Everyone has set off again, so we do too. ‘Go on,’ I say.
‘A virtual world must have one dimension less than the “real” one in which it is created. We are three-dimensional creatures, yet we can’t create anything very complex in three dimensions; not something that imitates life, anyway.’
‘I see what you mean,’ I say. ‘Who was I talking to about this recently? Um … Oh yeah. It was Grace. She was explaining how difficult robotics is because of that.’
‘Exactly. If you look at, say, a rabbit’s leg, it’s so bloody complicated that you could never recreate it. We can’t make prosthetic hands that are a convincing reproduction of the real thing. We can’t even begin to understand the human foot. But if you look at the latest generation of videogames and online worlds, we are very good at making two-dimensional worlds that, in some ways, work better than this one.’
‘Better?’ I think about the fragmented, geometric landscape of the last videogame I played and compare it with where I am now. This landscape is alive and exciting. The other one was a collection of dots.
‘Not better in every way. But in a two-dimensional world there is no pain. There is immortality. There is fairness. It’s a nice place to spend some time.’
My brain hurts. Did a 4-dimensional being create us? Can you have ‘life’ in two dimensions? I remember my grandmother explaining to me that the most complicated part of the Riemann Hypothesis is that all the maths is four-dimensional. That’s what you get when you run imaginary numbers through the zeta function: points you can only plot on a four-dimensional graph. For a second I imagine some ‘being’ in Violet’s two-dimensional world trying to figure out the secrets of its own universe. Would it try to do three-dimensional maths, even though it would never be able to see a three-dimensional object? Would it come up with theories about there being other dimensions ‘out there’, like we do? Would it consider an afterlife? Would it ever become aware of a lost book, accidentally (or, more likely, mischievously, as nothing is really an accident) dropped into its world: a blueprint for something, perhaps some world that never got made, and spend its life trying to work out the language and the pictures …?
I don’t feel very well.
While I have been thinking, Kieran has ambled over. I realise that he has all sorts of things strapped to him. A utility belt holds a pair of binoculars, a pair of pliers and a small flask. He has a compass hanging around his neck. Slung over his shoulder is a bag that looks a lot like a knapsack. He looks like a Hollywood version of a Victorian gentleman explorer.
‘What are you ladies talking about?’ he asks. ‘Hairstyles? Babies?’
‘Fuck off,’ says Violet, smiling.
Kieran looks at me. ‘So, tell me about your mate, whatshisname.’
‘Who?’
He feigns concentration. ‘Dan? Yeah, that’s right. So what’s he like, then?’
‘He’s a nice guy,’ I say. ‘Why?’
‘He approached me looking for a job in my team when we leave here. Don’t know if I’ll have anything for him. Good artist, though. Some odd ideas, however.’
Good artist. Odd ideas. Dan must have shown him the artwork he created for his non-existent world. Perhaps he realised that a non-existent world could easily become a virtual world. Who knows? We walk along through a small area of forest, trying not to trip over roots coming out of the ground. I’m thinking about zombie-fingers again, and I’d prefer to be out in the open.
‘So what are you into, Alice? Who are you, really?’
‘Huh?’ The way Kieran talks isn’t good for my head at the moment. ‘Sorry?’
‘What do you do when you’re not, well, doing PopCo?’
‘Ah, you want to know my hobbies,’ I say. Violet smiles at me and walks off to join Ben and Frank, who seem to be having an intense discussion. ‘I like crosswords,’ I offer.
‘What’s in your DVD collection?’
‘DVD collection?’
‘You can tell a lot about someone from their DVD collection. It used to be books, of course. And maybe videos. You’d go round someone’s house and decide whether to have sex with them on the basis of what they had on their shelves, wouldn’t you? Not that I’m deciding whether or not to have sex with you, you understand. Although if you weren’t already taken …’
‘I don’t have a DVD collection anyway,’ I say quickly.
‘Videos?’
‘Nope.’
