by Mark Haddon
Scott Smith, Ph.D., University of Florida
I am in shock that after being corrected by at least three mathematicians, you still do not see your mistake.
Kent Ford, Dickinson State University
I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for help with future columns.
W. Robert Smith, Ph.D., Georgia State University
You are utterly incorrect . . . How many irate mathematicians are needed to get you to change your mind?
E. Ray Bobo, Ph.D., Georgetown University
If all those Ph.D.'s were wrong, the country would be in very serious trouble.
Everett Harman, Ph.D., U.S. Army Research Institute
But Marilyn vos Savant was right. And here are 2 ways you can show this.
Firstly you can do it by maths like this
* * *
Let the doors be called X, Y and Z.
Let Cx be the event that the car is behind door X and so on.
Let Hx be the event that the host opens door X and so on.
Supposing that you choose door X, the possibility that you win a car if you then switch your choice is given by the following formula
P(HZ ^ CY) + P(HY ^ CZ)
= P(CY)•P (HZ| CY) + P(CZ)•P(HY | CZ)
= (1⁄3 • 1) + (1⁄3 • 1) = 2⁄3
Let the doors be called X, Y and Z.
Let Cx be the event that the car is behind door X and so on.
Let Hx be the event that the host opens door X and so on.
Supposing that you choose door X, the possibility that you win a car if you then switch your choice is given by the following formula
P(HZ ^ CY) + P(HY ^ CZ)
= P(CY)•P (HZ| CY) + P(CZ)•P(HY | CZ)
= (1⁄3 • 1) + (1⁄3 • 1) = 2⁄3
* * *
The second way you can work it out is by making a picture of all the possible outcomes like this
So if you change, 2 times out of 3 you get a car. And if you stick, you only get a car 1 time out of 3.
And this shows that intuition can sometimes get things wrong. And intuition is what people use in life to make decisions. But logic can help you work out the right answer.
It also shows that Mr. Jeavons was wrong and numbers are sometimes very complicated and not very straightforward at all. And that is why I like The Monty Hall Problem.
103. When I got home Rhodri was there. Rhodri is the man who works for Father, helping him do heating maintenance and boiler repair. And he sometimes comes round to the house in the evening to drink beer with Father and watch the television and have a conversation.
Rhodri was wearing a pair of white dungarees which had dirty marks all over them and he had a gold ring on the middle finger of his left hand and he smelled of something I do not know the name of which Father often smells of when he comes home from work.
I put my licorice laces and my Milky Bar in my special food box on the shelf, which Father is not allowed to touch because it is mine.
Then Father said, “And what have you been up to, young man?”
And I said, “I went to the shop to get some licorice laces and a Milky Bar.”
And he said, “You were a long time.”
And I said, “I talked to Mrs. Alexander's dog outside the shop. And I stroked him and he sniffed my trousers.” Which was another white lie.
Then Rhodri said to me, “God, you do get the third degree, don't you.”
But I didn't know what the third degree was.
And he said, “So, how are you doing, captain?”
And I said, “I'm doing very well, thank you,” which is what you're meant to say.
And he said, “What's 251 times 864?”
And I thought about this and I said, “216,864.” Because it was a really easy sum because you just multiply 864 × 1,000, which is 864,000. Then you divide it by 4, which is 216,000, and that's 250 × 864. Then you just add another 864 onto it to get 251 × 864. And that's 216,864.
And I said, “Is that right?”
And Rhodri said, “I haven't got a bloody clue,” and he laughed.
I don't like it when Rhodri laughs at me. Rhodri laughs at me a lot. Father says it is being friendly.
Then Father said, “I'll stick one of those Gobi Aloo Sag things in the oven for you, OK?”
This is because I like Indian food because it has a strong taste. But Gobi Aloo Sag is yellow, so I put red food coloring into it before I eat it. And I keep a little plastic bottle of this in my special food box.
And I said, “OK.”
And Rhodri said, “So, it looks like Parky stitched them up, then?” But this was to Father, not to me.
And Father said, “Well, those circuit boards looked like they'd come out of the bloody ark.”
And Rhodri said, “You going to tell them?”
And Father said, “What's the point? They're hardly going to take him to court, are they?”
And Rhodri said, “That'll be the day.”
And Father said, “Best to let sleeping dogs lie, I reckon.”
Then I went into the garden.
Siobhan said that when you are writing a book you have to include some descriptions of things. I said that I could take photographs and put them in the book. But she said the idea of a book was to describe things using words so that people could read them and make a picture in their own head.
And she said it was best to describe things that were interesting or different.
She also said that I should describe people in the story by mentioning one or two details about them so that people could make a picture of them in their head. Which is why I wrote about Mr. Jeavons's shoes with all the holes in them and the policeman who looked as if he had two mice in his nose and the thing Rhodri smelled of but I didn't know the name for.
