‘Dartmouth, eh?’ Gavin says. ‘Well, we’ll be going there soon, and you can visit some of your old haunts. Right. Now, so I can just get acquainted with what these people know, do the rest of you want to take a break for half an hour or so? See you back here at, say, 10:45?’
I notice that not one of the experienced sailors has followed instructions and talked about their strengths and weaknesses. No one does that voluntarily: you have to really interrogate people to get that kind of information out of them.
* * *
Esther and I fall into step and walk outside into the sunshine.
‘I’m scared of drowning and stuff,’ she says.
‘Yeah, me too.’
We lie down on the grass and start smoking. Ben and Hiro seem to be coming in our direction and Esther waves at them to come and sit with us. ‘That guy was looking for you yesterday, by the way,’ she says to me. ‘Did he find you?’
‘Yeah, thanks,’ I say.
Hiro flops down next to me. ‘Hi,’ he says. ‘How’s it going?’
‘We were saying that we are scared of drowning,’ I say.
‘Nah, there’s no water around here. This is all going to be theory, I reckon.’
Ben has sat down too. He is cleaning his glasses on the edge of his shirt.
‘What do you do? At PopCo, I mean?’ I ask Hiro.
‘Computer admin,’ he says quickly.
‘Oh, Esther does that too,’ I say. ‘Don’t you, Esther?’
She gives me a funny look. ‘Yeah,’ she says.
Esther and Hiro are fizzing now; something’s going on. They’re sitting still but yet they seem as if they are dancing around each other like spinning quantum particles. And suddenly they’re not looking at each other. Why? What did Mac want to see them both about on Saturday night? Maybe the computer admin staff needed some sort of special dispensation to come here. But I am fairly sure Esther doesn’t work in computer admin. Otherwise, surely she would have told me the other day in the gazebo, instead of saying that she couldn’t tell me what she did.
‘I can’t even bloody swim apart from the doggy paddle,’ Esther says, breaking the unnatural silence. ‘And a stupid head-in-the-air kind of breast-stroke.’ She mimes what she means and we all laugh.
‘I think we’ll have life-jackets,’ says Ben.
‘I love the phrase “breast-stroke”,’ says Hiro.
I lie on the grass, smoking my cigarette, listening to Esther, Hiro and, to a lesser extent, Ben, finish the sailing conversation and start chatting about clubs that play guitar music and where you can get dope around here. I have caught Ben’s eye only once and we have exchanged a half-smile. Now, mixed in with birdsong and the chatter of my colleagues, I can faintly pick out the noise of children playing: the Kid Lab sounds I first heard last week. Where do the kids go? I haven’t even seen one child in the time I have been here so far.
The Great Hall is cool and echoey despite the escalating heat outside. Once inside, we are quickly divided into our sailing ‘teams’, according to what seems to be some strange mathematical function in Gavin’s head. Some people have been split apart from friends and jumbled up but Esther and I are both assigned Dan as our team leader, while Hiro and Ben are put with Chloë. Our team also includes Grace from robotics, while Chloë’s team has Richard, her boss.
After an introductory lesson on ‘Parts of the Boat’, each team is assigned a half-hour slot to play around on the training yacht with Gavin and their particular skipper. Our slot isn’t until half-past four, so, after lunch, Dan, Esther, Grace and I get the chefs to make us big flasks of tea and we climb up to the hill fort to clear our heads. It’s already a hot day and I have my cardigan tied around my waist.
‘So how come you specialise in AI?’ Dan asks Grace, once we are settled among the old stones with our tea. ‘Did you have experience before you joined PopCo?’
‘Yeah, I worked on an Internet project after university.’
‘What was it?’ I ask.
Grace pushes some black, crimped hair out of her eye. ‘It was this chat-room programme,’ she says. ‘Designed to mimic real conversation. We programmed in responses to typical statements, and “taught” the programme how to respond to various types of conversation. If the human chat partner ended a statement with an exclamation mark, for example, the bot would say, “Really?” It didn’t work that well, although research is still going on in that area.’ She sounds a bit jaded by it all.
‘Weren’t you that into it?’ Esther asks.
