannot bring—it is the fear of knowing without heat or knowledge of another.