So I decided to do a description of the garden. But the garden wasn't very interesting or different. It was just a garden, with grass and a shed and a clothesline. But the sky was interesting and different because usually skies look boring because they are all blue or all gray or all covered in one pattern of clouds and they don't look like they are hundreds of miles above your head. They look like someone might have painted them on a big roof. But this sky had lots of different types of clouds in it at different heights, so you could see how big it was and this made it look enormous.
Furthest away in the sky were lots of little white clouds which looked like fish scales or sand dunes which had a very regular pattern.
Then next furthest away and to the west were some big clouds which were colored slightly orange because it was nearly evening and the sun was going down.
Then closest to the ground was a huge cloud which was colored gray because it was a rain cloud. And it was a big pointy shape and it looked like this
And when I looked at it for a long time I could see it moving very slowly and it was like an alien spaceship hundreds of kilometers long, like in Dune or Blake's 7 or Close Encounters of the Third Kind, except that it wasn't made of solid material, it was made of droplets of condensed water vapor, which is what clouds are made of.
And it could have been an alien spaceship.
People think that alien spaceships would be solid and made of metal and have lights all over them and move slowly through the sky because that is how we would build a spaceship if we were able to build one that big. But aliens, if they exist, would probably be very different from us. They might look like big slugs, or be flat like reflections. Or they might be bigger than planets. Or they might not have bodies at all. They might just be information, like in a computer. And their spaceships might look like clouds, or be made up of unconnected objects like dust or leaves.
Then I listened to the sounds in the garden and I could hear a bird singing and I could hear traffic noise which was like the surf on a beach and I could hear someone playing music somewhere and children shouting. And in between these noises, if I listened very carefully and stoo
d completely still, I could hear a tiny whining noise inside my ears and the air going in and out of my nose.
Then I sniffed the air to see if I could see what the air in the garden smelled like. But I couldn't smell anything. It smelled of nothing. And this was interesting, too.
Then I went inside and fed Toby.
107. The Hound of the Baskervilles is my favorite book.
In The Hound of the Baskervilles, Sherlock Holmes and Doctor Watson get a visit from James Mortimer, who is a doctor from the moors in Devon. James Mortimer's friend, Sir Charles Baskerville, has died of a heart attack and James Mortimer thinks that he might have been scared to death. James Mortimer also has an ancient scroll which describes the curse of the Baskervilles.
On this scroll it says that Sir Charles Baskerville had an ancestor called Sir Hugo Baskerville, who was a wild, profane and godless man. And he tried to do sex with a daughter of a yeoman, but she escaped and he chased her across the moor. And his friends, who were daredevil roisterers, chased after him.
And when they found him, the daughter of the yeoman had died of exhaustion and fatigue. And they saw a great black beast, shaped like a hound yet larger than any hound that ever mortal eye has rested on, and this hound was tearing the throat out of Sir Hugo Baskerville. And one of the friends died of fear that very night and the other two were broken men for the rest of their days.
James Mortimer thinks that the Hound of the Baskervilles might have scared Sir Charles to death and he is worried that his son and heir, Sir Henry Baskerville, will be in danger when he goes to the hall in Devon.
So Sherlock Holmes sends Doctor Watson to Devon with Sir Henry Baskerville and James Mortimer. And Doctor Watson tries to work out who might have killed Sir Charles Baskerville. And Sherlock Holmes says he will stay in London, but he travels to Devon secretly and does investigations of his own.
And Sherlock Holmes finds out that Sir Charles was killed by a neighbor called Stapleton who is a butterfly collector and a distant relation of the Baskervilles. And Stapleton is poor, so he tries to kill Sir Henry Baskerville so that he will inherit the hall.
In order to do this he has brought a huge dog from London and covered it in phosphorus to make it glow in the dark, and it was this dog which scared Sir Charles Baskerville to death. And Sherlock Holmes and Watson and Lestrade from Scotland Yard catch him. And Sherlock Holmes and Watson shoot the dog, which is one of the dogs which gets killed in the story, which is not nice because it is not the dog's fault. And Stapleton escapes into the Grimpen Mire, which is part of the moor, and he dies because he is sucked into a bog.
There are some bits of the story I don't like. One bit is the ancient scroll because it is written in old language which is difficult to understand, like this
Learn then from this story not to fear the fruits of the past, but rather to be circumspect in the future, that those foul passions whereby our family has suffered so grievously may not again be loosed to our undoing.
And sometimes Sir Arthur Conan Doyle (who is the author) describes people like this
There was something subtly wrong with the face, some coarseness of expression, some hardness, perhaps of eye, some looseness of lip which marred its perfect beauty.
And I don't know what some hardness, perhaps of eye means, and I'm not interested in faces.
But sometimes it is fun not knowing what the words mean because you can look them up in a dictionary, like goyal (which is a deep dip) or tors (which are hills or rocky heights).
I like The Hound of the Baskervilles because it is a detective story, which means that there are clues and Red Herrings.
These are some of the clues
1. Two of Sir Henry Baskerville's boots go missing when he is staying at a hotel in London. This means that someone wants to give them to the Hound of the Baskervilles to smell, like a bloodhound, so that it can chase him. This means that the Hound of the Baskervilles is not a supernatural being but a real dog.
