Scene five, like Scene four, is set in the modern day. Bernard is practicing his lecture for Valentine, Chloe, and Gus. Valentine is feeding lettuce to Lightning, his tortoise. Bernard is practicing the speech he will give to introduce his new, groundbreaking theory that Lord Byron killed Ezra Chater over a woman. As Bernard begins his dramatic oration, Hannah excitedly enters the room to talk to Valentine. Chloe quickly hushes Hannah, and Bernard begins his speech once again. Bernard elaborates his theory connecting Byron, the letters found in The Couch of Eros, and Ezra Chater. Hannah is still not convinced that Byron killed Chater or even wrote the letters found inCouch of Eros to Chater. Hannah and Valentine pose challenges to Bernard's theory, which infuriate Bernard. Byron wrote an unsatisfactory review of Chater's work in The Piccadilly Review, and Hannah just doesn't believe that Byron would have done this after killing Chater. Hannah doesn't think it is feasible that Byron actually borrowed Couch of Eros, reviewed it, posted the review, seduced Mrs. Chater, killed Chater, and then fled to Europe within two or three days. Bernard retorts that Hannah just doesn't understand Byron, as seen in her novelette. Bernard accuses Hannah of even putting the wrong picture on the dust jacket of the book.
Bernard and Hannah continue to bicker about each other's books. Bernard asks Hannah to come to London with him but for sex, not the lecture on Byron. Hannah refuses but nonetheless seems flattered. Bernard tells Hannah that he is coming back for the dance at Sidley Park, and he will be Chloe's date. Bernard reveals that he has become involved with Chloe, which surprises Hannah. Bernard then gives Hannah a book he found that mentions the hermitage and the hermit she has been studying. According to the book, the hermit had a tortoise named Plautus. Valentine has entered the room, and Hannah is finally able to talk to him. Hannah tells Valentine that Septimus Hodge and the hermit were born in the same year. Hannah begins to realize that the hermit she thought was an idiot was actually a great intellectual, a genius; it was Septimus Hodge.
Scene six again returns to the early nineteenth century. Jellaby lights the oil lamps in one of the rooms and calls outside to Septimus. Septimus walks in with a dead rabbit for Thomasina. Jellaby informs Septimus that Captain Brice, Mr. and Mrs. Chater, and Lord Byron have left the estate. Lady Croom has found two letters written by Septimus, written in the event of his death. Though she doesn't completely explain the letters' contents, one is for Thomasina, which makes Lady Croom angry. Apparently, the night before, Mrs. Chater was found in bed with Lord Byron, and Lady Croom kicked them all out. Septimus is brought a letter from Lord Byron that he burns in front of Lady Croom. Mr. and Mrs. Chater took off with Captain Brice to Malta, with Mr. Chater to act as botanist. Septimus burns the letters found by Lady Croom.
Tom Stoppard has used mathematics as the basis of many of his plays. Arcadia is influenced most by chaos theory or what is also called nonlinear dynamics. Chaos theory is often heralded as one of the greatest scientific advancements in the physical sciences after relativity and quantum mechanics. Stoppard's main source of chaos theory information came form James Gleick's book Chaos: Making a New Science. Chaos theory itself focuses the characteristic or knowable behaviors of nonlinear systems. Nonlinear dynamics are processes that are "chaotic" but not random. As David Peak and Michael Frame have pointed out, "Chaos is irregular output from a deterministic source. The future of chaotic behaviors is completely determined by its past. Chaos is not chance or randomness." Therefore, chaos systems are random, but have some degree of predictability that may bear some statistical long-term results.
The iteration, like that formulated by Thomasina, is central to chaos theory. Iteration is the repetition of a computation of a mathematical algorithm. Thomasina begins her iteration, but it remains impossible for her to complete. It is not until Valentine and Hannah discover her primer and diagrams that Thomasina's theory and algorithm can be completed. With Thomasina's set and completed algorithm, Valentine is able to create a fractal, which is the result of iteration. A fractal is the plotted set that results from calculating an algorithm thousands of time into a computer and then plotting the points it produces. In modern times, fractals are used to describe objects in nature—just as Thomasina uses one or attempts to create a fractal to describe the leaf off of Septimus's apple. Small sections of fractal images, blown up, represent the whole of the image. Thomasina is determined to find the fractal because she realizes there are pictures and equations to be had in natural forms.
Thomasina doesn't believe that God's imagination or the physical world doesn't extend beyond arcs and angles, simple geometric shapes. Gleick's describes this same principle in his work: "Clouds are not sphere Mountains are not cones. Lightning does not travel in a straight line." Iterations are central to nonlinear dynamics because the iteration can be described as a process that continues and changes; like life itself, the iteration changes and transforms randomly. Thomasina's observations do not end with the plotting of nature by use of algorithm and iteration. Thomasina also links her discoveries with thermodynamics, inspired by Mr. Noakes's steam engine. Thomasina plots a diagram of heat exchange that reveals the inevitability and non-reversible nature of life itself. Thomasina intuitively understands the inevitable end of life and heat. The consequence of the sensitivity to an algorithm or initial system is irreversibility. Speculation about the future of any chaotic system is limited, besides the knowledge that the system must eventually end. As Valentine suggests, he cannot go back to the original equation once it is set. The randomness of a chaotic system makes this nearly impossible. For instance, the randomness of heat energy and in the human system, as Chloe suggests, sexual energy is impossible to predict. One can never know how the system (or person) will react to its (his or her) environment.