The mathematician's patterns, like the painter's or the poet's, must be beautiful;
the ideas, like the colours or the words, must fit together in an harmonious way.
Beauty is the first test, there is no place in the world for ugly mathematics.
- G. H. Hardy, mathematician.
It is wintertime at Sidley Park, close to Christmas, and thus a few months since our last sightings of the Coverly families--in both eras. We begin in the present day. The room in which these scenes take place is identical to that featured previously, though we start with a relatively empty table in the centre of the room: only the tortoise, a plate of green leaves covered by a food umbrella, and a few paperbacks of modern philosophy, belonging (as we discover) to CHLOE COVERLY. A Christmas fir tree, undecorated, stands in one corner of the room.
CHLOE is standing on a chair by the french doors. There is a painting (Poussin's "Les bergers d'Arcadie") leaning against the wall; CHLOE has taken it down in order to peel at the wallpaper behind. HANNAH JARVIS and VALENTINE COVERLY come into the room, she carrying her coat, scarf, and two large folios, he carrying a tea tray.
HANNAH: Hello, Chloe. (She drapes her belongings over a chair and puts the folios on the table, moving Lightning the tortoise to make room, and tearing him a fresh piece of lettuce from the plate.)
CHLOE: (Turns, briefly.) Oh! Hello. You're back. He's been fed. (She doesn't sound very pleased.)
HANNAH: Lucky Lightning. Yes, it turns out I have one more chapter's material to research. Your mother found more of the Croom garden diaries. It's very kind of your family to be so accomodating to academics nosing around their libraries and follies.
CHLOE: Well, all the leaves have fallen. The park's completely bare now and we're all bored. Is that shortbread?
VALENTINE: Sorry, Chlo, the teapot's not big enough for three.
CHLOE: Typical. Trust you to choose the antique. (Looks meaningfully at Hannah) Mummy'll have a fit.
She pulls off a strip of wallpaper violently.
VALENTINE: You're the one vandalising the Regency-copy block prints. I think you should get down.
CHLOE: Rubbish. They're not right.
VALENTINE: There's nothing wrong with the walls! Get off the chair.
HANNAH: No, Chloe's right, they are wrong. It bothered me for weeks.
VALENTINE and CHLOE turn from their bickering to look at HANNAH, who is pouring the tea.
HANNAH: It's a post-Napoleonic purple. Well, it's mauve, to be exact. The Victorians went mad for lurid colours once they'd figured out the chemistry. Unfortunately they're all terribly unflattering to the pasty English complexion.
CHLOE: (More interested) That must be why all the best costume dramas are Austen and not Dickens.
VALENTINE: Chloe's reading Media Theory at Sussex.
CHLOE: Val, you're an arse. No one reads anymore. (To Hannah) I started my B.A. in September.
HANNAH: Good for you.
VALENTINE: (Dismissively) Redbrick.
CHLOE: (Irritated) Val!
HANNAH: Magnolia and chestnut are much kinder.
VALENTINE: But this is wallpaper. I thought you did gardens?
HANNAH: People in gardens. Promenades around the hedge maze. Liaisons in the summerhouse--oh. (She drinks her tea.)
CHLOE: I don't suppose you've heard from Bernard?
HANNAH: (Laughs) Hardly. You saw our exchange in the Times?
CHLOE: Oh, be like that then. (CHLOE turns back to the wallpaper. HANNAH and VALENTINE take their tea over to the window seat, where they sit.)
VALENTINE: You were terribly subtle.
HANNAH observes CHLOE for a moment before turning her attention to VALENTINE.
HANNAH: (Quietly) English departments are being sucked dry by Media Studies. Everyone wants to write a thesis on Eastenders.
VALENTINE: Did you know Reading closed its Physics department due to lack of interest? No-one's interested in the fundamentals of the universe anymore, it's all brand advancement strategies and book deals. I did mean your letter about Byron and whatnot. Dahlias.
HANNAH: Not too opaque, I hope?
VALENTINE: I had to read it over to make sure I didn't miss the implication. I'd become rather more accustomed to you calling Bernard a wanker.
