The Books: “Arcadia” (Tom Stoppard)

Next script on my script shelf:

Next play on the shelf is Arcadia: A Play by the marvelous Tom Stoppard.

This is just a great play. It truly is. The play takes place at two moments in time: April, 1809 and the present day. (Think of the movie Possession – and that’s the same idea. Past and present shuttling along beside one another. There are scholars in the present studying the people in the past … but all they have is what’s left behind: letters, journals, fragments … clues to put together … They cannot re-enter the past and relive it in all its everyday complexity. But that’s what scholars try to do.)

It takes place in a large country house in Derbyshire. Back in 1809, the Coverleys live there and they have a daughter who is pretty much a prodigy. Her name is Thomasina, and she is 13. Great part. She has a special tutor – Septimus Hodge – and the play opens with the two of them doing their lessons together.

200 years later, Hannah Jarvis stands in the same room. She is a garden historian and she has come to the house to investigate a scandal that was supposed to have happened in this very house when Lord Byrom stayed at Sidley Park. She believes it might have something to do with the “hermit” that lived on the grounds.

The plays moves fluidly back and forth between the centuries – and is really a nice big idea play – the kind that we don’t really get anymore, and when we do get them? They are usually badly written, didactic, and so self-righteous you could suffocate. Not so Tom Stoppard. He’s interested in ideas. In this play he is interested in, obviously, nature. Hannah Jarvis is a garden historian – the way people landscaped their lawns in 1809 is very different from how we landscape our lawns now – and stuff like that says everything about the society beneath it. The play is about time travel, in a way … what exactly is time? Would it be possible to step back into the past? Etc. etc.

Love this play. Sadly, I’ve never seen it. I missed the much-lauded first American production which was at Lincoln Center. I was in Chicago at the time.

I’ll excerpt one of the scenes from the present day (although I just love all of the scenes with Thomasina in them – she’s a great part). Hannah, wandering through the house, has come across Septimus Hodge’s old teaching portfolio. She looks through it. She is with Valentine Coverly, the son of the man who lives in the house now. (Actaully – the house has never passed out of the Coverly’s hands. It has been their family home for centuries.)

EXCERPT FROM Arcadia: A Play by Tom Stoppard

[Hannah and Valentine. She is reading aloud. He is listening. Lightning, the tortoise, is on the talbe and is not really distinguishable from Plautus. In front of Valentine is Septimus’s portfolio, recognizable so but naturally somewhat faded. It is open. Principally associated with the portfolio (although it may contain sheets of blank paper also) are three items: a slim math primer; a sheet of drawing paper on which there is a scrawled diagram and some mathematical notations, arrow marks, etc.; and Thomasina’s mathematics lesson book, ie. the one she writes in, which Valentine is leafing through as he listetns to Hannah reading from the primer.]

HANNAH. ‘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. This margin being too mean for my purpose, the reader must look elsewhere for the New Geometry of Irregular Forms discovered by Thomasina Coverly.’

[Pause. She hands Valentine the text book. Valentine looks at what she has been reading. From the next room, a piano is heard, beginning to play quietly, unintrusively, improvisationally]

HANNAH. Does it mean anything?

VALENTINE. I don’t know. I don’t know what it means, except mathematically.

HANNAH. I meant mathematically.

VALENTINE. [Now with the lesson book again] It’s an iterated algorithm.

HANNAH. What’s that?

VALENTINE. Well, it’s … Jesus … it’s an algorithm that’s been … iterated. How’m I supposed to …? [He makes an effort] The left-hand pages are graphs of what the numbers are doing on the right-hand pages. But all on different scales. Each graph is a small section of the previous one, blown up. Like you’d blow up a detail of a photograph, and then a detail of the detail, and so on, forever. Or in her case, till she ran out of pages.

HANNAH. Is it difficult?

