PopCo (27 page)

Interesting things have happened as a result of my fear (which my grandparents say is actually a ‘phobia’: like fear, but more important). Because the nights are so potentially horrific, so mind-curdlingly, heart-stoppingly terrifying, everything outside of this set of ‘things of which I am afraid’ (we have been doing sets in maths) seems just brilliant. For example, the daytime is brilliant. If, during the day, I ever feel sad about my father being lost, or I feel bored at school, or upset because of a fight at playtime or anything like that, I simply have to remind myself that it is not night and it is not dark and I am not alone. Other people seem moderately happy, or just the same kind of happy/sad, all the time. If the way they felt was a graph, it would be a single flat line, with maybe a blip for Christmas and another for their birthday, perhaps. But the graph of my moods has mountains and valleys galore. Dawn, for example, can make me soar on its own. A whole nine, or maybe ten, hours until it starts to get dark again! Hooray! In the summer it will be brilliant, because there will be a good deal less darkness than there is now. In some ways, fear is a good thing. It makes you appreciate life more: the bits it hasn’t spat all over seem all the more delicious for it.

For these reasons, I do not think I need to go to the doctor about my fear, and I have explained this to my grandparents. Of course, I never want to go to the doctor about anything. The doctor’s surgery is a potentially dangerous place from which I would not want to have to escape (if he got out his pliers, or revealed himself to be an alien with a bacterial weapon –
bang!
– I’m melting!). Also, I have heard that if a doctor thinks you are being mistreated, he can send you to live in a children’s home. I have never been mistreated but my family is unlucky in some ways, and we seem different, and sometimes that’s all it takes. If I got sent to a children’s home they would undoubtedly lock me in dark rooms and I would be forced to either run away (which would itself inevitably mean ending up in the dark on my own, probably in a forest) or kill myself. I don’t like the idea of killing myself but I would do it if I had to. I wish I had an emergency cyanide pill, like my grandfather did during the war.

It is almost two months since I met the men at the bus stop. Christmas is coming, and I have opened ten windows on my Advent calendar. My grandparents are still letting me stay in their room with them at night, and Rachel is coming home soon. Things don’t feel so bad. Some days I don’t think any bad thoughts at all, which is very nice, especially compared to some of the days I have had, where bad thoughts are snakes in a pit and you just fall into it with no ladder.

I am thinking about sets a lot. A set is something from maths that means a collection of things that share a property. You could have the set of even numbers, or a set of all numbers less than 100. You can make a set of anything and it seems neat and tidy, like putting thoughts in a drawer in your mind. Some sets are potentially confusing, though. For example, you could have something called ‘the set of all sets’. Would this set contain itself or not? It would have to; but how could it? This situation, where something seems to be right and wrong, or true and false, at the same time, is called a paradox. I love paradoxes! When I grow up I am going to have a cat and call it Paradox. A paradox is what happens when you go back into the past and kill one of your distant relatives. If you kill them, of course, you prevent yourself from being born. But if you did not exist, you couldn’t go back and kill them. I read a science book that said that this is why time travel to the past is
never possible. It said that any system that supports paradoxes is inherently flawed. Like sets, maybe?

My grandfather told me some more paradoxes. He uses them a lot in his magazine column. My favourite one is about time travel (lots of paradoxes are either about sets or time travel, it turns out). A scientist, Henry Humphrey, develops a method of travelling to the future. While there, he goes to a library and reads some science books that are way more advanced than those in his own time. One book in particular grabs his attention, and then he realises it has his name on it! He must have written this book in his own time. Extraordinary. When he gets back to his normal life, he starts his groundbreaking work, replicating the material from the book he saw in the future (well, it had his name on it – why not?). He publishes it to breathtaking acclaim, and only then realises that he has created, or been a victim of, two huge paradoxes. Who wrote this book? Where did it come from?

