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Mathematics, Nature, and Fate Theme Analysis

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Mathematics, Nature, and Fate Theme Icon
Romantic Conceptions of Beauty Theme Icon
Sex and Love Theme Icon
Academia and Education Theme Icon
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Mathematics, Nature, and Fate Theme Icon

Thomasina’s project, tragically cut short by her early death, is to find a formula that will express not lines, circles, or other perfect geometric shapes, but the natural forms of nature: “If there is an equation for a curve like a bell, there must be an equation for one like a bluebell” (Act 1, Scene 3). Thomasina also believes that a comprehensive formula to describe nature will allow her to predict the future. She makes several discoveries, even without advanced knowledge of math. One breakthrough is her understanding that hot things cool down to room temperature, but room temperature things don’t heat up, a concept that Newton did not describe in his laws of physics. In the modern day, Valentine, who studies similar topics at Oxford, interprets Thomasina’s discovery, explaining how this one-directional type of physics relates to the universe’s tendency towards equilibrium: “It’ll take a while, but we’ll all end up at room temperature” (82). Energy tends to leave, not arrive. So although the future is not as specifically predictable as Thomasina would like, she’s correct that what’s true of a bowl of rice pudding is true of the universe, and they both end up at the same low-energy point.

Another significant piece of Thomasina’s exploration is the graphing she makes by iteration, using the result of the previous function to make a new function. Valentine explains that contemporary science uses iteration to understand population changes and other major topics. However, iteration won’t allow predictions of the future either—instead, it shows how tiny changes can have a huge effect, and demonstrates that “the future is disorder” (Act 1, Scene 4). Thomasina’s discoveries and her focus on destiny not only link her to Valentine, but also to the play’s larger concerns about beauty, death, and truth.

Mathematics, Nature, and Fate ThemeTracker

The ThemeTracker below shows where, and to what degree, the theme of Mathematics, Nature, and Fate appears in each scene of Arcadia. Click or tap on any chapter to read its Summary & Analysis.
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Mathematics, Nature, and Fate Quotes in Arcadia

Below you will find the important quotes in Arcadia related to the theme of Mathematics, Nature, and Fate.
Act 1, Scene 1 Quotes

When you stir your rice pudding, Septimus, the spoonful of jam spreads itself round making red trails like the picture of a meteor in my astronomical atlas. But if you stir backward, the jam will not come together again. Indeed, the pudding does not notice and continues to turn pink just as before. Do you think this is odd?

Related Characters: Thomasina Coverly (speaker), Septimus Hodge
Page Number: 9
Explanation and Analysis:

Thomasina is very young, but she notices that she can't "unstir" her pudding; that is, she can make her bowl of pudding more and more disorderly, but she cannot recreate order in a "natural" way. Thomasina has stumbled upon an idea that's at the core of modern mathematics and science: the principle of entropy. The total entropy (i.e., disorder, heat energy) of a system is always increasing: thus, Thomasina can increase the entropy of her pudding, but she can't decrease it again. Thomasina's idea has been known since ancient times, (it was the Greek philosopher Heraclitus who said "you can't bathe in the same river twice," often interpreted as an observation about entropy), but as we'll learn by the end of the play, Thomasina is actually a mathematical prodigy. Furthermore, the concept of entropy could be interpreted in a more philosophical way, in that life itself tends towards disorder and decay, and it is only through human will and action that we cling to our senses of meaning and order.


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Act 1, Scene 3 Quotes

God’s truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?

Related Characters: Thomasina Coverly (speaker), Septimus Hodge
Related Symbols: The Apple and Its Leaf
Page Number: 41
Explanation and Analysis:

In this important section, we see the novelty of Thomasina's thinking. Thomasina has learned so much about mathematics from Septimus that she begins to think in terms that eclipse the intellectual dogma of her era (and her teacher). Thomasina has learned how to model curves like a bell curve or a circle; but now she wants to discover the curve that can model the shape of a leaf or a rose. In short, Thomasina wants to use mathematics to discover the source of the beauty of the natural world.

Where do we situate Thomasina in the Enlightenment-Romanticism binary? Perhaps Thomasina's example shows us that it's really not a binary at all. Like the Romantics, Thomasina embraces the link between mind and nature; at the same time, she seems to want to use mathematics to break down nature into a series of rigorous patterns, not unlike the Enlightenment thinkers. In general, Thomasina's project goes beyond anything that the Enlightenment or the Romantic era was capable of achieving: her ideas are actually more characteristic of chaos theory, a distinctly postmodern theory of mathematics. Thomasina, one could argue, is the truly "modern" character in the text, someone who belongs in the 20th or 21st century.

Act 1, Scene 4 Quotes

I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone.

Related Characters: Thomasina Coverly (speaker)
Page Number: 47
Explanation and Analysis:

Thomasina begins the scene by claiming that she's discovered a mathematical proof that will allow her to model the shapes of natural objects like trees and leaves. It's not immediately clear if Thomasina really has discovered such a proof, or if she's only pretending.