HANNAH: But that's the game! It would be extremely poor form to come right out and say nyah nyah nyah.
VALENTINE: Nature has a special section for clarifications and corrections.
HANNAH: (Bemused) Well. Mutation must drive our evolution. But it's not an aspiration for literary scholars.
VALENTINE: No, no, the journal, Nature. There's no dishonour in being incorrect. Science expects it.
HANNAH: It's a right jolly nuisance if you have to rely on force of personality to convince everyone you're right. Or how big your prick is.
CHLOE makes a disapproving sound but doesn't turn.
VALENTINE: Chloe thinks it's all dreadfully unfair and that everyone's viewpoint is valid and worth considering.
CHLOE: Situated! Contextual! (She steps down off the chair and we can see an area of wall different to the rest has been revealed.) You don't acknowledge where it is that you're speaking from so you can't be expected to appreciate your own biases.
HANNAH: (To VALENTINE) A budding relativist?
VALENTINE: Who's the philosopher you're reading, Chloe? Derrida?
CHLOE: (Sorting through her pile of books) We did him before half-term. Now it's Deleuze.
HANNAH: Post-structuralism already?
CHLOE: Yes, it's amazing.
HANNAH: Amazing is one word for it.
CHLOE looks sharply at HANNAH and VALENTINE. HANNAH is poker-faced. VALENTINE has switched off and is looking at the exposed area of the wall.
CHLOE: Where's Gus? I want him to help me move the other painting.
CHLOE frowns and leaves, calling for her brother. HANNAH goes to the table and looks through the books CHLOE has left.
HANNAH: Continental philosophy is its own very special brand of teenage rebellion.
VALENTINE: (Morosely) I'd rather she'd taken up crack cocaine. I think it'd do less long-term damage to her brain. In the summer she was reading PD James and now it's a constant stream of tripe by the--these obscurantist idiots who borrow terms from mathematics--beautiful, simple mathematics, raped and pillaged by such total frauds--and she thinks it's telling her something utterly profound about human nature.
HANNAH: You shouldn't rule out the possibility just because you go about things differently.
VALENTINE: Properly. With an hypothesis and a test!
HANNAH: There's great utility in theory!
VALENTINE: You know as well as I do that the only ideas worth a jot are derived empirically. Reasoning from flaky analogy won't contribute to the sum total of human knowledge. It just keeps people from working in marketing.
HANNAH: I almost wish the dogmatic Nightingale was here for this. You're not really saying that the sciences should have a stranglehold on knowledge?
VALENTINE: No, I'm just--
HANNAH: Sectarianism is tedious and it made you cry, if I remember rightly.
VALENTINE: Hannah! Science--starting from mathematics, up to its pinnacle in biology, (He laughs) no, you know it's true--
HANNAH: (Holds up her hands) Oh no, I'm having no part in it.
VALENTINE: And the arts. The ones where people create things.
HANNAH: So what about politics? Economics?
VALENTINE: If there was a desperate need, that could just be history with some predictive statistics.
VALENTINE: (On a roll) Again, history. Lawyers are glorified librarians. They just look things up.
HANNAH: I shall tell that to my solicitor when I want a mortgage. But Val. There's a great deal of psychology when one considers the social functions of law.
VALENTINE: Psychology is just biology writ large. It's organismal ecology with allowances for theory of mind and cultural inheritance. There's no need for any new ologies. (Scoffing) Social science, please.
HANNAH: And so what happened to chaos and contingency?
VALENTINE: (Darkly) Parasites.
The same room, in 1811. The only difference is that the wall which CHLOE was stripping free of wallpaper is now plain cream, and without any paintings hung upon. SEPTIMUS HODGE is sitting at the table folding a paper chain. Occasionally he stops to cut a new strip out of the newspaper in front of him, and adds it to the ever-lengthening chain. He is tapping his foot to the sounds of the piano--an innocuous folk song bearing some resemblance to Once in Royal David's City--coming through from the music room.
THOMASINA COVERLY (now 16) comes into the room holding a plate containing two oranges. She is followed by JELLABY, the butler, who is carrying a large basket of pine cones and trying not to sneeze.