Henry Humphrey suddenly doesn’t know if he has committed a gross act of inter-temporal plagiarism. Did he originally write the text of this book or not? In the story, he first encounters the book in the future.
Then
he writes it. Does this imply that the book existed in the future ‘before’ it did in the past? Or simply that Henry writes it after he returns from his trip to the future? Does it imply that it was actually written by someone else? It’s hard to tell. Even if the book ‘was’ written by someone else in the future, it will have Henry’s name on it when he sees it, as he is of course about to go back to the past and write it earlier. So who wrote the book? Can we ever know?

The real paradox, however, is in the existence of the book in the first place. To recap: Henry goes to the future, sees some information in a book, comes back and uses this information to create his own book which becomes the book he finds in the future, from which he gets the ideas, etc. etc. This is a very neat loop except for one thing. The information in the book comes from nowhere. It is never originally written! The scientist gets the information from the future. But who put it there? He did! So where did he get it? The future! This loop continues indefinitely.

‘I’ve solved it,’ I say to my grandfather one crisp day towards the middle of December. ‘It’s simple. Someone else writes the book …’

‘When?’

‘In the future.’ My grandfather frowns but I continue anyway. ‘So the book is there, with another author …’

‘Can we give him – or her – a name?’

‘Yes. It is by a woman called Tabitha Paradox.’

‘All right.’ My grandfather stirs the soup on the stove.

‘OK, so Tabitha writes this book. When Henry comes to the future, this is the book he finds.’

‘But it has his name on it.’

‘Yes, I know! That’s what I’m trying to explain. The moment he sees the book, time shifts and her name changes to his, as it is this moment that alters history. He doesn’t notice this, of course, as it happens in less than a split second. Perhaps all he feels is a crackle in the air, or a sudden rush of cold wind.’ I have been reading a lot of science-fiction books lately, and I think I have a feel for the sorts of things that would signify a ripple in time.

‘But he still goes back to his own time and writes the book?’

‘Yes.’

‘But then the paradox is still there. Tabitha can’t write her book because it will already exist. It will have been written before she was born. Her ideas won’t be groundbreaking, because they will already be there – in this book by Henry Humphrey …’

‘That
she
wrote!’ I say. ‘How could he write it without her?’

‘Well, there’s the paradox,’ my grandfather says. ‘Who did write it? If it was Henry, then he got the information from nowhere. But it can’t have been Tabitha, because by the time she is born, the book will already exist, with Henry’s name on it.’

While we have been talking, my grandmother has emerged from her study. Now my grandfather gets up to pour her drink, and to start making his pipe (he only smokes one after dinner now and it is the highlight of his day, so much so that he spends a good deal of time before dinner making and tinkering with it).

‘What have you two been mumbling about?’ my grandmother says.

‘Paradoxes,’ my grandfather says, straightening out his yellow pipe-cleaner.

‘What sort of paradoxes?’ she asks, sitting down with her drink.

‘Time travel paradoxes,’ I say.

She laughs. ‘Oh dear. No wonder you both look confused.’

I tell her our paradox, and she laughs some more. The soup is
simmering on the stove and I can smell sweet carrots, parsnips and herbs, as the windows steam up. I feel safe like this, even though darkness is falling. The steam on the windows is a protective film and I am not alone because my grandparents are here.

‘So you have a made-up story that doesn’t make sense,’ she says. ‘Is that actually a paradox, or just an implausible story?’ She is addressing my grandfather with a shiny look in her eyes and an almost naughty smile.

‘If you could travel to the future, and back, it could happen,’ he says. ‘That’s the point of the story.’

‘Perhaps it means that time travel will never be possible,’ I say.

‘It’s rather likely that travel to the past will never be possible, certainly,’ my grandmother says.

‘How do you know?’ I say, widening my eyes. In our family my grandmother is always, always correct. My grandfather is brilliant, with his crazy ideas and lateral solutions to his puzzles, but she is a flawless logician. If she says there will never be time travel to the past, there never will be.

‘Yes, how do you know?’ my grandfather says.

‘I know because I have never met anyone from the future,’ she says. ‘If there was ever going to be a way of coming back, people would be coming back. It is logical. History would be full of strange twists and turns caused by future people turning up and messing around with things. Betting shops would be full of people from the future. Things would disappear all the time. But none of these things happen. So, people can assume that time travel to the past will never be invented or discovered.’

