But sometimes it has nothing to do with cold winters or cats or herons. Sometimes it is just maths.
Here is a formula for a population of animals
Nnew = λ (Nold) (1 – Nold)
And in this formula N stands for the population density. When N = 1 the population is the biggest it can get. And when N = 0 the population is extinct. Nnew is the population in one year, and Nold is the population in the year before. And λ is what is called a constant.
When λ is less than 1, the population gets smaller and smaller and goes extinct. And when λ is between 1 and 3, the population gets bigger and then it stays stable like this (and these graphs are hypothetical, too)
And when λ is between 3 and 3.57 the population goes in cycles like this
But when λ is greater than 3.57 the population becomes chaotic like in the first graph.
This was discovered by Robert May and George Oster and Jim Yorke. And it means that sometimes things are so complicated that it is impossible to predict what they are going to do next, but they are only obeying really simple rules.
And it means that sometimes a whole population of frogs, or worms, or people, can die for no reason whatsoever, just because that is the way the numbers work.
157. It was six days before I could go back into Father's room to look in the shirt box in the cupboard.
On the first day, which was a Wednesday, Joseph Fleming took his trousers off and went to the toilet all over the floor of the changing room and started to eat it, but Mr. Davis stopped him.
Joseph eats everything. He once ate one of the little blocks of blue disinfectant which hang inside the toilets. And he once ate a £50 note from his mother's wallet. And he eats string and rubber bands and tissues and writing paper and paints and plastic forks. Also he bangs his chin and screams a lot.
Tyrone said that there was a horse and a pig in the poo, so I said he was being stupid, but Siobhan said he wasn't. They were small plastic animals from the library that the staff use to make people tell stories. And Joseph had eaten them.
So I said I wasn't going to go into the toilets because there was poo on the floor and it made me feel uncomfortable to think about it, even though Mr. Ennison had come in and cleaned it up. And I wet my trousers and I had to put on some spare ones from the spare clothes locker in Mrs. Gascoyne's room. So Siobhan said I could use the staff room toilets for two days, but only two days, and then I would have to use the children's toilets again. And we made this a deal.
On the second, third and fourth days, which were Thursday, Friday and Saturday, nothing interesting happened.
On the fifth day, which was a Sunday, it rained very hard. I like it when it rains hard. It sounds like white noise everywhere, which is like silence but not empty.
I went upstairs and sat in my room and watched the water falling in the street. It was falling so hard that it looked like white sparks (and this is a simile, too, not a metaphor). And there was no one around because everyone was staying indoors. And it made me think how all the water in the world was connected, and this water had evaporated from the oceans somewhere in the middle of the Gulf of Mexico or Baffin Bay, and now it was falling in front of the house and it would drain away into the gutters and flow to a sewage station where it would be cleaned and then it would go into a river and go back into the ocean again.
And in the evening on Monday Father got a phone call from a lady whose cellar had flooded and he had to go out and fix it in an emergency.
If there is only one emergency Rhodri goes and fixes it because his wife and his children went to live in Somerset, which means he doesn't have anything to do in the evenings apart from playing snooker and drinking and watching the television, and he needs to do overtime to earn money to send to his wife to help her look after the children. And Father has me to look after. But this evening there were two emergencies, so Father told me to behave and to ring him on his mobile phone if there was a problem, and then he went out in the van.
So I went into his bedroom and opened up the cupboard and lifted the toolbox off the top of the shirt box and opened the shirt box.
I counted the letters. There were 43 of them. They were all addressed to me in the same handwriting.
I took one out and opened it.
Inside was this letter
3rd May
451c Chapter Road
London NW2 5NG
0208 887 8907
Dear Christopher,
We have a new fridge and cooker at last! Roger and I drove to the tip at the weekend to throw the old ones away. It's where people throw everything away. There are huge bins for three differant colours of bottles and cardboard and engine oil and garden waste and household waist and larger items (that's where we put the old fridge and cooker).
Then we went to a secondhand shop and bought a new cooker and a new fridge. Now the house feels a little bit more like home.
I was looking through some old photos last night, which made me sad. Then I found a photo of you playing with the train set we bought for you a couple of Christmas's ago. And that made me happy because it was one of the really good times we had together.
Do you remember how you played with it all day and you refused to go to bed at night because you were still playing with it. And do you remember how we told you about train timetabels and you made a train timetabel and you had a clock and you made the trains run on time. And there was a little woodden station, too, and we showed you how people who wanted to go on the train went to the station and bought a ticket and then got on the train? And then we got out a map and we showed you the little lines which were the trains lines connecting all the stations. And you played with it for weeks and weeks and weeks and we bought you more trains and you knew where they were all going.
I liked remembering that a lot.
I have to go now. It's half past three in the afternoon. I know you always like to know exactly what time it is. And I have to go to the Co-op and buy some ham to make Roger's tea with. I'll put this letter in the post box on the way to the shop.