SEPTIMUS: (Suprised) My lady! I thought you were a-wassailing all this afternoon.
THOMASINA: My brother did not care to walk out and sing! He has said he is a man now and cannot make the high part. We shall never have harmony again.
SEPTIMUS: I would venture to say that you perhaps never did.
THOMASINA: Do they teach the arts of sororal distress alongside Homer and Lavoisier at Eton? You are very right, though perhaps you should not say so. Augustus is quite intolerable.
SEPTIMUS: I refer only to music.
THOMASINA: I do not.
THOMASINA places the plate of oranges on the table. Plautus the tortoise starts to walk towards the fruit; THOMASINA redirects him with a lettuce leaf.
SEPTIMUS: Jellaby, has the lady of the house converted us all to some new form of conifer subsistence?
He nods at the basket of pine cones, still folding the paper chain.
SEPTIMUS: I have become accustomed to tea at a quarter to four. Are pine cones the fashion now, rather than fine scones?
THOMASINA laughs at the attempted rhyme.
JELLABY: Lady Croom means for their construction as a Christmas centerpiece for your table, Sir.
THOMASINA: (Disgusted) Mama sent me into the garden to gather them like a squirrel. Just put them on the table, Jellaby, I shall pile them haphazard in the Romantic fashion once we have done our lessons.
JELLABY puts the basket on the table with a patient air. He takes up the empty tray and teapot left by VALENTINE and HANNAH.
JELLABY: Tea, my lady, Mr Hodge?
SEPTIMUS: We are creatures of habit. Please.
JELLABY leaves. The music stops.
SEPTIMUS: (To the basket) My schoolroom table needs no decoration beyond the fruits and seeds of thought.
THOMASINA: I have brought you an orange, Septimus, do not be cross. You may either eat it or I shall preserve it for your wardrobe.
SEPTIMUS: Am I so fortunate as to choose my own Christmas gift?
THOMASINA: Mama wishes me to demonstrate I have learned not only Pythagorus this year. She would prefer I embroider you a case for your eye-glasses but you would only use it for an ink-blotter. I shall approximate the golden ratio with cloves stuck in your orange instead; that will be a happy medium of art and science.
SEPTIMUS: She cannot object to such a project.
THOMASINA: She will, though she should not. It will be my excuse to have the Jerusalem artichokes as a reference rather than be made to eat them. We may share the other orange. Will you peel it for me?
SEPTIMUS holds up his arms, around which are draped lengths of paper chain.
SEPTIMUS: I am twelve foot in chains of your making already.
THOMASINA: (Looking at the bare Christmas tree.) Oh! I did not mean for you to make such a great deal while I was gone.
SEPTIMUS: You were out hoarding for winter. We have been industrious. (He tears a final strip off the newspaper.)
THOMASINA: Is that the Times?
SEPTIMUS: No! I would not make baubles from such erudite reviews of literature. It is your mother's Gazette. From Thursday.
THOMASINA: So we are hanging our tree with royal proclamations and engagements!
SEPTIMUS: And bankcruptcy and war.
THOMASINA: (Thinking) All the world's affairs.
SEPTIMUS: (Quietly, collecting the paper chain into a neat pile.) You are very pensive. I suggest Hegel as a remedy.
SEPTIMUS slides one of CHLOE's philosophy textbooks over the table. THOMASINA hands him the orange which he proceeds to peel carefully, taking all the peel off in a single piece. THOMASINA flicks through the book.
THOMASINA: I would rather Bernoulli or Fibonacci.
She sits at the table, opening one of the folios that HANNAH brought into the room. Inside, the sheets are ruled in tables, and they are densely filled with numbers.
SEPTIMUS (Offhand) I have been continuing with your rabbit equation in idle moments.
THOMASINA: (Delighted) Septimus! Is this meant to be my Christmas gift?
SEPTIMUS: Hush! That is a scandalous thing for a young lady to suggest.
THOMASINA: (Leafing through the pages) There are hundreds of figures.
