Arcadia

The procession is very long and life is very short. We die on the march. But there 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.

  Ancient cures for diseases will reveal themselves once more. Mathematical

  discoveries glimpsed and lost to view will have their time again. You do not

  suppose, my lady, that if all of Archimedes had been hiding in the great library of

  Alexandria, we would be at a loss for a corkscrew? I have no doubt that the

  improved steam-driven heat-engine which puts Mr Noakes into an ecstasy that he

  and it and the modern age should all coincide,

  38

  was described on papyrus. Steam and brass were not invented in Glasgow. Now,

  where are we? Let me see if I can attempt a free translation for you. At Harrow I

  was better at this than Lord Byron. He takes the piece of paper from her and

  scrutinizes it, testing one or two Latin phrases speculatively before committing

  himself.) Yes - 'The barge she sat in, like a burnished throne... burned on the

  water... the - something - the poop was beaten gold, purple the sails, and - what's

  this? - oh yes, - so perfumed that -

  Thomasina: (Catching on and furious) Cheat!

  Septimus: (Imperturbably)'- the winds were lovesick with them. ..'

  Thomasina: Cheat!

  Septimus: '... the oars were silver which to the tune of flutes kept stroke...'

  Thomasina: (Jumping to her heels) Cheat! Cheat! Cheat!

  Septimus: (As though it were too easy to make the effort worthwhile) >'... and made the water which they beat to follow faster, as amorous of their strokes. For her own person, it beggared all description - she did lie in her pavilion -'

  Thomasina, in tears of rage, is hurrying out through the garden.)

  Thomasina: I hope you die!

  (She nearly bumps into Brice, who is entering. She runs out of sight, Brice enters.)

  Brice: Good God, man, what have you told her?

  Septimus: Told her? Told her what?

  Brice: Hodge!

  (Septimus looks outside the door, slightly contrite about Thomasina, and sees that

  Chater is skulking out of view.)

  Septimus: Chater! My dear fellow! Don't hang back-come in, sir!

  Chater allows himself to be drawn sheepishly into the room, where Brice stands on

  his dignity.)

  Chater: Captain Brice does me the honour- I mean to say, sir, whatever you have to

  say to me, sir, address yourself to Captain Brice.

  39

  Septimus: How unusual. (To Brice) Your wife did not appear yesterday, sir. I trust

  she is not sick?

  Brice: My wife? I have no wife. What the devil do you mean, sir?

  (Septimus makes to reply, but hesitates, puzzled. He turns back to Chater.)

  Septimus: I do not understand the scheme, Chater. Whom do I address when I want to speak to Captain Brice?

  Brice: Oh, slippery, Hodge - slippery!

  Septimus: (To Chater) By the way, Chater - (he interrupts himself and turns back to Brice, and continues as before) by the way, Chater, I have amazing news to tell

  you. Someone has taken to writing wild and whirling letters in your name. I

  received one not half an hour ago.

  Brice: (Angrily) Mr Hodge! Look to your honour, sir! If you cannot attend to me

  without this foolery, nominate your second who might settle the business as

  between gentlemen. No doubt your friend Byron would do you the

  service. (Septimus gives up the game.)

  Septimus: Oh yes, he would do me the service. (His mood changes, he turns to

  Chater.) Sir -I repent your injury. You are an honest fellow with no more malice in you than poetry.

  Chater: (Happily) Ah well! - that is more like the thing! (Overtaken by doubt.) Is he apologizing?

  Brice: There is still the injury to his conjugal property, Mrs Chater's-

  Chater: Tush, sir!

  Brice: As you will - her tush. Nevertheless -

  (But they are interrupted by Lady Croom, also entering from the garden.)

  Lady Croom: Oh - excellently found! Mr Chater, this will please you very much.

  Lord Byron begs a copy of your new book. He dies to read it and intends to include

  your name in the second edition of his English Bards and Scotch Reviewers.

  Chater: English Bards and Scotch Reviewers, your ladyship, is a doggerel aimed at

  Lord Byron's seniors and betters. If he intends to include me, he intends to insult

  me.

  Lady Croom: Well, of course he does, Mr Chater. Would you rather be thought not

  worth insulting? You should be proud

  40

  to be in the company of Rogers and Moore and Wordsworth -ah! The Couch of

  Eros!' (For she has spotted Septimus's copy of the book on the table.)

  Septimus: That is my copy, madam.

  Lady Croom: So much the better - what are a friend's books for if not to be

  borrowed? (Note: 'The Couch of Eros' now contains the three letters, and it must do

  so without advertising the fact. This is why the volume has been described as a

  substantial quarto.) Mr Hodge, you must speak to your friend and put him out of his

  affectation of pretending to quit us. I will not have it. He says he is determined on

  the Malta packet sailing out of Falmouth! His head is full of Lisbon and Lesbos,

  and his portmanteau of pistols, and I have told him it is not to be thought of. The

  whole of Europe is in a Napoleonic fit, all the best ruins will be closed, the roads

  entirely occupied with the movement of armies, the lodgings turned to billets and

  the fashion for godless republicanism not yet arrived at its natural reversion. He

  says his aim is poetry. One does not aim at poetry with pistols. At poets, perhaps. I

  charge you to take command of his pistols, Mr Hodge! He is not safe with them.

  His lameness, he confessed to me, is entirely the result of his habit from boyhood

  of shooting himself in the foot. What is that noise?

  (The noise is a badly played piano in the next room. It has been going on for some

  time since Thomasina left.)

  Septimus: The new Broadwood pianoforte, madam. Our music lessons are at an

  early stage.

  Lady Croom: Well, restrict your lessons to the piano side of the instrument and let her loose on the forte when she has learned something. (Lady Croom, holding the book, sails out back into the garden.)

  Brice: Now! If that was not God speaking through Lady Croom, he never spoke

  through anyone!

  Chater: (Awed) Take command of Lord Byron's pistols!

  Brice: You hear Mr Chater, sir - how will you answer him?

  (Septimus has been watching Lady Croom's progress up the garden. He turns

  back.)

  41

  Septimus: By killing him. I am tired of him.

  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: Yo
u lie, or you will answer to me!

  Septimus: (Wearily) Oh, very well -I 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.)

  42

  SCENE FOUR

  Hannah and Valentine. She is reading aloud. He is listening. Lightning, the

  tortoise, is on the table and is not readily distinguishable from Plautus. In front of

  Valentine 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 mathemati cal notations, arrow

  marks, etc.; and Thomasina' 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.

  43

  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

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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 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 offish. It's about the

  behaviour of numbers. This thing works for any phenomenon which eats its own

  numbers -

  45

  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 unfortu
nately 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?

  46

  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!