Arcadia by Tom Stoppard Read Free Book Online Page B

She is reading aloud. He is
listening. Lightning, the tortoise, is on the table and is not readily distinguishable
fromPlautus. 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 mathematical notations, arrow marks, etc.; and Thomasina 9 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.
    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