SEPTIMUS: And they are all different. (He looks over the table at the folio, passing THOMASINA a piece of orange.) I shall leave it to you to plot them, Cartesian-style. You may intimate to your mother that you are planning a pattern for lacework.
THOMASINA: (Gloomily) We do not have a sheet of paper large enough.
She plays with her pencil and eats pieces of the orange, absently staring at the wall. JELLABY enters, carrying the tea tray, which he sets down on the table after nudging Plautus aside.
JELLABY: Will that be all?
THOMASINA: (Suddenly) Oh! Of course we do!
THOMASINA takes her pencil and the first sheet from the folio, and crosses the room to stand on the chair that CHLOE had previously stood on.
SEPTIMUS: (To JELLABY) One moment. (To THOMASINA) My lady?
THOMASINA: (Drawing lines of a grid across the wall) Here is our imperfect Cartesian surface.
SEPTIMUS: I am sure Lady Croom referred to it as magnolia, newly painted. Please step down.
THOMASINA: Oh no, I am quite safe.
SEPTIMUS: Jellaby, if you would be so good as to stay. Perhaps ... by the door.
SEPTIMUS crosses to stand beside THOMASINA, holding out his hand as if to offer assistance from a carriage.
SEPTIMUS: I did not mean my tables to encourage such vandalism. We shall apply to the butcher for lengths of paper. Come down now.
THOMASINA: No, no. My Uncle Brice has sent back rubber from India that will take the marks off when we are done. (She stands on her toes, leaning on Septimus's shoulder.) You shall need to draw the lines where I am not tall enough.
SEPTIMUS: (Mock-defeat) You have the only pencil in the room.
THOMASINA: Then you shall read out each pair of numbers and I shall place a mark at each junction. Jellaby shall hang the tree with your paper chain of the world's accomplishments, and we shall see what secrets become revealed.
THOMASINA, SEPTIMUS and JELLABY do not leave the room but remain, carrying out their tasks quietly in the background: JELLABY trimming the Christmas tree, and THOMASINA plotting coordinates on her grid according to SEPTIMUS's instructions. At some point JELLABY leaves, and THOMASINA and SEPTIMUS switch roles. A fern-frond pattern begins to emerge from the numbers produced by Thomasina's equation.
The present day.
HANNAH: So I take it your grouse weren't part of an iterative equation in the end?
VALENTINE: It's all very seductive, this chaos thing, patterns within patterns. Californian dinner parties thrive on it. Everyone who's everyone in system dynamics is at the Santa Fe Institute. Chartered flights to Oslo to pick up the Nobel, that sort of thing. But it's ultimately a dead-end. It doesn't tell you anything new about ecology. Just gives a pithy description to the indescribable. Sells popular science books.
HANNAH: You are bitter. Who was the parasite? Did you get scooped?
VALENTINE: No, not really. (Pause) You could say chaos was the parasite. Itchy little bloodsucker of an idea, hitchhiking along proper biology--you know, useful science--using up one's valuable resources.
HANNAH: You don't believe it?
VALENTINE: There's nothing to believe. It's all interpretive, like Chloe's post-structuralism. It's just not useful. Might as well have been your hermit, stuck out in the park scaring small children with his long fingernails and integrative calculus. That was the one thing Bernard was right about.
HANNAH: Oh, I missed you just a little bit, Val. (She smiles.)
VALENTINE: (Laughs) So what was the upshot of it all? Bernard. There was no Radio 4 follow-up for us not in literary circles.
HANNAH: The good stuff happens at conferences, of course. He'd submitted a paper and had to retract it at the last minute--literally last minute, after the program was printed. Flyers posted in the foyer: "Cancelled - Dr Nightingale's plenary on Byron: Backstabbing, Bad Reviews and Bloodsport".
VALENTINE: Oh, how awful.
HANNAH: His department passed him over for Chair, too. Hung out to dry like the sheets on your washing line.
HANNAH nods in the direction of the garden visible through the french doors. There is a silence, during which both of them try not to smile or laugh, but are not completely successful.