‘It was all right.’ Grace frowns. ‘I did always want to work in mechanical robotics, though. It’s what I specialised in at university. There are so many exciting things going on in robotics. I mean, it’s such a young area. No one even knows how to get a bot to walk on two legs yet.’
‘Really?’ Dan says, sounding surprised.
‘Yeah. Well, have you ever seen a fully functional two-legged robot?’
‘I’m sure I have,’ Dan says. ‘Don’t they have them on all those Science Channel programmes about Japanese inventions? I’m sure I’ve seen two-legged robots.’
‘Yeah, but have you ever seen the way they move? You can’t get them to navigate any sort of three-dimensional terrain; they just fall over. Getting a robot to navigate its way across a flat surface takes more programming than you’d imagine. It would take millions of neural processes for your brain to get your body to climb over one of these rocks. Trying to replicate those processes in a robot is pretty impossible. It makes you wonder about GM food …’
‘GM food?’ Dan says. ‘What’s that got to do with it?’
‘We have had various forms of robotics much longer than we have had gene technology,’ Grace explains. ‘And we can’t even make something walk on two legs. When you work in something like robotics – and I have heard biologists say this too – you start thinking all sorts of things about nature, and about whether living creatures were designed or not. It’s easy for normal people to forget just how complex creatures and plants are. When you think about all the billions of things a biological organism can do at the same time as walking on two legs, such as think, sweat, talk, menstruate and so on, you realise that its design is something so far beyond our understanding. We couldn’t make anything that complicated, or a hundredth as complicated, or a thousandth as complicated … How anyone thinks they can splice genes in and out of different species and actually improve on nature is just absurd, you know? It’s like breaking something you can’t fix. It’s a one-way function, if you know what that is …?’
I am nodding. ‘Yeah,’ I say.
‘What is it?’ asks Dan.
‘In maths, it is a function that only goes one way,’ I explain. ‘It is sometimes called a “trap door function” as well. The idea is that, like falling into a trap door, it is something that is easy to do but hard to get out of. You can feed a number into a one-way function and get a result, but, for whatever reason, you can’t easily take the result, feed that into anything and get the number you started with. So the function works one way.’
He looks blank. I am not explaining it very well.
‘It’s like, if I take the function x+5, and say the result equals y, I can always find x again by taking 5 away from y. But many one-way functions are so complicated, or lead to numbers so big, that you simply can’t unravel them. It’s the mathematical equivalent of mixing paint. If I have a tin of blue paint and a tin of yellow paint and I mix them, I will get two tins of green paint. Once I have that green paint, there’s no way of getting the tin of blue paint back again. You can’t un-mix paint.’
‘That’s it exactly,’ Grace says. ‘With GM technology, you could mess around mixing up genetic equivalents of the blue paint and yellow paint not even realising that you’d never be able to get those paints back again. We already see super weeds, resistant to any kind of herbicide or predator – they already exist. You can’t undo the spread of mutation once it’s there. It’s terrifying. Don’t even get me started on nanotechnolog
y …’
‘I heard that some of the bio-tech companies have made plants with no seeds,’ Esther says. ‘So that the growers have to go back to the company each time for more. I imagine that if that spread it would be the end of the world. If all plants stopped producing seeds …’
‘Well, at least that can’t happen,’ Grace says. ‘Think about it. If there are no seeds, the attribute can’t spread. Barrenness seems to be the one thing nature forbids. It can’t spread because there are no seeds.’
‘Oh yeah,’ says Esther. She looks embarrassed. ‘I still don’t like the idea of eating all that stuff, though. I don’t like the idea of having vegetables with locust genes in them or whatever, especially since I’m a vegan.’
‘Me neither,’ says Grace.
For a few minutes we lie on the grass in silence, all our eyes looking up at the sky. I think about how I am looking at the same sky I looked at when I was a kid, but everything underneath it has changed. And when you are a child you know things will change, because everyone says that things do, and they do, too, but slowly enough for you not to notice. Political regimes change, things blow up and people die and suddenly the world is completely different. But the sky stays the same, and the moon waxes and wanes the same each month. But if people could change those things they would. Imagine if you could advertise using the moon. It could be – what? – a giant hamburger, or some company’s logo. Usually when I think things like this I get a tingle and then think about something else. For some reason today I vow that if this happens in my lifetime I will seriously think about killing myself. What sort of person would sell the moon if they could? For a million pounds, would I sell the moon if I could?