VALENTINE. The maths isn’t difficult. It’s what you did at school. You have some x-and-y equation. Any value for x gives you a value for y. So you put a dot where it’s right for both x and y. Then you take the next value for x which gives you another value for y, and when you’ve done that a few times you join up the dots and that’s your graph of whatever the equation is.

HANNAH. And is that what she’s doing?

VALENTINE. No. Not exactly. Not at all. What she’s doing is, every time she works out a value for y, she’s using that as her next value for x. And so on. Like a feedback. She’s feeding the solution back into the equation, and then solving it again. Iteration, you see.

HANNAH. And that’s surprising, is it?

VALENTINE. Well, it is a bit. It’s the technique I’m using on my grouse numbers, and it hasn’t been around for much longer than, well, call it twenty years.

[Pause]

HANNAH. Why would she be doing it?

VALENTINE. I have no idea. [Pause] I thought you were doing the hermit.

HANNAH. I am. I still am. But Bernard, damn him … Thomasina’s tutor turns out to have interesting connections. Bernard is going through the library like a bloodhound. The portfolio was in a cupboard.

VALENTINE. There’s a lot of stuff around. Gus loves going through it. No old masters or anything …

HANNAH. The maths primer she was using belonged to him — the tutor; he wrote his name in it.

VALENTINE. [reading] ‘Septimus Hodge.’

HANNAH. Why were these things saved, do you think?

VALENTINE. Why should there be a reason?

HANNAH. And the diagram, what’s it of?

VALENTINE. How would I know?

HANNAH. Why are you cross?

VALENTINE. I’m not cross. [Pause] 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.

HANNAH. This feedback thing?

VALENTINE. For example.

HANNAH. Well, could Thomasina have —

VALENTINE. [snaps] No, of course she bloody couldn’t!

HANNAH. All right, you’re not cross. What did you mean you were doing the same thing she was doing? [Pause] What are you doing?

VALENTINE. Actually I’m doing it from the other end. She started with an equation and turned it into a graph. I’ve got a graph — real data — and I’m trying to find the equation which would give you the graph if you used it the way she’s used hers. Iterated it.

HANNAH. What for?

VALENTINE. It’s how you look at population changes in biology. Goldfish in a pond, say. This year there are x goldfish. Next year there’ll be y goldfish. Some get born, some get eaten by herons, whatever. Nature manipulates the x and turns it into y. Then y goldfish is your starting population for the following year. Just like Thomasina. Your value for y becomes your next value for x. The question is: what is being done to x? What is the manipulation? Whatever it is, it can be written down in mathematics. It’s called an algorithm.

HANNAH. It can’t be the same every year.

VALENTINE. The details change, you can’t keep tabs on everything, it’s not nature in a box. But it isn’t necessary to know the details. When they are all put together, it turns out the population is obeying a mathematical rule.

HANNAH. The goldfish are?

VALENTINE. Yes. No. The numbers. It’s not about the behavior of fish. It’s about the behavior of numbers. This thing works for any phenomenon which eats its own numbers — measles epidemics, rainfall averages, cotton prices, it’s a natural phenomenon in itself. Spooky.

HANNAH. Does it work for grouse?

VALENTINE. I don’t know yet. I mean, it does undoubtedly, but it’s hard to show. There’s more noise with grouse.

HANNAH. Noise?

VALENTINE. Distortions. Interference. Real data is messy. There’s a thousand acres of moorland that had grouse on it, and always did till about 1930. But nobody counted the grouse. They shot them. So you count the grouse they shot. But burning the heather interferes, it improves the food supply. A good year for foxes interferes the other way, they eat the chicks. And then there’s the weather. It’s all very, very noisy out there. Very hard to spot the tune. Like a piano in the next room, it’s playing your song, but unfortunately it’s out of whack, some of the strings are missing, and the pianist is tone deaf and drunk — I mean, the noise! Impossible!

HANNAH. What do you do?