2. Stapleton is the only person who knows how to get through the Grimpen Mire and he tells Watson to stay out of it for his own safety. This means that he is hiding something in the middle of the Grimpen Mire and doesn't want anyone else to find it.
3. Mrs. Stapleton tells Doctor Watson to “go straight back to London instantly.” This is because she thinks Doctor Watson is Sir Henry Baskerville and she knows that her husband wants to kill him.
And these are some of the Red Herrings
1. Sherlock Holmes and Watson are followed when they are in London by a man in a coach with a black beard. This makes you think that the man is Barrymore, who is the caretaker at Baskerville Hall, because he is the only other person who has a black beard. But the man is really Stapleton, who is wearing a false beard.
2. Selden, the Notting Hill murderer. This is a man who has escaped from a prison nearby and is being hunted down on the moors, which makes you think that he has something to do with the story, because he is a criminal, but he hasn't anything to do with the story at all.
3. The Man on the Tor. This is a silhouette of a man that Doctor Watson sees on the moor at night and doesn't recognize, which makes you think it is the murderer. But it is Sherlock Holmes who has come to Devon secretly.
I also like The Hound of the Baskervilles because I like Sherlock Holmes and I think that if I were a proper detective he is the kind of detective I would be. He is very intelligent and he solves the mystery and he says
The world is full of obvious things which nobody by any chance ever observes.
But he notices them, like I do. Also it says in the book
Sherlock Holmes had, in a very remarkable degree, the power of detaching his mind at will.
And this is like me, too, because if I get really interested in something, like practicing maths, or reading a book about the Apollo missions or great white sharks, I don't notice anything else and Father can be calling me to come and eat my supper and I won't hear him. And this is why I am very good at playing chess, because I detach my mind at will and concentrate on the board and after a while the person I am playing will stop concentrating and start scratching their nose, or staring out of the window, and then they will make a mistake and I will win.
Also Doctor Watson says about Sherlock Holmes
His mind . . . was busy in endeavouring to frame some scheme into which all these strange and apparently disconnected episodes could be fitted.
And that is what I am trying to do by writing this book.
Also Sherlock Holmes doesn't believe in the supernatural, which is God and fairy tales and Hounds of Hell and curses, which are stupid things.
And I am going to finish this chapter with two interesting facts about Sherlock Holmes
1. In the original Sherlock Holmes stories Sherlock Holmes is never described as wearing a deerstalker hat, which is what he is always wearing in pictures and cartoons. The deerstalker hat was invented by a man called Sidney Paget, who did the illustrations for the original books.
2. In the original Sherlock Holmes stories Sherlock Holmes never says “Elementary, my dear Watson.” He only ever says this in films and on the television.
109. That night I wrote some more of my book, and the next morning I took it into school so that Siobhan could read it and tell me if I had made mistakes with the spelling and the grammar.
Siobhan read the book during morning break when she has a cup of coffee and sits at the edge of the playground with the other teachers. And after morning break she came and sat down next to me and said she had read the bit about my conversation with Mrs. Alexander and she said, “Have you told your father about this?”
And I replied, “No.”
And she said, “Are you going to tell your father about this?”
And I replied, “No.”
And she said, “Good. I think that's a good idea, Christopher.” And then she said, “Did it make you sad to find this out?”
And I asked, “Find what out?”
And she said, “Did it make y
ou upset to find out that your mother and Mr. Shears had an affair?”
And I said, “No.”
And she said, “Are you telling the truth, Christopher?”
And then I said, “I always tell the truth.”
And she said, “I know you do, Christopher. But sometimes we get sad about things and we don't like to tell other people that we are sad about them. We like to keep it a secret. Or sometimes we are sad but we don't really know we are sad. So we say we aren't sad. But really we are.”
And I said, “I'm not sad.”
And she said, “If you do start to feel sad about this, I want you to know that you can come and talk to me about it. Because I think talking to me will help you feel less sad. And if you don't feel sad but you just want to talk to me about it, that would be OK, too. Do you understand?”
And I said, “I understand.”
And she said, “Good.”
And I replied, “But I don't feel sad about it. Because Mother is dead. And because Mr. Shears isn't around anymore. So I would be feeling sad about something that isn't real and doesn't exist. And that would be stupid.”
And then I practiced maths for the rest of the morning and at lunch I didn't have the quiche because it was yellow, but I did have the carrots and the peas and lots of tomato ketchup. And for afters I had some blackberry and apple crumble, but not the crumble bit because that was yellow, too, and I got Mrs. Davis to take the crumble bit off before she put it onto my plate because it doesn't matter if different sorts of food are touching before they are actually on your plate.
Then, after lunch, I spent the afternoon doing art with Mrs. Peters and I painted some pictures of aliens which looked like this
113. My memory is like a film. That is why I am really good at remembering things, like the conversations I have written down in this book, and what people were wearing, and what they smelled like, because my memory has a smelltrack which is like a soundtrack.