‘Sorry. I, er—’
A tap on the door was followed by Hannah, one of the administrators, poking her head inside and saying, ‘Alex really needs you, Geoffrey, to sort out that budget thing.’
‘It’s all right,’ Gavriela said. ‘If that’s the meson data over there, why I don’t I just poke through it by myself?’
‘Oh. Yes, why not?’
She was supposed to be good at this, making sense of columnar figures, allowing patterns to emerge in her mind’s eye as easily as a collection of printed characters might be perceived as a movie actress wearing a bikini. But the office was warm and perhaps she was feeling her age, because she jerked her eyes open and realised she had been dozing. At least Geoffrey had not discovered her that way: luckily, his bureaucratic task seemed to be dragging on.
On an A4 pad she wrote, in pencil, some fragments of Fortran code that might group the data in more useful ways, so that the patterns she was unable to see might grow apparent. Why she thought there were patterns, she could not say. Geoffrey could piece the subroutines into a program on the PDP11, and if he spotted nothing in the output, perhaps she might wander in again next week and have another try.
‘Er . . .’
‘Hello, Geoffrey. I thought you’d been sucked into a bureaucratic hell for ever.’
Geoffrey’s expression was the same as when he spotted Gavriela looking at the printout on the back of the door. ‘I, um, sort of was. The thing is, some people think we’re falling behind King’s College – London, I mean – because they’re working on new stuff, on black holes.’
‘Seriously?’ said Gavriela. ‘You can’t mean that.’
The phenomenon might be allowed by general relativity, yet that did not mean such objects existed, any more than quarks, which to her mind were mathematical figments reflecting the choice of equations in the model, having little to do with what was really there. A meson might be a paired quark-plus-anti-quark, but it seemed unlikely.
‘Anyway,’ said Geoffrey, ‘I kind of volunteered to investigate the field. But that means . . .’
‘Abandoning this line of research. I understand.’ She looked at the stack of printed numbers, and her scribbled lines of Fortran. ‘Archive this where I can find it, Geoffrey, and I’ll come pootling along to browse when I’m able. No doubt I’m verging on senility, but when I pick up my Nobel Prize, I’ll mention you in my speech.’
‘You think I’ll be working on a flawed theory?’
‘I do.’
‘And didn’t Bohr win the Nobel for his pre-quantum atomic model?’
It predicted the energy spectrum of helium, hence the prize, but his theory was wholly inadequate to a proper understanding of the atom, and in a real sense was incorrect.
‘Good point,’ said Gavriela. ‘When you make the speech, maybe you can mention me.’
Geoffrey grinned at her.
‘More importantly,’ he said, ‘I hear they’ve got fresh doughnuts in the tea-room.’
‘You mean we’re wasting time talking about the nature of the universe when we could be doing something useful. Was that plain doughnuts or jam?’
‘Jam, of course. We’re not barbarians.’
There were little pings of arthritis when she stood.
‘I’ll race you,’ she lied.
Outside the college, she stood looking at the redbrick grandeur of the Royal Albert Hall, while music drifted from the Royal College of Music behind her, next to Imperial. She smiled and listened: it was the whimsical Bach piece that they used on the telly – dum, da-da-dum, da-da-dum, da-da-dum; da-da-da, da-dum, da-da-da, da-dum – as the countdown to educational programmes.
But some forty seconds in, the pleasantness was disturbed by a discordant intrusion – da, da-dum, da-da-da-dum, da-da – far off to her right. When she looked, a thin man might have just disappeared around the corner, or she might have imagined it. Her sense of being in the presence of darkness faded.
‘Are you all right, Dr Woods?’ It was Hannah from Admin, her hair freshly permed, with a silk headscarf to protect it. ‘You seem a little pale.’
‘Too many doughnuts,’ said Gavriela. ‘But I’m fine now, thank you.’
Nothing untoward happened on the journey home, and in the end she said nothing to Rupert about her possible brush with the darkness, because what could he have done about it?
That night, in her comfortable bedroom that felt so right, she knew as she was falling asleep that she was going to dream, vividly and in strong colours. Yet she encountered neither crystalline beings nor wolves and swords as she expected; instead, the world in which she found herself was constructed of mathematical metaphor, and in the middle of the dream she had the thought that Lewis Carroll would be proud.
Wonderfuler and wonderfuler, she decided.
Strolling across a meadow of integers, she laughs at the sight of matrices flying in V-formation above, then picks irrational chrysanthemums with florets arranged in infinite recursion, while a row of fractions watches, nudging each other and winking.
An infinity symbol comes bounding across the integers, then stops in front of her, bouncing up and down slowly, like a Lissajous figure trapped upon an oscilloscope screen.
‘I’m boundless,’ mutters the infinity.
An apparently identical infinity comes bounding into view.
‘So am I,’ it says. ‘Isn’t it obvious?’
She waits while they bounce in place.
‘You look bare and boundless to me,’ she says. ‘Has Möbius been stripping again?’
The infinities titter.
‘What will happen if you divide us?’ they say. ‘What will happen then? Can you tell, or do we need to swallow you up for all eternity?’
She clears her throat.
‘I can tell straight away,’ she tells them, ‘provided you answer me two questions.’
The infinities, still bouncing, angle inwards to look at each other, then face her once more.
‘Ask us,’ says the infinity on the left. ‘We’ll tell you the answer.’
‘Anything at all,’ says the infinity on the right. ‘Really anything.’
‘Or imaginary anything,’ says Left Infinity.
‘As complex as you like,’ says Right Infinity.
She lets out a breath, knowing that these two are rascals but bounded by their promise, if nothing else. All around, the meadow of integers stretches for ever, but you can tell that the infinities are different . . . though whether from each other, it is hard to tell.
‘If you were to twist yourselves into alephs,’ she asks thoughtfully, ‘what would your subscripts be?’
‘I say.’ That’s Left Infinity.
‘That’s a little personal.’ Right Infinity.
‘Do you want to stay bound by a promise for ever?’ she asks.
‘Oh, dear.’
‘Suppose not.’
They bounce a little more, then wriggle into knots, and re commence bouncing in their new forms.
‘Unity,’ she says.
‘We beg your pardon?’ they say together.
‘You’re both aleph nulls,’ she points out. ‘So you’ll divide to produce one, and it doesn’t matter which of you is on top.’ Which would have been her other question, of course.
‘Well . . .’
‘How risqué.’
‘Little people can be so rude.’
‘Can’t they just.’
She calls up: ‘I’m not little!’
But her voice is tiny because she is shrinking, with integers growing large around her. Already they are above her head, and the twin infinities are about to be obscured from sight, which seems hardly fair because she asked only one question.
‘You promised two answers!’
‘By George, she’s right.’
‘By Cantor, so are you.’
The integers are so very big, taller than trees and still growing.
‘What is—?’ She forces her voice to grow louder. ‘What’s the pattern in the numbers?’