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  The final scene in Arcadia is an unusual and thought-provoking scene; in it, two groups of people from two entirely different times seem to coexist, even interact, even though we know that neither group can know about the other.  This scene emphasizes the inherent repetition of time, the congruency of past, present, and future.  As a twist in this scene, the characters in it, those of both past and future, come to the conclusion that "you can't run the film backwards" (Stoppard 93), that time, in fact, cannot repeat itself.  These are clearly contradictory conclusions, yet this scene shows that they can coexist; that, in fact, they are both, in a way, true; the universe never repeats itself exactly, but pieces of it do sometimes re-surface, providing short periods of symmetry.

  Valentine and Thomasina each conclude that time "won't work backwards" (93) because of heat; that the heat that is produced by virtually every interaction of matter cannot be regained.  This idea is implicit in the scientific concept of entropy.  Entropy basically says that the universe is moving towards chaos; that ordered things will eventually crumble, become disordered and fragmented.  Just as the pieces of a tower will scatter as they fall, so have the "pieces" of Thomasina's time, her fractals, Chater's books, knowledge of the grouse population, been strewn about the world.  Where once there was order, with all the pieces in one place, now there is chaos, with the pieces "go[ne] into the mix" (94).

 But pieces that are dropped into the mix may well surface in new and different ways.  As Septimus says,

We shed as we pick up, as travelers who must carry everything in their arms, and what we let fall will be picked up by those behind.  ... [T]here is nothing outside the march so nothing can be lost to it.  The missing plays of Sophocles will turn up piece by piece, or be written again in another language. (Stoppard 38)

  It's like mixing jam into the rice pudding; "if you stir backward, the jam will not come together again", but if you keep stirring, you will eventually see each and every particle that once composed the jam, if in a somewhat different way.  Sometimes, lumps of jam will stick together; maybe there is a seed or the skin of a fruit still more or less whole that gets mixed into the pudding.  From time to time these lumps will surface; they represent the things that seem to repeat in our lives and in our history, the things depicted by Arcadia.

  So what does science have to say about all of this?  From the lesson given by Mr. Bridger the other day, modern science clearly has a link to this book.  In this case the link is especially interesting, in that the development of modern science reflects the initial indecisiveness of this idea, that the past will repeat itself, but never in quite the same way.  Per Mr. Bridger, first there was Determinism, which states that there exists somewhere an equation that governs the universe, and that if we knew the equation we could predict the future exactly.  As an interesting aside, by crossing information theory and chaos theory with Newtonian physics, one can prove that the universe itself is the only computer that can calculate the future of the universe; we, being elements of that computer, can theoretically alter its outcome.  But by the time that was realized, Newtonian physics had been destroyed, so it was a moot point.

  Within the last century two new branches of physics have arisen, relativity and quantum mechanics, the latter of which especially completely destroys Newtonian determinism.  Heisenberg's uncertainty principle, at the core of quantum mechanics. stated that we can't know anything with absolute accuracy.  We can't plug numbers into some grand equation and figure out the future, nor can we look at the current state of things and predict the past.  So science has shown both determinism and "self-determinism", as has Arcadia with Bernard's historical research and Thomasina's pudding.

  And science, with fractals, as Arcadia with its final scene, seems to be leading toward a middle ground.  Fractals imply an overall pattern in the chaos; with them, it is possible to predict and understand parts of the universe, if not all of it.  Arcadia ends with the same conclusion:

[Hannah] gets up and [she and Gus] hold each other, ... and start to dance, rather awkwardly.

Septimus and Thomasina continue to dance, fluently, to the piano.
(Stoppard 97)

  While they are both dancing, they are dancing differently.  Modern science and Arcadia both conclude, at least for now, on a single idea:  The one single pattern of the universe, if there ever was one, has shattered, but its pieces keep showing up in the pudding.