VALENTINE: (Perhaps tactfully trying to steer the conversation elsewhere) I nearly had a mental breakdown in a laundromat.
HANNAH: Hmmm? Oh, washing. Are we still on parasites?
We again hear music from the adjoining room, a ragtime jazz version of Christmas carols.
HANNAH: Is that Gus?
VALENTINE: Yes. He's the brilliant one in the family.
HANNAH: (Fondly) Yes.
VALENTINE: I'll get to the parasites, I promise. I was watching the towels go around and around in the dryer. This was when I was an undergraduate. The halls of residence at my college were so rubbish the laundry room was always flooded. So in winter we had to traipse off to the laundromat.
HANNAH: (Snorts) I can see how that would cause you great distress.
VALENTINE: Now it's you that's being the class snob.
HANNAH: Did you actually ever go near a household appliance before you left for university?
VALENTINE: I did--
HANNAH: Television and hi-fi doesn't count.
VALENTINE: Yes! The microwave.
HANNAH: It's mostly a gender issue, I imagine, anyhow.
VALENTINE: (Grumbles, crossing his arms) Why can't you people say sex when you mean sex?
HANNAH: I only say sex when I'm having my picture taken. Like cheese, only not as manic.
VALENTINE: Prude. (He doesn't mean it.)
HANNAH: So what was your breakdown about?
VALENTINE: I had this one green towel. Everything else was grey or blue. I kept watching the way it circled around inside the drum, but I could never predict just when it would fall from its arc.
He draws circles in the air to demonstrate the motion of the tumble dryer.
HANNAH looks very serious and thoughtful. She is looking at the patch of wall where SEPTIMUS and THOMASINA have plotted out the pattern from the "rabbit equation". It has taken the shape of a coiled fern. While VALENTINE continues his story, SEPTIMUS files the folio page back in the covers.
SEPTIMUS: You may continue your plotting tomorrow. I shall find a suitable piece of artwork to conceal your efforts so far. (He leaves the room.)
HANNAH: I am paying attention, sorry. You must admit this is an odd story.
THOMASINA piles the pine cones on the plate, stacking them neatly in a tower. She pulls a ribbon from her hair and ties it around the top cone.
VALENTINE: I got quite obsessed with the thing. I started taking my laptop into the laundromat. That's not such a smart thing to do in the dodgy bit of the Cowley Road. But I wanted to work it out. I thought perhaps I would write to the manufacturers with what I'd found, but the woman who gave out the change and soap wouldn't let me have an address.
HANNAH: Val, most of us read Hello or think about what we'll have for tea if we're sat watching the dryer. Try not to make eye-contact with anyone else. She probably thought you were on something.
VALENTINE: (Somewhat exasperated) Oh, how very pragmatic of you.
SEPTIMUS comes back in, carrying the Poussin painting. He props it on the chair, but it hardly covers the fern pattern. He looks, suppressing laughter, at THOMASINA, who shrugs merrily back. He puts the painting on the floor and they both sit at the table to read.
HANNAH: Pragmatism isn't a bad thing. (She stands, brushing crumbs off her trousers.)
VALENTINE: (Hurriedly) No. Sorry, sorry, no, I didn't mean it to sound like that. Sit down. It's a virtue really. We should all aspire to it. It's just that, well. You'd get the leeway, wouldn't you?
HANNAH: Asking questions in a laundromat?
VALENTINE: No! Bollocks. No--
VALENTINE: Hannah, I'm rubbish today, I'm sorry. I'd blame Chloe but that's just lazy. No. I mean, as an author. An historian. If you were scribbling poetry in a desperate-looking notebook, wearing an interesting scarf. I had a laptop and probably some mustard on my shirt collar. And I was incoherent about an equation. I'm not very good with communicating.
HANNAH: Yes, yes, you're positively atrocious!
VALENTINE: Don't tease. I don't teach, you know. Just research. I'm alright at conferences, when I can just reassure myself that everyone speaks the jargon and knows what I'm on about. I don't have a clue about explaining things without being a patronising bore. Best not to.
HANNAH: And now you've really lost me. A green towel, a nervous breakdown, no students ... and mustard? (She's properly teasing VALENTINE now.)
