‘So how did they do it?’ I ask.
He chuckles. ‘Bombes.’
‘Bombs?’
He spells it out. ‘Bombes. They were early computers, originally conceived by a Polish scientist but refined by Alan Turing, who was the most well-known cryptanalyst at Bletchley. In fact, Turing’s machines formed the basis for all computing today.’
I have never seen a computer, although I have heard that James has something called a ZX Spectrum on which he plays games to do with space. Before I became shipwrecked and moved, there was a craze at my school for hand-held games, which are like little computers. I had a go on my friend’s Frogger game once, but my frog died immediately and then she took the game back.
‘Turing,’ says my grandmother wistfully. ‘He really was a genius. How could they have let that happen to him?’
‘What happened to him?’ I ask.
‘He killed himself. With a poisoned apple.’
‘Like Snow White?’
‘Just like Snow White.’
I shudder. I’ve only recently become aware of people killing themselves and the very concept gives me nightmares. I cannot imagine any reason that someone would actually want to die and I don’t think I’ll understand it as a grown-up, either.
‘Turing was a great man,’ my grandfather says. ‘As well as his bombes, he invented “mind machines”, imaginary computers that showed what would happen with certain maths problems.’
‘But they did actually have computers in the war?’ I say. I thought they had only just invented computers a few years ago. Everyone talks about them as if they are new.
‘Yes, sort of,’ says my grandfather. ‘Anyway, it was because Turing was such a mathematical genius that he was able to construct all these ways of cracking the Enigma ciphers. Of course, there were lots of other people there too, working in the same sorts of ways, but they say that without his input the Allied war effort would have been put back several years. Interestingly, Turing also wanted to prove the Riemann Hypothesis. Anyway, there you go. The most important maths. It won the war for us, or so people say.’
‘Why did they have musicians and crossword people at Bletchley Park?’ I ask, not yet finished with this conversation.
‘Because people like that are good at seeing patterns. A lot of cryptanalysis is about having half of something – or less – and being able to guess the rest. Obviously, crossword people would be good at that, and linguists. Meanwhile, the mathematics experts were able to finish patterns using their knowledge of the patterns of numbers, and probability and so on. Those who know a lot about music theory understand music mathematically, and music has patterns based on maths. Musicians understand intuitively which notes fit where in a melody. A lot of code-breaking demanded those sorts of skills as well. And music is, after all, completely based around numbers …’
‘Is it?’ My eyes must be wide. I thought music was the furthest thing from maths in the world. I thought music was all about letters: A, B, C and so on, all the way up to G, which is where the notes run out and you have to start again.
‘Oh yes. Have you ever heard of Pythagoras and his urn?’
‘No.’
‘Have you heard of Pythagoras at all?’
‘No.’
‘Well, Pythagoras was a famous mathematician in Ancient Greece. He invented something called Pythagoras’s Theorem, which will be very important when you do geometry and trigonometry in a couple of years …’
‘Can you explain it now?’
‘No, we’ll get so far from our starting-point we’ll never find our way back.’ My grandfather smiles. ‘I can show you tomorrow if you’re still interested. Anyway, Pythagoras filled his urn with water and banged it with a stick – or something like that. The urn made a pleasing sound. A musical note, is how we would describe what he got. Pythagoras experimented with water in the urn until he came upon the following observation. If, after playing his first note, he tipped exactly half of the water out of the urn and hit it with his stick, the note he got was very pleasing next to the first one. If he tipped half the water out again, so he was left with a quarter of the amount he started with, and banged it with his stick, this note was also pleasing when played next to the first two. If he tipped out two-thirds of the original amount, leaving him with a third, this was a pleasing note too. If, however, he left some other quantity of water in the urn, an amount that wasn’t a precise fraction of the original amount, he got dissonance, which means that the note sounded wrong. And that’s the basis of music theory.’
‘Did he use lots of urns?’ I ask.
‘What do you mean?’
‘Well, rather than keep filling and emptying the same urn …’
‘Yes. I’ve never really thought about that but yes, he must have done.’ My grandfather looks pleased, like I have just solved one of the riddles he always gives me, but it’s so obvious. In my mind, when I imagine this man Pythagoras, I don’t see him all flustered, trying to mark off points on one urn, with his robes all twisted and his face all red. I imagine him calm and serene, with a row of urns lined up like keys in a glockenspiel, all measured out perfectly, playing beautiful music. But something else about this doesn’t make sense to me.
‘Why does a third work?’ I ask.
My grandfather makes his concentrating face. ‘Sorry?’
‘You said he kept halving the amount of water. One, a half, a quarter and so on … Why a third?’
‘Oh, Alice,’ he says. ‘You do ask good questions.’ He laughs and glances over at my grandmother, who is also smiling. ‘The pattern is 1, ½, ⅓, ¼, ⅕, ⅙ and so on. It doesn’t reduce by half every time, but by whole number denominators of one …’
‘Whole number … What?’
‘In a fraction, the bit on the underneath is called a denominator,’ my grandmother explains. ‘That’s the bit that goes down by one every time.’ And this is amazing, because it’s the first time she has ever explained anything to me – and she has made an effort to explain it in child-language as well. At this moment, I feel closer to her than I ever have before and I resolve to really try to understand what she does, so we can talk about it all the time.
