How is chaos theory a theme in Tom Stoppard's Arcadia?

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The best way to approach chaos theory as a theme in this work is to consider the way that the play explores the concept of free will vs. determinism, and how chaos theory falls within this exploration. The various characters explores free will through looking at humans and their emotions, taking scientific principles and exploring them to their logical extreme. Thomasina's efforts are basically trying to use the laws of physics to predict the future, which makes us question free will. Yet chaos theory perhaps throws into doubt the use of science to predict the future. Note what Valentine says about chaos thory in the following quote:

The unpredictable and the predetermined unfold together to make everything the way it is... We're better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it'll rain on auntie's garden party three Sundays from now. Because the problem turns out to be different. We can't even predict the next drip from a dripping tap when it gets irregular. Each drip sets up the conditions for the next, the smallest variation blows prediction apart, and the weather is unpredictable in the same way, will always be unpredictable.

Context is all important, and although science is able to yield some concrete results about the future, at the same time it is vitally important to realise the limits of science and how chaos theory plays into that. Just as it is impossible to "predict the next drip from a dripping tap," so humans themselves can be impossible to predict, thanks to emotions and the way that they are shown to govern and rule our lives. Chaos theory therefore is important in this play as it shows the limits of science when trying to understand how we as humans operate.