VALENTINE: It was--it was a tractable problem. Something that I could solve. If I could work it out, we would know something that we didn't before. I don't know. It seemed so very important at the time.
HANNAH: It was just a blow to your ego. Like all of this business.
She waves her hand at the room, the folios, and at SEPTIMUS and THOMASINA, who are leaving. The ragtime music stops, but the piano soon starts again as 19th century carols.)
HANNAH: We simply all want to be correct, no matter what our discipline. I'm back here to look at these interminable diaries, these pages upon pages of numbers, because I want to be correct about the version of events I tell.
VALENTINE: But I don't care about it being me that solved the problem. It's getting the problem solved at all.
HANNAH: Bollocks. Academics don't make natural cogs in the system, Val. Ego drives us just as much as politicians.
VALENTINE: But it's not the only thing. We have ... nobler goals. (He's laughing at himself now.) Less tea and more festive sherry required, I think. But you must agree that our goals are Facts. Capital F. Even you.
VALENTINE: You're more of an empiricist than a theorist anyhow.
HANNAH: That's your highest form of compliment.
VALENTINE: I did ask you to marry me.
HANNAH: Well. That's factually incorrect. You asked me to be your fiancee.
VALENTINE: Ah. Back to parasites. On that issue I shall have to publish a retraction.
HANNAH: (Bemused) Oh?
VALENTINE: Will you ever forgive me? Tell a fib and say I've broken your heart for evermore.
HANNAH: I'm crushed, Valentine, you're as fickle as your namesake--what were your parents thinking?
VALENTINE: Tradition, I think it's in Burke's ...
VALENTINE trails off. He looks properly at THOMASINA's drawing on the wall, frowning slightly.
HANNAH: InsistentlyBut what about parasites?
CHLOE comes back in with GUS, who smiles broadly at HANNAH.
HANNAH: Hello, Gus. Wonderful music.
CHLOE: Valentine's seeing a bug lady.
CHLOE and GUS set to work taking down another painting, this time one over the fireplace. It is awkward and takes them some time.
VALENTINE: I met a parasitologist. Conferences, like you said, it's where the good stuff happens. I was talking about my chaos model and the grouse. "Lagopus lagopus population levels demonstrated by random but patterned chaotic cycling."
VALENTINE: Accurate. Or not, as it turns out. She put up her hand and told me she had a paper coming out the next week demonstrating that it was all caused by parasites. Nematode worms, revolting little creatures. It made perfect sense. Terribly elegant experiments, too. I was quite beside myself.
HANNAH: I'm amazed you spoke to her after that.
VALENTINE: Oh no, we had plenty to discuss. Field studies, genetics ... much more exciting than oscillating peaks on a laptop. We're collaborating now.
CHLOE: (Snickers) We call it shagging.
HANNAH: I'm very happy for you. Scientifically and romatically.
VALENTINE: (Pleased) Thank you.
They both consider the fern while GUS and CHLOE take down the picture.
VALENTINE: The resemblance is remarkable.
HANNAH: It can't be anything but the girl and her tutor.
VALENTINE: I'll look through that folio with you. I never thought that's what the tables could be.
HANNAH: I'd just thought them random numbers. Chaos, I suppose.
VALENTINE: It's much more beautiful, hand-drawn.
CHLOE: (Scraping away above the matelpiece) I have no idea what you two are on about, but I've got a friend who works at Laura Ashley.
VALENTINE: See if they'll call it the Coverly Pattern.
HANNAH: (Surprised) That's not too trivial for you?
VALENTINE: You write books. I publish papers. We could give Thomasina's equation a bigger audience through Homes and Gardens than any citation index would measure.
HANNAH: I think this is called outreach activity. How modern we are.
HANNAH and VALENTINE sit at the table, slowly going through the folio, while CHLOE keeps to her task, and GUS is heard playing in the background.
Written for Yuletide 2007, here, in a version with an embarrassing large number of formatting errors and a rubbish title, doh. The title is from Aristotle ("All men by nature desire to know").