‘No one ever cracked that Go problem, did they?’ Dan says lazily.
‘No,’ Grace says. ‘That would be such a breakthrough. It’s not just PopCo offering prizes for the person who works out how to get a machine to play Go properly. I think Microsoft has a huge prize, too. Half of us in Robotics and AI are working on something in our spare time but it’s pretty impossible. Are any of you any good at Go?’
‘Alice is,’ Dan says.
I shake my head. ‘I’m not that good.’
Esther’s rolling a joint. ‘You know that guy I was talking to before? Hiro? Well it turns out that he’s the reigning PopCo champion. Cool, huh?’
‘You should play him,’ Dan says to me.
‘I’m really not that good,’ I say again. ‘I bet Grace is good.’
‘Are you?’ Esther says.
‘Not really. I’d never played before I came to work here,’ Grace says. ‘But I play almost every day now. It really is the ultimate AI geek game, it turns out. Don’t know how I never played it before.’ She grins.
‘Why can’t computers play Go?’ Dan asks. ‘I’ve never really understood that.’
‘Pattern recognition,’ Esther says, frowning. ‘Or something like that.’
‘Yeah,’ says Grace. ‘Machines can’t recognise subtle patterns the way humans can. It’s one of the main things that separates people from machines, actually: machines process data a lot faster than normal humans, but humans can recognise faces and voices in a way that no one can get computers to match – or even come close to. You could pick out your best friend in a crowd but a computer would only see light and shade. With Go, a lot of it is about seeing patterns. The Go masters think a lot about the shapes they create on a board, and strive for beauty as well as victory. Computers can’t do that. Another problem is that computers can’t understand that sometimes you may have to sacrifice some territory to make gains later on. You know all that vaguely Zen stuff about not being able to lose without winning and vice versa? That’s what you can’t teach computers.’
Dan frowns. ‘Can’t they be taught to do something like a risk assessment, to work out the consequences of every possible move? Then, if it seemed that the computer would be successful from making what seems to be a “losing” move, it would simply see it as a winning move and play it anyway?’
‘Well, that’s how chess programs work,’ Grace explains. ‘They call it the “brute force” method. A chess programme simply runs a set of what ifs to see whether particular moves would be successful. But there are too many possible moves in Go. A chess-board only has 64 places you can move but a Go board has 361. The computing power required to work out all the possible combinations of moves would be pretty staggering. But it’s like the whole thing with recognising faces. A good human player can look at a Go board and instinctively know whether territory can be captured or not. It seems to be almost impossible to teach a computer to do the same thing. People are just better at seeing patterns.’
361. The square of 19. Still looking at the sky, I find myself thinking about prime numbers. It used to be a habit – almost an obsession – of mine, to immediately wonder if a number is prime or not. I even just did it with 361, even though I know it’s a square. Perhaps it’s because I have a prime number birthday: the 19th of July 1973.19 is prime, as is 7, as is 1973. These numbers have no whole number divisors apart from one and themselves. There aren’t many prime years in which to have been born, actually. In the twentieth century you’ve basically got 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997 and 1999. When I realised I had a prime number birthday, I then wanted everything about my life to be prime. The primes are, after all, the most mysterious and beautiful numbers in the universe. You can’t ever break them apart, but every other number breaks down into its prime factors eventually. They are the building blocks of everything.
So I am sitting here on sun-warmed earth, leaning against grey rock and I close my eyes. Behind them, all I can see, suddenly, are building blocks abstracted in the dark. The rock behind me, the rocks under the ground, the blocks in all the structures on the PopCo Estate below me. You can build something and you can smash it up and bury it, but the blocks always stay the same. Prime numbers, genes, atoms. The blocks have to stay the same, don’t they?
Chapter Fourteen
My grandfather is making marmalade while my grandmother works in her study.
‘What does she do up there all day?’ I ask, keeping away from the big pan like I have been told to do.