Also: I bet I could solve the Riemann Hypothesis, whatever that is. I bet I could solve anything if I tried hard enough. I am definitely going to be famous for solving a mystery or a puzzle that has stumped grown-ups for ever. This is my plan. Sometimes, when my grandfather is out and my grandmother is working, I make up recipes in the kitchen. I am absolutely certain that one day I will stumble on the special combination of ingredients that will make me rich and famous. Magic biscuits that make you fly; invisible blancmange; mould that has healing properties. I imagine having the Riemann Hypothesis explained to me and the answer arriving in my brain a split-second later, like it was running for a train.
I look at my grandmother, wisps of her grey hair escaping from her long plait, and my grandfather, with his blue shirt-sleeves still rolled up, and they suddenly exchange a comfortable, happy smile. The house still smells heavy and sweet with freshly made marmalade and the sun is now setting outside. I know that in about five minutes my grandfather will get up and switch on the electric light and my grandmother will play one of her records, probably something by Bach. But just now, as they exchange their smile and sip their drinks, I imagine us suspended here in this moment of happiness for ever and I have no shipwrecked feelings at all.
The next day my grandfather receives a package.
‘Aha,’ he says. ‘This is it.’
‘What is it?’ I ask him, intrigued. His face is lit up like Christmas. ‘Is it a present?’
‘What? No. Not a present. But very exciting. Look.’
He shows me pages of what seems to be a copy of an old-looking manuscript. There are handwritten words that I can’t read, and strange pictures of plants and people and animals. Something about it makes me feel strange. I don’t quite know why. Perhaps it’s because I don’t recognise anything on the pages. It
looks like you should be able to recognise things: the words, the illustrations and so on; but it’s like a book you’d find in a dream; almost real but not quite.
‘What is it?’ I ask.
‘This is the Voynich Manuscript,’ my grandfather says proudly.
‘And what do you do with it?’
‘You try to read it.’
‘Is it in code, then?’
‘Oh yes. Or at least, that’s what people think. This …’ He fans the pages carefully. ‘This is one of the oldest unbroken codes in history. And I am going to break it.’
‘Can I help?’ I immediately ask, unable to stop myself.
‘Yes,’ he says. ‘You certainly can help.’
What? I am actually being allowed to help with an important, secret, grown-up project? Bloody hell. Slightly dazed, I go upstairs and immediately sharpen all my pencils.
Once school starts, I fall into the following routine. I get up at seven-thirty, which leaves me just enough time to get dressed and have breakfast before I have to run for the village bus. Tracey waits at the same bus stop as me for her special school bus (which I will also take next year when I move up to the comprehensive) but we never speak. Sometimes on the bus I reply to letters from Rachel, who is back at her boarding-school. More often, though, I take a fragment of the Voynich Manuscript that I have traced the night before, and study that. After school, I walk to the bus stop in town, breathing the bonfirey, marshmallowy smells of autumn. I love this time of year, when people start to rehearse for Christmas plays and pantomimes, and the air feels like it’s full of magic spells. This is the time of year when arriving home after school feels cosy, like going back to bed.
When my bus arrives back in the village it is usually almost dark and I walk across the green and through Hang Man’s Lane, down the alley leading to our garden and then in through the back door. My grandfather cooks stew most evenings, with root vegetables and prunes, and while it bubbles away on the stove, we sit down and he fills me in on the work he has done so far that day. I am not old enough to have homework yet, so we spend most of the evening working on the manuscript, except for when my grandmother comes downstairs, and we are expected to put our work away and fetch drinks for her. We also stop for dinner, and sometimes I watch my grandparents play chess or Risk together afterwards. Occasionally I am allowed to play too, but I never win. The only night our routine is different is on a Tuesday, when my grandfather compiles the crossword for the local newspaper. On a Wednesday morning he cycles into town to deliver it to the newspaper offices. (He has decided that using the car all the time is too ‘lazy’.) He always buys toffee on his way back, and so on a Wednesday evening we eat toffee while we work, and I have to clean my teeth for twice as long on a Wednesday night.
One Wednesday afternoon, I am waiting at the bus stop thinking about toffee when these two men come up to me. I wouldn’t notice, except that, as they approach, I can hear one say to the other, ‘No, that’s definitely the Butler kid. Look at her hair.’ I consider running for it but that always looks suspicious so I stand my ground.
‘Hello,’ one of them says to me.
I say nothing back. Is this danger? Or are these people just friends of my grandfather? I remember that in our Stranger Danger sessions at school, we were told not to believe a grown-up if they say something like, ‘I’m a friend of your dad and he asked me to drive you home.’ So I am ready for this. I don’t have many self-defence moves but I will knee one of them in the balls if I have to.
The other one takes a step towards me and I instinctively move back.
‘Don’t scare her,’ says the other one. Then to me: ‘Don’t mind him. He’s got no manners. My name is Mike and my friend is called John. We’ve been trying to get in touch with your grandfather.’
Still, I don’t say anything.