VALENTINE. You start guessing what the tune might be. You try to pick it out of the noise. You try this, you try that, you start to get something — it’s half-baked but you start putting in notes which are missing or not quite the right notes … and bit by bit … [He starts to dumdi-da to the tune of ‘Happy Birthday’] Dumdi-dum-dum, dear Val-en-tine, dumdi-dum-dum to you – the lost algorithm!

HANNAH. [soberly] Yes. I see. And then what?

VALENTINE. I publish.

HANNAH. Of course. Sorry. Jolly good.

VALENTINE. That’s the theory. Grouse are bastards compared to goldfish.

HANNAH. Why did you choose them?

VALENTINE. The game books. My true inheritance. Two hundred years of real data on a plate.

HANNAH. Somebody wrote down everything that’s shot?

VALENTINE. Well, that’s what a game book is. I’m only using from 1870, when butts and beaters came in.

HANNAH. You mean the game books go back to Thomasina’s time?

VALENTINE. Oh yes. Further. [And then getting ahead of her thought] No — really. I promise you. I promise you. Not a schoolgirl living in a country house in Derbyshire in eighteen-something!

HANNAH. Well, what was she doing?

VALENTINE. She was just playing with the numbers. The truth is, she wasn’t doing anything.

HANNAH. She must have been doing something.

VALENTINE. Doodling. Nothing she understood.

HANNAH. A monkey at a typewriter?

VALENTINE. Yes. Well, a piano.

[Hannah picks up the algebra book and reads from it]

HANNAH. ‘… a method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone.’ This feedback, is it a way of making pictures of forms in nature? Just tell me if it is or isn’t.

VALENTINE. [irritated] To me it is. Pictures of turbulence — growth — change — creation — it’s not a way of drawing an elephant, for God’s sake!

HANNAH. I’m sorry. [she picks up an apple leaf from the table. She is timid about pushing the point] So you couldn’t make a picture of this leaf by iterating a whatsit?

VALENTINE. Oh yes, you could do that.

HANNAH. Well, tell me! Honestly, I could kill you!

VALENTINE. If you knew the algorithm and fed it back say ten thousand times, each time there’d be a dot somewhere on the screen. You’d never know where to expect the next dot. But gradually you’d start to see this shape, because every dot will be inside the shape of this leaf. It wouldn’t be a leaf, it would be a mathematical object. But yes. 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. To be at the beginning again, knowing almost nothing. People were talking about the end of physics. Relativity and quantum looked as if they were going to clean out the whole problem between them. A theory of everything. But they only explained the very big and the very small. The universe, the elementary particles. The ordinary-sixed stuff which is our lives, the things people write poetry about — clouds — daffodils — waterfalls – and what happens in a cup of coffee when the cream goes in — these things are full of mystery, as mysterious to us as the heavens were to the Greeks. 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 th enext, the smallest variation blows prediction apart, and the weather is unpredictable the same way, will always be unpredictable. When you push the numbers through the computer you can see it on the screen. The future is disorder. A door like this has cracked open five or six times since we got up on our hind legs. It’s the best possible time to be alive, when almost everything you thought you knew is wrong.

[Pause]

HANNAH. The weather is fairly predictable in the Sahara.

VALENTINE. The scale is different but the graph goes up and down the same way. Six thousand years in the Sahara looks like six months in Manchester, I bet you.

HANNAH. How much?

VALENTINE. Everything you have to lose.

HANNAH. [Pause] No.

VALENTINE. Quite right. That’s why there was corn in Egypt.

[Hiatus. The piano is heard again]

HANNAH. What’s he playing?

VALENTINE. I don’t know. He makes it up.

HANNAH. Chloe called him ‘genius’.

VALENTINE. It’s what my mother calls him — only she means it. Last year some expert had her digging in the wrong place for months to find something or other — the foundations of Capability Brown’s boat-house — and Gus put her right first go.

HANNAH. Did he ever speak?

VALENTINE. Oh yes. Until he was five. You’ve never asked about him. You get high marks here for good breeding.

HANNAH. Yes, I know. I’ve always been given credit for my unconcern.