by Tom Stoppard
chater: (Startled) Eh?
brice: (Pleased) Ah!
Septimus: Oh, damn your soul, Chater! Ovid would have stayed a lawyer and Virgil a farmer if they had known the bathos to which love would descend in your sportive satyrs and noodle nymphs! I am at your service with a half-ounce ball in your brain. May it satisfy you - behind the boat-house at daybreak - shall we say five o'clock? My compliments to Mrs Chater -have no fear for her, she will not want for protection while Captain Brice has a guinea in his pocket, he told her so himself.
brice: You lie, sir!
Septimus: No, sir. Mrs Chater, perhaps.
brice: You lie, or you will answer to me!
Septimus: (Wearily) Oh, very well -1 can fit you in at five
minutes after five. And then it's off to the Malta packet out of Falmouth. You two will be dead, my penurious schoolfriend will remain to tutor Lady Thomasina, and I trust everybody including Lady Croom will be satisfied! (SEPTIMUS slams the door behind him.)
brice: He is all bluster and bladder. Rest assured, Chater, I will let the air out of him.
(brice leaves by the other door, chater's assurance lasts only a moment. When he spots the flaw .. .
chater: Oh! But...
(He hurries out after brice.)
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SCENE FOUR
HANNAH and valentine. She is reading aloud. He is listening. Lightning, the tortoise, is on the table and is not readily distinguishable fromPlautus. In front ofValentine is Septimus's portfolio, recognizably 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 maths primer; a sheet of drawing paper on which there is a scrawled diagram and some mathematical notations, arrow marks, etc.; and Thomasina9 s mathematics lesson book, i.e. the one she writes in, which valentine is leafing through as he listens 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.) 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.
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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 fory. So you put a dot where it's right for both x andy.
Then you take the next value for x which gives you another
value fory> 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
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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 bey goldfish. Some get born, some get eaten by herons, whatever. Nature manipulates the x and turns it into y.Theny goldfish is your starting population for the following year. Just like Thomasina. Your value fory 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 offish. It's about the behaviour of numbers. This thing works for any phenomenon which eats its own numbers -
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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 -1 mean, the noisel 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 somethin
g - 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?
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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 it 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: (Off-hand) Oh yes, you could do that.
hannah: (Furiously) 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
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between them. A theory of everything. But they only explained the very big and the very small. The universe, the elementary particles. The ordinary-sized stuff which is our Jives, 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 the next, 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 is 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.
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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.
(BERNARD enters in high excitement and triumph.) BERNARD: English Bards and Scotch Reviewers. A pencilled
superscription. Listen and kiss my cycle-clips!
(He is carrying the book. He reads from it.) 'O harbinger of Sleep, who missed the press And hoped his drone might thus escape redress! The wretched Chater, bard of Eros' Couch, For his narcotic let my pencil vouch!'
You see,,y0w have to turn over every page. hannah: Is it his handwriting? Bernard: Oh, come on. hannah: Obviously not. Bernard: Christ, what do you want? hannah: Proof.
valentine: Quite right. Who are you talking about? Bernard: Proof? Proof? You'd have to be there, you silly bitch! valentine: (Mildly) I say, you're speaking of my fiancee. hannah: Especially when I have a present for you. Guess what I
found. (Producing the present for Bernard.) Lady Croom
writing from London to her husband. Her brother, Captain
Brice, married a Mrs Chater. In other words, one might
assume, a widow.
(BERNARD looks at the letter.) Bernard: I said he was dead. What year? 1810! Oh my God,
1810! Well done, Hannah! Are you going to tell me it's a
different Mrs Chater? hannah: Oh no. It's her all right. Note her Christian name. Bernard: Charity. Charity . . . 'Deny what cannot be proven for
Charity's sake!' hannah: Don't kiss me! valentine: She won't let anyone kiss her. BERNARD: You see! They wrote - they scribbled - they put it on
paper. It was their employment. Their diversion. Paper is
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what they had. And there'll be more. There is always more.
We can find it! hannah: Such passion. First Valentine, now you. It's moving. BERNARD: The aristocratic friend of the tutor-under the same
roof as the poor sod whose book he savaged - the first thing he
does is seduce Chater's wife. All is discovered. There is a duel.
Chater dead, Byron fled! P. s. guess what?, the widow married
her ladyship's brother! Do you honestly think no one wrote a
word? How could they not! It dropped from sight but we will
write it again! hannah: You can, Bernard. I'm not going to take any credit, I
haven't done anything.
(The same thought has clearly occurred to BERNARD. He becomes
instantly po-faced.) Bernard: Well, that's - very fair - generous -hannah: Prudent. Chater could have died of anything, anywhere.
(The pa-face is forgotten.) Bernard: But he fought a duel with Byron! hannah: You haven't established it was fought. You haven't
established it was Byron. For God's sake, Bernard, you
haven't established Byron was even here! Bernard: I'll tell you your problem. No guts. hannah: Really? Bernard: By which I mean a visceral belief in yourself. Gut
instinct. The part of you which doesn't reason. The certainty
for which there is no back-reference. Because time is reversed.
Tock, tick goe
s the universe and then recovers itself, but it
was enough, you were in there and you bloody know. valentine: Are you talking about Lord Byron, the poet? BERNARD: No, you fucking idiot, we're talking about Lord Byron
the chartered accountant. valentine: (Unoffended) Oh well, he was here all right, the poet.
(Silence.) hannah: How do you know? valentine: He's in the game book. I think he shot a hare. I read
through the whole lot once when I had mumps - some quite
interesting people -hannah: Where's the book?
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valentine: It's not one I'm using - too early, of course -
hannah: 1809.
valentine: They've always been in the commode. Ask Chloe. (HANNAH looks to BERNARD. BERNARD has been silent because he has been incapable of speech. He seems to have gone into a trance, in which only his mouth tries to work. HANNAH steps over to him and gives him a demure kiss on the cheek. It works. BERNARD lurches out into the garden and can be heard croaking for'Chloe... Chloe!9)
valentine: My mother's lent him her bicycle. Lending one's bicycle is a form of safe sex, possibly the safest there is. My mother is in a flutter about Bernard, and he's no fool. He gave her a first edition of Horace Walpole, and now she's lent him her bicycle.
(He gathers up the three items [the primer, the lesson book and the diagram] and puts them into the portfolio.) Can I keep these for a while?
hannah: Yes, of course.
(The piano stops. GUS enters hesitantly from the music room.)
valentine: (To gus) Yes, finished . .. coming now. (To hannah) I'm trying to work out the diagram. (GUS nods and smiles, at hannah too, but she is preoccupied.)
hannah: What I don't understand is . . . why nobody did this feedback thing before - it's not like relativity, you don't have to be Einstein.
valentine: You couldn't see to look before. The electronic calculator was what the telescope was for Galileo.
hannah: Calculator?
valentine: There wasn't enough time before. There weren't enough pencilsl (He flourishes Thomasina's lesson book.) This took her I don't know how many days and she hasn't scratched the paintwork. Now she'd only have to press a button, the same button over and over. Iteration. A few minutes. And what I've done in a couple of months, with only a pencil the calculations would take me the rest of my life to do again - thousands of pages - tens of thousands! And so boring!