Love,
Your Mum
x x x x x x
Then I opened another envelope. This was the letter that was inside
Flat 1, 312 Lausanne Rd
London N8 5BV
0208 756 4321
Dear Christopher,
I said that I wanted to explain to you why I went away when I had the time to do it properly. Now I have lots of time. So I'm sitting on the sofa here with this letter and the radio on and I'm going to try and explain.
I was not a very good mother, Christopher. Maybe if things had been different, maybe if you'd been differant, I might have been better at it. But that's just the way things turned out.
I'm not like your father. Your father is a much more pacient person. He just gets on with things and if things upset him he doesn't let it show. But that's not the way I am and there's nothing I can do to change that.
Do you remember once when we were shopping in town together? And we went into Bentalls and it was really crowded and we had to get a Christmas present for Grandma? And you were frightened because of all the people in the shop. It was the middle of Christmas shopping when everyone was in town. And I was talking to Mr. Land who works on the kichen floor and went to school with me. And you crouched down on the floor and put your hands over your ears and you were in the way of everyone. So I got cross, because I don't like shopping at Christmas, either, and I told you to behave and I tried to pick you up and move you. But you shouted and you knocked those mixers off the shelf and there was a big crash. And everyone turned round to see what was going on. And Mr. Land was realy nice about it but there were boxes and bits of broken bowl on the floor and everyone was staring and I saw that you had wet yourself and I was so cross and I wanted to take you out of the shop but you wouldn't let me touch you and you just lay on the floor and screamed and banged your hands and feet on the floor and the maniger came and asked what the problem was and I was at the end of
my tether and I had to pay for two broken mixers and we just had to wait until you stoped screaming. And then I had to walk you all the way home which took hours because I knew you wouldn't go on the bus again.
And I remember that night I just cried and cried and cried and your father was really nice about it at first and he made you supper and he put you to bed and he said these things happen and it would be OK. But I said I couldn't take it anymore and eventually he got really cross and he told me I was being stupid and said I should pull myself together and I hit him, which was wrong, but I was so upset.
We had a lot of argumants like that. Because I often thought I couldn't take any more. And your father is really pacient but I'm not, I get cross, even though I don't mean too. And by the end we stopped talking to each other very much because we knew it would always end up in an argumant and it would go nowere. And I felt realy lonley.
And that was when I started spending lots of time with Roger. I mean obviously we had always spent lots of time with Roger and Eileen. But I started seeing Roger on his own because I could talk to him. He was the only person I could really talk to. And when I was with him I didn't feel lonley anymore.
And I know you might not understand any of this, but I wanted to try to explain, so that you knew. And even if you don't understand now, you can keep this letter and read it later and maybe you might understand then.
And Roger told me that he and Eileen weren't in love with one another anymore, and that they hadn't been in love with one another for a long time. Which meant that he was feeling lonely too. So we had a lot in common. And then we realized that we were in love with one another. And he suggested that I should leave your father and that we should move into a house together. But I said that I couldn't leave you, and he was sad about that but he understood that you were realy important to me.
And then you and me had that argumant. Do you remember? It was about your supper one evening. I'd cooked you something and you wouldn't eat it. And you hadn't eaten for days and days and you were looking so thin. And you started to shout and I got cross and I threw the food across the room. Which I know I shouldn't have done. And you grabbed the chopping board and you threw that and it hit my foot and broke my toes. Then, of course, we had to go to the hospital and I had that plaster put on my foot. And afterward, at home, your father and I had a huge argumant. He blamed me for getting cross with you. And he said I should just give you what you wanted, even if it was just a plate of lettuce or a strawberry milk shake. And I said I was just trying to get you to eat something healthy. And he said you couldn't help it. And I said well I couldn't help it either and I just lost my rag. And he said that if he could keep his temper then I should bloody well keep my temper. And it went on and on like this.
And I couldn't walk properly for a month, do you remember, and your father had to look after you. And I remember looking at the two of you and seeing you together and thinking how you were really differant with him. Much calmer. And you didn't shout at one another. And it made me so sad because it was like you didn't really need me at all. And somehow that was even worse than you and me arguing all the time because it was like I was invisible.
And I think that was when I realized you and your father were probably better off if I wasn't living in the house. Then he would only have one person to look after instead of two.
Then Roger said that he had asked the bank for a transfer. That means he asked them if he could have a job in London, and he was leaving. He asked me if I wanted to come with him. I thought about it for a long time, Christopher. Honestly, I did. And it broke my heart, but eventualy I decided it would be better for all of us if I went. So I said yes.
I meant to say goodbye. I was going to come back and pick up some clothes when you were back from school. And that was when I was going to explain what I was doing and say that I would come back and see you as often as I could and you could come down to London sometimes to stay with us. But when I rang your father he said I couldn't come back. He was really angry. He said I couldn't talk to you. I didn't know what to do. He said that I was being selfish and that I was never to set foot inside the house again. So I haven't. But I have written you these letters instead.