‘She does maths,’ he says simply.
‘What sort of maths?’
‘Complicated maths.’
‘What sort of complicated maths exactly?’
‘She’s trying to prove the Riemann Hypothesis.’
‘The what?’
He laughs. ‘Quite. And she says I set myself impossible tasks.’
I don’t know what he means by this.
At the end of the afternoon I am allowed to help slip pieces of muslin over the jars and secure them with elastic bands. Then we write on the labels, Orange, 1983 and put them in the larder. Soon after that, my grandmother comes down from her study and yawns, which is my grandfather’s cue to pour her a whisky over ice.
‘What’s the Riemann Hypothesis?’ I ask her immediately.
She laughs. ‘It’s the work of the Devil.’
‘Is it important?’ I ask next.
‘Yes, to some people,’ she says, with an amused expression.
It’s always hard to know what to talk about with my grandmother. It’s not that she is frightening but she really is incredibly busy, all the time. My grandfather will chat with me about anything: how weather works, Ian Botham, electrical circuits, the right way to sand wood, how to mix paint and so on; but my grandmother has always been frustratingly enigmatic. Occasionally I have shyly asked her questions like, ‘What are we having for supper?’ or ‘Do you think it’s going to rain?’ and she has just absent-mindedly said something back like, ‘Oh, um, ask your grandfather,’ and then disappeared upstairs to her study. Once, to avoid this response, I asked her what her favourite colour was. She just looked at me with a really puzzled expression and then simply said she didn’t know. I think she likes me, but definitely not as much as my grandfather does. Anyway, I have aske
d her about the Riemann Hypothesis because this is obviously the thing she is most interested in and perhaps she will like me more if I understand the thing she is most interested in. But answers are not forthcoming, so I change tack.
‘What’s the most important maths anyone has ever done?’ I ask.
My grandfather comes and sits opposite me on his favourite chair. ‘Now there’s a question,’ he says. ‘There’s a question indeed.’ He glances over at my grandmother, and then back at me. ‘The most important maths. Hmm.’
‘Euclid?’ says my grandmother, more to him than me.
‘Hmm. It has to be Bletchley Park, really, doesn’t it?’
She looks sad for a second. ‘Well …’
He looks at me. ‘Have you ever heard of Bletchley Park?’
I shake my head, imagining ducks in a pond.
‘This was classified information until very recently …’
‘Is it to do with the war?’ I ask, instantly thrilled.
‘Oh, yes.’
My grandmother sips her drink while my grandfather starts telling me all about how, during the Second World War, the most intelligent mathematicians, linguists, crossword addicts, music theorists and chess players were rounded up and sent to this secret mansion between Oxford and Cambridge to crack German codes. He tells me in such detail about this mansion, with its outside units called ‘huts’ and its ballroom and its gardens that it almost seems as if he was there himself. My grandmother is quiet as he speaks but occasionally she nods and raises her eyebrows, as if confirming what he is saying. He tells me all about something called the Enigma machine, which turned messages into (supposedly) unbreakable code, and how the German operators often made mistakes in its use so that it was easier for the British cryptanalysts to break their messages.
‘The German keys changed at midnight,’ he says. ‘Intercepted messages would start pouring in and then the race would be on to find that day’s key …’
‘What do you mean, the key?’ I ask.
‘The setting for the Enigma machine,’ he says. ‘Once you know what the setting is, you can unscramble the message. There was a certain amount of information that the cryptanalysts would use to their advantage, like how the same setting couldn’t be used more than twice, that the new setting couldn’t use consecutive wheels and so on … Enigma would never encipher a letter as itself, so that also helped to narrow things down … But people really did think Enigma was unbreakable. Sometimes, British Intelligence forces even had to stage events – the movement of a particular fleet, perhaps – so that they would know what the German messages for that day would say. Of course, once you know roughly what a message says, it is easier to unravel the cipher version of it. The cryptanalysts would also look for encrypted messages that looked like they might be weather reports. After all, everyone knows what the weather has been. But with Enigma, a key is only valid for twenty-four hours and then it changes. The Allied Forces needed to find a way to crack the code, not just get individual keys.’