Rice, Jam and Cups of Tea
'Arcadia' was written in 1993, the year Fermat's last theorem was eventually proved and shortly after James Gleick's bestselling book about Chaos Theory hit the bookshops. Stoppard, being Stoppard, did not simply write a play about scientific and mathematical breakthroughs. Instead he incorporated these ideas into a play about love, poetry and madness. And he did so by writing about rice, jam and cups of tea.
Rice and Jam
'When you stir your rice pudding, Septimus, the spoonful of jam spreads itself around...but if you stir backward, the jam will not come together again.'
What Thomasina has noticed is the effect of entropy on everyday objects. When the jam is stirred into the rice pudding, the molecules of jam are mixed with the molecules of rice pudding. This mix is chaotic, and cannot be separated with only the help of a spoon. Stirring backwards only mixes the jam and rice in a different pattern.
Cups of Tea
'Your tea gets cold by itself, it doesn't get hot by itself. Do you think that's odd?'
A cup of tea, left to itself, will happily grow cold without any help from us. However, to heat it up again, we must become actively involved, using hot water, or microwaves.
Why?
The reason is known as the Second Law of Thermodynamics. The energy in the tea will disperse irreversably from being in one place (the tea cup), to a general place (spread in the atmosphere), if it is not stopped (by being drunk).
The same principle applies to the universe, when it is known as heat death; it used to be thought that when all the heat in the universe has dispersed, as in the cup of tea, then the chaotic universe, like a certain character in the play, will suffer heat death.
This is an apparent contradiction of Newton's laws, which are reversable. In Newtonian physics any process that can flow one way in time can also flow the other.
And a few more ideas...
Fermat's Last Theorem
'Fermat's theorem...asserts that when x, y and z are the whole numbers each raised to the power of n, the sum of the first two can never equal the third when n is greater than 2.'
Fermat, a mathematician, wrote in the margin of a book that he had discovered the proof for his theorem, but that as the margin was too small, he could not expand further. The puzzle Fermat posed kept mathematicians going until 1993, when it was finally solved.
The Deterministic Universe
The theory of the deterministic universe states that if everything could be stopped; all atoms frozen in space and time, then there would be an equation which could be found which would be able to predict each atoms future movements; in other words, predict the future.
Iterated Algorithms
An algorithm is a procedure or formula which solves a problem, such as 3x=y. To iterate this, the value of y is taken for the next value of x, which makes a new value of y, which in turn can be used as the next x value.
This can also be used for graphs, when the first graph has a smaller section blown up which makes the second graph, and so on, as in the Mandlebrot Set.