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.
4. Mathematical procedure for computing results through a series of repeated operations.
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2784 / TOM STOPPARD
HANNAH This feedback thing?
VALENTINE For example.
HANNAH Well, could Thomasina have?
VALENTINE [Swaps.] 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 as 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 behaviour of fish. It's about the behaviour 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, 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.
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ARCADIA II.5 / 2785
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 beaters5 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.J 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?6 VALENTINE Yes. Well, a piano.
[HANNAH picks up the algebra booh and reads from it.]
