This book is a delightful read. You won't want to put it down. It is
like nothing you have ever read. A murder mystery where the victim
is a dog. A lead character with autism that is passionate about
mathematics. A mathematical proof is given in the appendix...and
the list goes on. Even the chapters are numbered differently, but I
don't want to give too much away.
Note: The title is a reference to an entertaining brief dialogue in the Sherlock Holmes story "Silver Blaze".
[Inspector Gregory: "Is there any point to which you would wish to draw my
attention?" Holmes: "To the curious incident of the dog in the night-time."
Inspector: "The dog did nothing in the night-time." Holmes: "That was the
A whole chapter is devoted to The Monty Hall Problem. Towards the end of this chapter, Christopher remarks that "logic can help you work out the right answer." Rather ironically (though the irony will probably be unnoticed by the vast majority of readers), Christopher's answer is wrong, because he assumes (an unstated assumption - very sloppy for someone who aspires to be a mathematician!) that all six theoretically possible outcomes are equally likely. Once you accept that this is not necessarily so, all the mathematical reasoning becomes completely worthless: it all hinges on whether you think the game show host (presumably Monty Hall himself?) is trying to help you or prevent you from winning the car. If the former, then you should definitely switch (if he's wholeheartedly trying to help, he won't offer the possibility of switching if you've already made the right choice); if the latter then you definitely shouldn't. And the only way to determine whether the host is being helpful or not is by using all the things that Christopher is unable to cope with - nuances of voice, body language, and a basic understanding of game show economics and the motivation of game show hosts.
Peter, I do not agree with your assessment of the Monty Hall problem. Both the way the problem is worded and the way it worked on the show, after an initial choice is made, a door is opened revealing a prize which is not the car, and then the contestant is always offered the choice of switching. In particular, being offered the chance to switch does not tell you whether or not your original choice was the car. There is no way (intentionally or unintentionally) that the host can follow these rules and change the fact that you will win the car twice as often by switching after the non-car prize is revealed. For an explanation and a demonstration of this fact, please see my Monty Hall Problem page.
Although I "only" rated it excellent, the book is definitely at the top of the list of excellent. My excellent rating is not related to the math in the book. My wife who is not into math at all liked it a lot as well. It is good because of the unusual voice in which it is told. It is a voice that a mathmatician would understand and appreciate.
The Curious Incident of the Dog at Night Time is one of the best books I have ever read. When I started reading it I couldn't stop! It is a wonderfull story about an average life seen from a different perspective. Through the eyes of a talented autistic boy we learn a lot about his parents, his neighbours, his school, ... Sometimes the book made me laugh and sometimes it made me cry. What fascinated me the most is the fact that different mathematical areas are included. Mathematical fiction usually consists of only one narrow area of mathematics. But this one consist of at least five different mathematical fields. By reading this book we get to know more about autism, we see life from a different perspective and we learn a lot about mathematics. It is one of those books that you simply have to read!
I forgot to add this: After I read it I told my sister that she has to read it! She doesn't like reading so she asked me to tell her what the book is about. It took me more than an hour to tell her everything that I remembered. Which is unusual, because normally it doesn't take me more than 15 minutes to tell the whole plot of the story. What is even more unusual is that my sister, who is not interested in books and stories, kept asking me "What was next?", "Did he make it?", "Did he do it?", "What did he do?", "What did he say?". In my opinion, that is the biggest success of this book - making my sister interested in the story. No other book has done that before.
I enjoyed the first half of this book immensely, but the solution to the whodunnit was revealed half way through, which to me, left the rest of the book a bit aimless. Perhaps I was supposed to be interested in the situation between the boys parents, but as the boy, as the narrator, didn't really have an interest in that, neither did I. If only he'd had to go to London in order to solve the mystery.
An earlier comment about the Monty Hall problem depending on equal probabilities is wrong. Many mathematicians struggle with this one.
The problem is stated like this:
There is a prize behind one of the three doors A,B,C. We don't know which.
We pick a door, Monty opens a door with a goat behind it. Do we switch doors?
Suppose we pick a door at random to begin with and relabel the doors and prizes behind so that we pick door A.
If the prize is behind A, monty opens B or C. When we switch we lose.
If the prize is behind B, monty opens C, we switch to A and win.
If the prize is behind C, monty opens B, we switch to A and win.
There are three scenarios, and in two of them, we win. The only difference Monty can make to that is where he puts the prize to begin with.
What are the relative probabilities of A, B and C?
If we always pick our first choice at random, the relative probabilities will always be one third, whatever Monty does (unless he cheats and starts moving the prizes around), as each combination will include one third of three proabilities that must add to one.
Yes, the Monty Hall problem does seem to confuse people, but it is just a matter of smoke and mirrors. In the end, I don't think it is as complicated as people make it seem. I've written a simple interactive version of it, with explanations, to try to help people understand what is going on. Click here to try it yourself or here my (hopefully simple) explanation.
This book has more interesting math in it than the Monty Hall problem. There is a nice description of "Conway's Soldiers" with some figures describing the narrator's attack on the problem. He mentions that it is not possible to advance a soldier more than 4 steps above the starting line.
This book is also currently being made into a movie by Warner Bros. Let's hope they don't cut out all the math.
I love it how the author writes in an autistic voice.
Peter Grave is thinking of the Monty problem too literally - it is a mathematical problem and has nothing to do with body language of a game show host. The problem is based on the assumption that the contestant is ALWAYS offered the chance to swap. Therefore it seems obvious to me that it is ALWAYS best to swap. I am in no way a professional mathematician but find it hard to understand how a professor of mathematics (multiple examples quoted in the book) could contest the answer.
Quirkie has completely missed the point of the book which I find a shame. The book is primarily about Aspergers syndrome of which I think Mark has accurately and endearingly described the logic behind the seemingly illogical reactions to 'normal' life a person with this condition can display. The book described how awe inspiring a parent's unconditional love for their child can be - especially faced with the extra challenges that raising a child with autistic tendencies can bring.
The tragedy in this story is how the limited perception of the main character (the result of him being a child as much as him having Aspergers Syndrome) causes him to misjudge the situation with his parents completely and misinterpret the actions of his father with heart-wrenching consequences.
I think this is a beautiful book that gives a clever insight into a widely misunderstood condtion and demonstrates how beautiful and solid love can be.