I wonder if you can understand any of this. I know it will be very difficult for you. But I hope you can understand a little.
Christopher, I never meant to hurt you. I thought that what I was doing was the best for all of us. I hope it is. And I want you to know that this is not your fault.
I used to have dreams that everything would get better. Do you remember, you used to say that you wanted to be an astranaut? Well, I used to have dreams where you were an astranaut and you were on the television and I thought that's my son. I wonder what it is that you want to be now. Has it changed? Are you still doing maths? I hope you are.
Please, Christopher, write to me sometime, or ring me on the telephone. The numbers at the top of the letter.
Love and kisses,
Your Mother
x x x x x x
Then I opened a third envelope. This was the letter that was inside
18th September Flat 1
312 Lausanne Road
London N8
0208 756 4321
Dear Christopher,
Well, I said I'd write to you every week, and I have. In fact, this is the second letter this week, so I'm doing even better than I said.
I have got a job! I'm working in Camden, at Perkin and Rashid, which is a Chartered Survayors. That means they go around looking at houses and work out how much they should cost and what work needs to be done on them and how much that work will cost. And also they work out how much new houses and offices and factories will cost to build.
It's a nice office. The other secretary is Angie. Her desk is covered in little teddy bears and furry toys and pictures of her children (so I've put a picture of you in a frame on my desk). She's really nice and we always go out for lunch together.
I don't know how long I'll stay here, though. I have to do a lot of adding up of numbers for when we send bills out to clients and I'm not very good at doing this (you'd be better at it than I am!).
The company is run by two men called Mr. Perkin and Mr. Rashid. Mr. Rashid is from Pakistan and very stern and always wants us to work faster. And Mr. Perkin is weird (Angie calls him Pervy Perkin). When he comes and stands next to me to ask a question he always puts his hand on my sholder and squots down so his face is really near mine and I can smell his toothpaste which gives me the creeps. And the pay is not very good, either. So I shall be looking for something better as soon as I get the chance.
I went up to Alexandra Palace the other day. It's a big park just round the corner from our flat, and the park is a huge hill with a big conference center on the top and it made me think of you because if you came here we could go there and fly kites or watch the planes coming into Heathrow airport and I know you'd like that.
I have to go now, Christopher. I'm writing this in my lunch hour (Angie is off sick with the flu, so we can't have lunch together). Please write to me sometime and tell me about how you are and what your doing at school.
I hope you got the present I sent you. Have you solved it yet. Roger and I saw it in a shop in Camden market and I know you've always liked puzles. Roger tried to get the two pieces apart before we wrapped it up and he couldn't do it. He said that if you managed to do it you were a genius.
Loads and loads of love,
Your Mother
x x x x
And this was the fourth letter
23rd August Flat 1
312 Lausanne Road
London N8
Dear Christopher,
I'm sorry I didn't write last week. I had to go to the dentist and have two of my molars out. You might not remember when we had to take you to the dentist. You wouldn't let anyone put their hand inside your mouth so we had to put you to sleep so that the dentist could take one of your teeth out. Well, they didn't put me to sleep, they just gave me wh
at is called a local anathsetic which means that you can't feel anything in your mouth, which is just as well because they had to saw through the bone to get the tooth out. And it didn't hurt at all. In fact I was laughing because the dentist had to tug and pull and strain so much and it seemed really funny to me. But when I got home the pain started to come back and I had to lie on the sofa for two days and take lots of painkillers . . .
Then I stopped reading the letter because I felt sick.
Mother had not had a heart attack. Mother had not died. Mother had been alive all the time. And Father had lied about this.
I tried really hard to think if there was any other explanation but I couldn't think of one. And then I couldn't think of anything at all because my brain wasn't working properly.
I felt giddy. It was like the room was swinging from side to side, as if it was at the top of a really tall building and the building was swinging backward and forward in a strong wind (this is a simile, too). But I knew that the room couldn't be swinging backward and forward, so it must have been something which was happening inside my head.
I rolled onto the bed and curled up in a ball.
My stomach hurt.
I don't know what happened then because there is a gap in my memory, like a bit of the tape had been erased. But I know that a lot of time must have passed because later on, when I opened my eyes again, I could see that it was dark outside the window. And I had been sick because there was sick all over the bed and on my hands and arms and face.
But before this I heard Father coming into the house and calling out my name, which is another reason why I know a lot of time had passed.
And it was strange because he was calling, “Christopher . . . ? Christopher . . . ?” and I could see my name written out as he was saying it. Often I can see what someone is saying written out like it is being printed on a computer screen, especially if they are in another room. But this was not on a computer screen. I could see it written really large, like it was on a big advert on the side of a bus. And it was in my mother's handwriting, like this