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Arcadia explores the nature of evidence and truth in the context of modern ideas about history, mathematics and physics. It shows how the clues left by the past are interpreted by scholars. The play refers to a wide array of subjects, including mathematics, physics, thermodynamics, computer algorithms, fractals, population dynamics, chaos theory vs. determinism (especially in the context of love and death), classics, landscape design, romanticism vs. classicism, English literature (particularly poetry), Byron, 18th century periodicals, modern academia, and even South Pacific botany. These are the concrete topics of conversation; the more abstract philosophical resonances veer off into epistemology, nihilism, the origins of lust and madness.
The themes presented within Arcadia are based in a series of dichotomies. The most prominent of these is the idea of chaos versus order, presented through Stoppard's discussion of chaos theory within the play. The action of Arcadia and the characters within it reflect this theory; everything is gradually dispersing into a state of chaos and entropy (represented by the final scene), and yet within that chaos, order can be found. Valentine summarizes this idea: "In an ocean of ashes, islands of order. Patterns making themselves out of nothing." Within the chaos that develops over the course of the play—through the overlap of time periods, through increasingly complicated ideas that are presented, through the variances between what is correct and what is assumed—connections and order can still be recognized. The characters attempt to define the order of the world through their ideas and theories, and they are continually overturned (as with Bernard's theory).
The table which collects props from both time periods throughout the play is a strong example of the chaos/order dichotomy. In Science in Hapgood and Arcadia Paul Edwards, professor of English and History of Art at Bath Spa University, explains what this represents: "At the end of the play, the table has accumulated a variety of objects that, if one saw them without having seen the play, would seem completely random and disordered. Entropy is high. But if one has seen the play, one has full information about the objects and the hidden 'order' of their arrangement, brought about by the performance itself. Entropy is low; this can be proved by reflecting that tomorrow night's performance of the play will finish with the table in a virtually identical 'disorder'—which therefore cannot really be disorder at all."
A secondary theme within Arcadia is the dichotomy of Classicism versus Romanticism. It is exemplified primarily through the argument between Lady Croom and Mr. Noakes over the changes being made to the garden. This shows a direct shift between the tidiness and order of Classic style to the rugged, Gothic appearance of the Romantic. This dichotomy is also presented through Septimus and Thomasina, as she argues her new theories and ideas that refute classic Newtonian ideals while he defends them. Hannah's search for the poetic meaning behind the hermit of Sidley Park also remarks on this theme. She passionately exclaims to Bernard, "The whole Romantic sham, Bernard! It's what happened to the Enlightenment, isn't it? A century of intellectual rigour turned in on itself. A mind in chaos suspected of genius...The decline from thinking to feeling."
Another theme of the play, which falls under the category of chaos, is the irreversibility of time. This is examined scientifically through Thomasina's remarks on Newtonian equations, which work both backwards and forwards. And yet in reality, things, like Thomasina's rice pudding (which inspires these remarks), cannot be "unstirred." Heat flows in only one direction. The idea of heat (and the second law of thermodynamics) is thus represented through the actions of the characters. They burn bridges in relationships, they burn letters, candles burn, and in the end, it is revealed that Thomasina will burn to death. The finality of things is always present.
Thomasina's insights into thermodynamics and heat transfer, and the idea that the universe is cooling, echo the poem Darkness by her "real life" contemporary, Lord Byron. Written by in 1816—the "Year Without Summer" caused by atmospheric volcanic ash from the Mount Tambora eruption in the Dutch East Indies – "Darkness" depicts a world grown dark and cold because the sun has been extinguished.
The end of the play brings all of these dichotomies and themes together, showing that though things may appear to contradict—Romanticism and Classicism, intuition and logic, thought and feeling — they can exist, paradoxically, in the same time and space. Order is found amid the chaos.
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