Arcadia (7 page)

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.

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 andy.

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.Theny
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—

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
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 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 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.

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 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.