‘Maybe it just hasn’t been discovered yet, in the future,’ I say.

‘Think it through logically, Alice,’ she says. ‘It doesn’t matter when in the future time travel to the past is invented. If it is
ever
invented, people could come back to this time, now.’

‘Maybe you can’t see time travellers,’ my grandfather suggests. ‘And they can’t change anything. If that was the case, then people could be travelling to the past all the time and no one would know.’

‘Well, yes, that would solve your paradox problem, wouldn’t it?’

‘Why do you keep saying “time travel to the past”?’ I ask my grandmother. ‘What about time travel to the future?’

‘Well, time travel to the future is theoretically possible, using Einstein’s theories. All you need to do is get in a space-ship and
travel somewhere very, very fast. When you come back, more time will have elapsed on Earth than in your speeding space-craft.’

This shuts me up. I never knew this. While I think about whizzing off to the future, a place where women wear silver mini-skirts and have hard cones for breasts, my grandmother gets up and puts a Bach record on the turntable.

Later, while we eat our soup, I keep asking my grandmother questions about time travel and the potential paradoxes it could create. It seems that all these paradoxes specifically concern travel to the past: changing something that has already happened. There are no paradoxes in going to the future, just as long as you don’t try to come back.

‘Einstein’s universe is a one-way system, that’s for sure,’ she says, and my grandfather laughs a lot.

‘What we really need is a bypass,’ he says, still laughing.

They have just built a small one-way system in our village centre, which everyone is always joking about for some reason. There is also a plan to build a bypass, whatever that is. Cue more jokes. I didn’t know roads could be so funny.

‘A bypass,’ she repeats. ‘Ha ha ha …’

‘What about wormholes?’ my grandfather says suddenly.

‘What’s a wormhole?’ I ask.

‘It’s a potential short-cut through time,’ my grandmother says to me. To my grandfather she says, ‘Don’t be so silly, Peter. It’s quite clear that wormholes can’t exist, or if they did, no one could actually travel through one.’

‘Hmm,’ is all he says. I know what that
Hmm
means. It means
Maybe not mathematically; but then you can’t explain ghosts mathematically,
or telepathy
. He has been interested in such things only since we began working on the Voynich Manuscript, but it is almost an obsession now: that there might be ‘things’ out there that we don’t have the tools to understand. Is the Voynich Manuscript then one of the tools, or one of the things?

It strikes me then that he and my grandmother are engaged in completely opposite occupations. He in the realm of the ‘what if’, and she in the realm of the ‘not very likely’. In order to progress, my grandfather has to sometimes formulate hypotheses that are counter-intuitive, or seem ridiculous. What if aliens created the Voynich Manuscript? What if it isn’t supposed to be read? What
if it came from the future, written in a language we don’t yet know (another reason for all the time-travel conversations)? Then again, my grandmother works with imaginary numbers all day, and something called the zeta function. Maybe I am wrong. Maybe what they do is exactly the same; creeping up on impossible problems with a few made-up stories and invisible theories and trying to convince them to come out of the bushes. My grandmother’s leaps into the unknown are just slightly harder to understand, sometimes.

My grandmother has been explaining to my grandfather about wormholes, and now they are talking about some other part of time travel, and she is saying something about the mathematician Gödel, whom she met once, a long time ago. She finishes what she is saying and glances at me.

‘If you really want to investigate paradoxes, Alice,’ she says. ‘You should look at what Gödel did with them.’

My grandfather gives her an odd look.

‘What did he do?’ I ask.

‘Well, I can’t explain the whole thing right now, but do you know of the Liar Paradox?’

‘“All Cretans are liars”?’ I say. ‘That one?’ The Liar Paradox is one of the oldest puzzles in the world. Epimenides, a Cretan, makes the statement, ‘All Cretans are liars.’ If he is telling the truth, then he is lying. But, if he is lying, he is telling the truth, which means he is lying. This kind of thing makes my brain fuzzy, in a nice way. It’s like the set of all sets, anyway.