Arcadia | Context

Chaos Theory

In 1993, when Stoppard completed Arcadia, chaos theory had captured the imagination of scholars in many fields outside physics. Chaos theory is a mathematics branch that addresses seemingly random, or chaotic, data systems that are sensitive to slight changes; such slight changes might yield great consequences. The theory quickly became a symbol of postmodernism, an artistic movement that addresses disorder in the universe with a kind of lightheartedness. Stoppard's incorporation of mathematics, physics, philosophy, and history into his literary work reflects the intellectual environment of the 1990s, which promoted interdisciplinary approaches to knowledge and attempts to find grand theories of everything. From Stephen Jay Gould's Time's Arrow, Time's Cycle to Murray Gell-Mann's The Quark and the Jaguar: Adventures in the Simple and the Complex to James Gleick's Chaos: Making a New Science, the popular consciousness of intellectuals was flooded with the ideas of chaos and complexity and the patterns that emerge over time.

Chaos theory refers to the patterns that naturally emerge through analyzing large data sets over time, and it shows that small variations can cause wildly different results. This kind of analysis can require millions of calculations before a pattern becomes visible and would have been impossible from a practical standpoint before the invention of the computer in the 20th century.

Chaos theory applies directly to quantum physics (based on the atom) in the unexpected and disorderly behavior of subatomic particles. Before the rise of quantum physics, Newtonian physics explained the natural world as an orderly and predicable system. Sir Isaac Newton had spelled out three simple laws that explained the physical motion of all objects. However, with the discovery of quarks and other subatomic particles, physicists found Newtonian laws of motion no longer applied. Subatomic particles behave in unexpected and unpredictable ways, not following the laws of Newtonian physics. Many scientists have tried to find a theory—a theory of everything—that explains both the orderly and chaotic behavior of atoms, but it has not been found yet. Chaos theory was thought to be one explanation. Stoppard includes references to chaos theory in Arcadia and attempts to apply its principles metaphorically to the events of the story.

Fermat's Last Theorem

For hundreds of years French mathematician Pierre de Fermat's Last Theorem was thought to be impossible to prove. In a margin note scribbled in a copy of Arithmetica by Diophantus, Fermat claimed in 1637 that the equation xⁿ + yⁿ = zⁿ is unsolvable if the positive integers are greater than 2—or, in mathematical language, if n>2. Discovered after Fermat's death and later published by his son, this seemingly simple problem stumped mathematicians for more than 350 years. In 1993 British mathematician Andrew Wiles made headlines worldwide when he produced the first proof of the famous problem. He had spent most of his career working alone and even in secret to prove that the equation was indeed unsolvable.

After Wiles published his proof in 1993, it was found to contain an error; he worked for another year on the proof, eventually found one, and then published the corrected proof, approved by the mathematical community in 1995. Fermat's Last Theorem is featured throughout Arcadia as Thomasina works on finding a proof of it. It is significant in that her tutor seems to assign it to her to keep her busy because he assumes it is unprovable, but later it is clear that Thomasina has the genius that could have led to a proof of the problem if she had enough time.

Classical and Romantic Thinking

History has shown that patterns of thought, art, and culture follow trends based on the general ideas of classical or romantic thinking. In general, classical thinking is based on reason: logical, orderly understanding, focusing on systems of knowledge that can be proven. The emphasis is on logic and reason; emotion is scorned. Conversely, romantic thinking is driven by emotion: intuitive understanding, sentiment, individualism, and self-expression. It is gut instinct and feeling rather than logical analysis—the personal rather than the universal.

In the early 19th century, many poets and artists were reacting against the logical, or classical, thought patterns of the Enlightenment of the previous century by focusing on instinctive sensibilities and natural experiences as sources of higher truth. This paradigm shift affected music, literature, landscape architecture, and art—classically ordered Arcadian landscapes by Nicolas Poussin and Claude Lorrain as opposed to wilder, seemingly uncultivated Gothic landscapes by Salvator Rosa and other 17th-century painters. This transformation from classical thinking to romantic thinking is a theme of the play Arcadia. The shift is discussed repeatedly in the context of the history of the garden and is also demonstrated in the personal journey of some of the characters, such as Hannah Jarvis.

Determinism

Determinism is the application of classical thinking to philosophy. It is the belief that all outcomes are inevitable as the logical result of actions at the moment they are set in motion. Determinism depends on the universe functioning in a logical, orderly manner; therefore, in theory, prediction of the future would be possible if all variables were known. Determinist philosophy inevitably raises the question of free will if all actions and reactions are predetermined.

In contrast to classical determinist thinking, the romantic movement, in celebrating the random and unpredictable aspects of life, is a complete rejection of determinism. The philosophy of determinism is discussed by the characters Thomasina Coverly and Septimus Hodge in Arcadia as they debate the possibility of predicting the future mathematically.