Thomasina's discovery (and it is a real discovery, we later learn) is important because it anticipates chaos theory, a school of science and mathematics that wouldn't appear for more than 100 years. Thus, Thomasina's discovery seemingly confirms Septimus's observations about the cyclical nature of all knowledge: certain discoveries get lost in time, only to be rediscovered later on. It's also worth noting that Thomasina's discovery seems to be lost in part because she's a young woman--the sexism of her society ensures that her contributions to mathematics aren't valued, let alone remembered.

When your Thomasina was doing maths it had been the same maths for a couple of thousand years. Classical. And for a century after Thomasina. Then maths left the real world behind, just like modern art, really. Nature was classical, maths was suddenly Picassos. But now nature is having the last laugh. The freaky stuff is turning out to be the mathematics of the natural world.

Related Characters: Valentine (speaker), Thomasina Coverly
Page Number: 49
Explanation and Analysis:

In the present-day, Valentine, a mathematics student at Oxford, discovers Thomasina's proof for how to model chaotic natural structures. He acknowledges that Thomasina wasn't just bluffing: she really had stumbled upon a form of chaos theory 100 years earlier than anybody else. Valentine goes on to give an informal history of modern mathematics. Mathematics was once seen as a way to model the world in an orderly and predictable fashion. But over time, mathematics became increasingly abstract and alien to the natural world: innovations like non-Euclidean geometry and set theory seemed to have little application to the real world. But in the end, it became clear that the world of mathematics really was applicable to reality: the only way to truly model natural objects like leaves and trees was to use chaos theory.

There's a lot to unpack here. Notice that Lady Croom's theory of the orderliness and regularity of the natural world is nonsensical: as it turns out, the natural world is infinitely chaotic, to the point where only the most abstract of mathematical formulae can represent it. Furthermore, notice the analogy Valentine makes between mathematics and painting: the boundaries between different intellectual disciplines fades away as civilization enters the 20th century.

The unpredictable and the predetermined unfold together to make everything the way it is. It’s how nature creates itself, on every scale, the snowflake and the snowstorm. It makes me so happy.

Related Characters: Valentine (speaker)
Page Number: 51
Explanation and Analysis:

In this passage, Valentine continues to explain chaos theory in a lyrical, nontechnical way. Chaos theory, he claims, argues that the world is both predictable and uncontrollable. The tiniest differences in scale or size can have enormous consequences (a principle often called the "butterfly effect," based on the idea that butterfly flapping its wings in Tokyo could cause a hurricane in Florida). Interestingly, Valentine claims that small, unpredictable events can sometimes, but not always, be balanced out by large, predictable events. Thus, the world consists of a constant interplay between randomness and predictability: uncertainty, but not too much uncertainty, freedom, but not too much freedom.

The passage is another good example of the "poetic" nature of modern mathematics and science, particularly as Stoppard portrays it. There's something poetic, even magical, about Valentine's vision of the world, even though he's a man of math and science, and can back up his ideas with rigorous proofs. Math is a kind of religion for Valentine, something that makes him "happy"--it gives his life meaning, and seems to have major applications for religion, morality, metaphysics, etc.

Act 2, Scene 7 Quotes

…There’s an order things can’t happen in. You can’t open a door till there’s a house.

Related Characters: Valentine (speaker)
Page Number: 83
Explanation and Analysis:

In this passage, Valentine analyzes Thomasina's notes on chaos theory, which she saw as an algorithm for predicting the randomness of the universe. Valentine admits that Thomasina understood the basic mechanisms of chaos theory very well: she saw the universe as a fundamentally unpredictable place, in which there was limited room for patterns and order. And yet Valentine also claims that Thomasina didn't really understand what she'd discovered: she didn't understand that chaos theory and the laws of thermodynamics predict the end of the universe. Everything in the universe proceeds from a place of low entropy to high entropy; i.e., things flow from hot to cold, until everything in the universe is exactly the same temperature. (As Valentine puts it, "you can't open a door till there's a house.") Thomasina had unknowingly predicted the end of the world by "heat death."

Valentine's observations illustrate a couple of important ideas. It's strange to think that Thomasina could discover something and yet not see the full implications of her own ideas: and yet such a phenomenon is common in intellectual history. Thomasina's ideas also illustrate a fundamentally pessimistic view of life: the world is getting more chaotic, and all human attempts to reverse the chaos will prove futile in the end. (That is, death exists "even in Arcadia.) In the end, both Enlightenment and Romantic notions of the world prove wrong, since they both hinge on a "pattern" (either intellectual or emotional) that, mathematics teaches us, must eventually break down. And yet perhaps Valentine's notions of life and fate are just as culturally determined as Thomasina's and Septimus's: perhaps Valentine's pessimism about the fate of the universe is just as arbitrary and mythological as his predecessors' optimism.