‘CDs?’
‘Yeah, I’ve got a few CDs. But not on shelves. Nobody would look at them and decide to have sex with me. Or not.’
‘Dan said you’d be like this.’
‘What’s Dan got to do with it?’
‘He said you were hard to get to know.’
I frown. ‘I’m not “hard to get to know”.’
‘But you won’t tell me anything about yourself!’
‘I won’t tell you what I own,’ I say. ‘Which is different.’
‘Shall I tell you what’s in my DVD collection instead, then?’
‘If you like. It won’t make me want to have sex with you, though.’
We exchange a grin. Kieran happily rambles for the next ten minutes or so about American remakes of Japanese independent films, B-movies, anime and old westerns until he seems satisfied that I know what he is all about. He doesn’t tell me where he grew up, how many brothers and sisters he has, what he is scared of, whether he likes his toast done well or not, whether his hair colour is actually natural, what he would do to improve the world, whether he believes in God (although I already know the answer to that one, I think), who he would vote for, what his perfect political party would stand for, what items he would take with him if he was to be stranded on a deserted island or anything at all about this cyber-paganism in which he is supposed to be so interested.
Is this how it works now? Do we just let film-makers create identities for us that we can buy for £12.99? Is that what identity costs? Or is it how you put the units together that counts? Does a zombie film plus an experimental Parisian inner-city heist film make you a different person than two Hollywood romantic comedies do? Would either of these people get on with the person who has every series of their favourite SF TV show on DVD, arranged in such a way that their edges make one picture on the shelf? You can string this stuff into lines of cultural DNA that can be seen without any kind of microscope, until anyone looking at your shelves can use this information to establish ‘who you are’ and whether or not they want to have sex with you. Can’t people just desire you because of your breasts any more? Maybe they do, sometimes. But if your cultural DNA can’t link up with theirs then they’ll fuck you and leave before you wake up, just like everyone said they would. Or you’ll do the same to them, because they like alt country music two years after it was fashionable, or they own Titanic on DVD.
*
The numbers of the Stevenson/Heath manuscript form a strange wallpaper in my bedroom. You can look at them until you get dizzy but they don’t mean anything without the document that will turn them into words. I have asked my grandfather to tell me what it is so many times but he never will. He doesn’t like it when I bring the subject up anyway, not any more.
My job in the evenings and at weekends is as follows. I have to count all the words on each page of the Voynich Manuscript and note down the results in a column for my grandfather to look at. Winter turns into spring, and snowdrops and then daffodils come up, and there I am, night after night, transcribing first the numbers of words, and then the numbers of letters, on every page of this huge manuscript. Sometimes I have to use a magnifying glass, and I think about being a detective. Mostly, though, this is boring work and sometimes I wish I could just read a book with real words instead.
On April 1st, my grandfather announces that he has completed his decipherment of the Voynich text. Then he laughs and says April Fool! Many years later this will become a tradition of ours, to claim, every April Fool’s Day, that we have solved this riddle. Something else happe
ns on this date as well. On April 1st, 1984, my grandfather’s first book, a collection of his Mind Mangle columns, is published. He has received a sum of money for this that he will not disclose. ‘Not quite enough for a swimming pool,’ is what he keeps saying. On April 2nd, we have a new burglar-alarm system installed. My grandmother is against it.
‘We can’t live inside a fortress,’ she says. ‘It’s unhealthy.’
But it happens anyway. Thanks to my father, people in Cambridge know that we have a treasure map in here. My grandfather has become increasingly convinced, since the incident at the bus stop, that someone will break in to get it. Personally, I say good luck to them. I live here, and I haven’t had any luck finding it. And I have the biggest clue of all: my necklace, with its strange numbers that don’t mean anything to me. I think that perhaps I, with my necklace, am the treasure map – or at least the proof that my grandfather knows what it is, which must amount to the same thing. So I am the treasure map and even I don’t know where it is. I do not point any of this out, however. There are other reasons for the alarm, it turns out.