‘We had his number a couple of years ago but we lost it. And we don’t know where he lives any more. We wondered if you could point us in the right direction? We’re old mates of his from the Fountain. We’ve got a proposition for him. So …?’
Now I know they are lying. My grandparents have only had a telephone in the house for about a year at the most. And it was my father who always drank in the Fountain, not my grandfather. Knowing this makes me frightened; my small heart an elastic-band ball, bouncing in my chest. These are definitely bad men. Do I run now?
‘I’m not allowed to talk to strangers,’ I say.
‘We’re not strangers. We’re friends of your…’
The one called John interrupts. ‘Oh leave it, Mike. They’re taught to ignore all this stuff now. You can’t ask kids the bloody time these days. Let’s just leave it. This little bitch isn’t going to tell us anything.’
Tears spring into my eyes. No one has ever spoken to me like this before. My bus, welcoming, warm and full of nice grown-ups pulls up but something tells me not to get on it. If these men know my bus route, they’ll have a much greater chance of working out where I live, and I really, really never want to see these men again. So, although every part of me wants to get on the bus, I glance at it dismissively and then look at my watch, as if I am thinking, Hmm, this isn’t my bus. Wonder what time my bus will be along? The bus soon moves off and I am left alone with the two men again. I wait until the split-second when it seems right and then, seeing no alternative, I run for it. I run through the shopping arcade and out into the main part of town, not looking to see if they are running after me. In a few minutes I make it to the police station, and, after telling them that some strange men asked me to go with them to look at some puppies, they drive me home.
When the police have gone, I tell my grandparents everything.
‘Excellent,’ my grandfather says. ‘You did the right thing.’
My grandmother isn’t so pleased. ‘You should have got on the bus, Alice.’
‘But then they would have known …’
‘There are other ways of finding out where someone lives. You shouldn’t put yourself in danger.’
I can’t help it. I know I have been brave, but now I start to cry.
‘And lying to the police …’
‘That was quite right, Alice,’ my grandfather says, emphatically. He looks at my grandmother. ‘We don’t want other people knowing about this. Especially not the police. Imagine going to court and having to be completely public about all of this? It would cause mayhem. And it served those two right. If they get picked up for this then … Well, it’ll teach them to swear at a child.’
‘Maybe the police should know. What are these people going to do next? Kidnap Alice? Try to take the necklace? I don’t know why she even has the bloody necklace anyway, Peter. It’s like you’ve made her into your walking, living proof. You’ve branded her. It’s like Hardy’s postcard: utterly ridiculous. It’s not safe. And it’s not fair, either.’
I have never heard my grandparents argue before. I wish they would stop. This is all too confusing. What on earth is Hardy’s postcard? What’s wrong with me having the necklace? Although it’s the most exciting thing I own, I suddenly don’t want it any more. My grandmother gets up and pours herself a drink, which she almost never does, and fetches me a glass of water.
My grandfather is pacing the room now.
‘This is nothing like Hardy’s postcard. He didn’t have proof. I do.’
‘Well, why don’t you just publish it, then?’
‘Beth, we have talked about this. You understood.’
‘That was before strange men started abusing my granddaughter in the street.’
‘Look, can you stop making this more dramatic than it actually is? Yes, I admit that those men aren’t particularly nice but they would never, ever hurt a child. They want my address so that they can come and try to persuade me to tell them what I know. They, like every other bugger out there, think that one day someone is simply going to give them a treasure map and they’ll be able to just go off around the world and claim something that doesn’t belong to them. Well, I??
?m not having it. Even if they did come here, I could deal with them. What happened tonight was very frightening for Alice, I know, but it’s not as sinister as it seemed. Alice did the right thing, and I am very proud of her. Now, I am going to go out for a while to make sure this does not happen again. Give Alice some strong, sweet tea, please.’
The door slams and I am left alone with my grandmother. Although she is obviously cross, she makes me a cup of tea with several sugars in it, and strokes my hair for a while as I drink it. Then she distractedly makes herself another drink and looks at the clock on the mantelpiece. She sits down and sighs.
‘What is going on?’ I ask, simply.
She laughs nervously. ‘Where would I start?’
I put on my best grown-up voice and say: ‘At the beginning.’
Chapter Fifteen
At half-past four we walk down the hill to the Great Hall and clamber into the boat. I had expected it to feel solid but it is actually on some kind of spring system and wobbles when you walk on it. We learn what things to hold on to to avoid going overboard and Gavin explains that if we were on water we would have to wear lifejackets. On rough water, he says, we would be tied to the boat with a line. Gavin controls the ‘wind’ with these big fans and we have a go at putting sails up and taking them down again. We learn not to get in the way of the big boom when it gybes from one side to the other (being hit by it is, apparently, the number-one cause of going overboard) and not to get the sails tangled when putting them up. Gavin keeps explaining that this thing or that thing is much better on water, and easier to understand, which is odd considering that he has invented this indoor training boat. It’s quite thrilling when the boat heels over in the ‘wind’, though, and I feel quite excited imagining doing that in the water. In fact, the more I think about it, the more keen I am to actually get in some water: it’s turned into a very hot day.