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 mathematical 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.

HAN:  '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 VAL the text book.  VAL 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?

VAL:  I don't know.  I don't know what it means, except mathematically.

HAN:  I meant mathematically.

VAL: (Now with the lesson book again)  It's an iterated algorithm.

HAN:  What's that?

VAL:  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 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.

HAN:  Is it difficult?

VAL:  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 thata few times you join up the dots and that's your graph of whatever the equation is.

HAN:  And is that what she's doing?

VAL:  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.

HAN:  And that's surprising, is it?

VAL:  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)

HAN:  Why would she be doing it?

VAL:  I have no idea.

(Pause)

I thought you were doing the hermit.

HAN:  I am.  I still am.  But Bernard, damn him....Thomasina's tutor turns out to have interesting connections.  Bernard's going through the library like a bloodhound.  The portfolio was in a cupboard.

VAL:  There's a lot of stuff around.  Gus loves going through it.  No old masters or anything....

HAN:  The maths primer she was using belonged to him - the tutor; he wrote his name in it.

VAL: (Reading)  'Septimus Hodge.'

HAN:  Why were these things saved, do you think?

VAL:  Why should there be a reason?

HAN:  And the diagram, what's it of?

VAL:  How would I know?

HAN:  Why are you cross?

VAL:  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.

HAN:  This feedback thing?

VAL:  For example.

HAN:  Well, could Thomasina have -

VAL: (Snaps)  No, of course she bloody couldn't!

HAN:  All right, you're not cross.  What did you mean you were doing the same thing as she was doing?  (Pause.)  What are you doing?

VAL:  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.

HAN:  What for?

VAL:  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.

HAN:  It can't be the same every year.

VAL:  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.

HAN:  The goldfish are?

VAL:  Yes.  No.  The numbers.  It's not about the behaviour of fish.  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.

HAN:  Does it work for grouse?

VAL:  I don't know yet.  I mean, it does undoubtedly, but it's hard to show.  There's more noise with grouse.

HAN:  Noise?

VAL:  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 - I mean, the noise!  Impossible!

HAN:  What do you do?

VAL:  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!

HAN: (Soberly.)  Yes, I see.  And then what?

VAL:  I publish.

HAN:  Of course.  Sorry.  Jolly good.

VAL:  That's the theory.  Grouse are bastards compared to goldfish.

HAN:  Why did you chose them?

VAL:  The game books.  My true inheritance.  Two hundred years of real data on a plate.

HAN:  Somebody wrote down everything that's shot?

VAL:  Well, that's what a game book is.  I'm only using from 1870, when butts and beaters came in.

HAN:  You mean the game books go back to Thomasina's time?