On April 3rd, my grandfather comes home with a big box.
‘Here you go, Beth,’ he says to my grandmother. Her eyes shine as she unpacks a BBC microcomputer. The Riemann Hypothesis, which I now know to be something to do with a line of zeros plotted on a four-dimensional graph (the question being, Does the line go on forever, or eventually stop or change?) is now put to one side for a whole week while she sits in her room making a tap-tap-tap noise, occasionally asking me in to test programmes she has written in BASIC that, on the basis on a Y/N input, reveal more information as you go along.
Is your name Alice? Y/N
Y
Do you want to read Part Four of ‘Alan Turing and the Computer’?
Y
This particular instalment of the story takes me back in time to learn about someone called Georg Cantor. He invented set theory! And he also found out that there isn’t just one level of infinity but various levels of something called transfinity. I love the names for the levels of transfinity. Aleph-null is the first one; ordinary infinity that everyone understands. Aleph-one is the next level, and is obtained when you take 2 to the power of aleph-null. It’s confusing but I still like it and I almost understand Cantor’s famous diagonal proof.
My grandmother loves the computer. She, of course, actually discussed Turing’s ideas with him as he was having them. She has read Ada Lovelace’s thoughts on programming Babbage’s Analytical Engine. She knows the mechanics of this thing, and nothing about it scares her. I am fascinated by it for various reasons, but partly because she has it connected to a new black and white portable TV. A TV in the house! But it will never, ever be used to pick up broadcasts. It isn’t even referred to as a TV. We all call it the ‘screen’.
After I read what my grandmother has written about Georg Cantor, I start talking about aleph-null all the time. When my grandfather asks now many biscuits I want, for example, I say ‘Aleph-null, please.’ He twinkles whenever I do this, so I do it more. One day, I am sitting reading on the old armchair in the sitting room. I am flicking through the Mind Mangle collection, although I have read most of the pieces before (and only understood about half of them). I look at my name in the acknowledgements for the aleph-nullth time and only this time do I notice that, on the following page, there is a symbol: ℵ0. I realise that this is the symbol from my necklace! My grandfather is out, so I tear into my grandmother’s study.
‘What is this?’ I demand, out-of-breath from running up the stairs.
‘It’s aleph-null, silly,’ she says. ‘Your favourite expression.’
‘Aleph-null? But …’
She suddenly smiles. ‘Oh, of course. You would never have seen the symbol, would you? I can’t type Hebrew letters on my keyboard so I just wrote the words out phonetically. Gosh, how funny.’
This isn’t funny at all. I’ve been trying to work out what that symbol was for ages.
‘So it’s a clue, then?’ I say. ‘To the treasure.’
‘No,’ she says firmly. ‘Not at all. Your grandfather puts that symbol on everything. Have you not noticed before?’
Of course I haven’t. But now it’s been pointed out to me, I do start to notice the way he adds it to his letterhead, or to envelopes before he posts them. He even has a little stamp so he can print it on everything. How could I not have noticed this before? Oh well. Now it’s just me and this other thing: 2.14488156Ex48. What on earth does it mean? I know better than to ask my grandmother anything else about the necklace, though. Neither of them like talking about it. I don’t know why.
Soon, my grandmother starts writing programmes for her computer in assembly code, complex little things of no more than 22k, which she uses to back-up and password-protect some of her most secret and important work. She keeps all this work on tapes, which only run with her programme and her password. Then she starts building cellular automata. I have been a bit worried that my grandmother can never share any of her work with my grandfather and I, because it is simply too complicated for us to understand. Now, however, she calls us in all the time to see what she has done. Cellular automata are ace! My grandmother has been in touch with another mathematician called John Horton Conway, and he has told her about his ‘game’, which is called Life.
The game isn’t really a game. A grid, rather like a chess-board, is created on the computer. Each square on the board is known as a cell and there can be infinite numbers of them, although in reality you can only see a certain amount on screen. A black cell is known as ‘living’ and a white cell is known as ‘dead’. In Conway’s version, there are four rules: A black cell with zero or one black, or living, neighbours dies from isolation. A black cell with four or more living neighbours dies from overcrowding. A dead, or white, cell with exactly three living neighbours becomes alive. All other cells remain unchanged. You start the programme and it really does seem to take on a life of its own, like a very basic cartoon, as all the rules are implemented simultaneously and little kaleidoscopic patterns move around the screen. You can do it by hand if you want to see what happens, by placing black markers on a white grid, but it is slower that way, and you don’t get such a good impression of the expanding /contracting patterns as new generations of cells are ‘born’ or ‘die’. It is fun to make up your own shapes to begin the ‘game’ and see what happens as a result of them. Even very clever people can’t necessarily work out what the outcome of every starting position in this game could be. That’s why my grandmother finds it so interesting.
I am occasionally allowed to sit with my grandmother and feed in the numbers which set the programme off, and we watch while the black blobs expand, expand and die, turn into little flashing lines or just die after a single generation. With this odd background of pixels on a black and white screen, we sometimes talk about other things. I have learnt some more about the Riemann Hypothesis at last, and I know how to use four-dimensional co-ordinates (although I don’t know what the resulting graph would look like). My grandmother has explained that after all these years of working with four dimensions, she can actually see them in her head, even if it is supposedly impossible. I have read a science-fiction book that says the fourth dimension is time. My grandmother corrects this.
‘Time has only one dimension,’ she says. ‘In the physical world we can experience three dimensions of space, and one of time.’ A fourth dimension of space would be very different, she explains, with outside and insides of things becoming infinitely complicated, and cubes becoming simply the edge of something else.
As the game of Life trickles away in the background, we talk about mathematical proof, and my mother and father, and even what my grandmother was like as a young woman. One day I ask about my necklace again.
‘What did you mean,’ I ask, ‘when you said I’d been turned into a living proof? Is this actually the answer, written on here?’ I pull out my necklace and open the small silver locket. I point at the num
bers inside. ‘I know now that the aleph-null symbol is a red-herring, but this – this other bit – is that his proof?’
‘You should ask your grandfather,’ she says, like she used to when I asked her about the weather.
‘I can’t ask him,’ I say, sadly. ‘He won’t talk about it any more.’
The screen on the desk has been full of activity – large geometric patterns in every part of the screen – for the last five minutes. Now, inexplicably, the patterns start to die off, eventually ending as three small lines of three blobs each which flash horizontal and then vertical ad infinitum. I think it’s OK to say ad infinitum about these patterns as everyone knows they are final positions in this game; they won’t change any more, now.
‘It’s a code,’ she says, after a long pause. ‘A code he thinks you will be able to work out.’
‘But I can’t …’
‘Not now. When you grow up. When he is dead, you will inherit all his papers, you know that, don’t you?’
I didn’t but I nod dumbly anyway.
‘He thinks that, if you want to, you can work out the code then and make your own choice about what to do about it. It’s hard for him. He doesn’t want anyone to recover the treasure, but at the same time he very much wants to be known as the person who solved the Stevenson/Heath puzzle. Perhaps one day there won’t be a bird sanctuary on the site any more, or perhaps, rather than digging up the treasure yourself, you would want to give the solution to an archaeology department of a university and let them organise a proper dig …’
‘Why doesn’t he do that?’
‘He hates universities.’
‘Oh, yes.’ We both smile.
‘Perhaps war will break out again, or perhaps one day you won’t have all you need like we do now. It’s there and you do have the key. What you do with it will be your choice.’
‘Unless there is no treasure,’ I say, experimentally. I have been considering what my grandfather said about the Stevenson/Heath manuscript being a hoax. Even if Stevenson did exist (which, according to my grandfather’s evidence, he certainly did), it could still be a hoax.