dog 101

in chapter 101 of "the curious incident of the dog in the night-time" by mark haddon (the chapters are numbered after prime numbers rather than consecutively) the precocious, 'Asperger's syndrome' narrator, Christopher, explains what is known as the 'Monty Hall problem', a question about conditional probabilities phrased in the terms of a game show where you are offered the chance to switch doors and potentially improve your prize. this chapter is slightly strange.
christopher explains the problem well, and the solution as well as, if not better than, at least one account of it i have seen in a popular maths book.
(like excuses, explanations are never quite so convincing when you need more than one of them.) he exposes (and solves) quite a few other interesting maths problems in the book. his purpose is this chapter is given by the opening paragraph(s):
Mr Jeavons said that I liked maths because it was safe. He said I liked maths because it meant solving problems, and these problems were difficult and interesting, but there was always a straightforward answer at the end. And what he meant was that maths wasn't like life because in life there are no straightforward answers at the end. I know he meant this because this is what he said.
This is because Mr Jeavons doesn't understand numbers.
Here is a famous story called The Monty Hall Problem which I have included in this book because it illustrates what I mean.

you can find this problem very easily ("as Eugene Northrop observes in his Riddles in Mathematics, it 'has been used as an illustrative example in almost every subsequent textbook'", The Magical Maze, Ian Stewart) if you want to see if you can understand it and avoid making the obvious mistake that is what the problem is all about. christopher goes on to quote several letters from people at universities, some with Phds, who wrote to tell a popular maths writer her solution to the problem was wrong (when in fact and of course it was correct).

I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.
Robert Sachs, PhD., George Mason (?) University

these quotes to me make very little sense. the story is such a classic, a cliche and a cautionary legend, that it would maybe need further justification to recount it here. the frets and foibles of PhDs are perhaps a long way removed from the concern of 15 yr-old autistic children, however good at maths they may be. and do we not learn every time we do maths that the more straightforward our answer (and, if it is maths, straightforward it _must_ be), the more complex its relation to the world of real problems?
since my own opinion leans more and more towards the idea that mathematics is simply the study of certain properties of the mind, the imagination, and parts of our cultural heritage, i find it difficult to speculate on its meaning to others.
all i know is that parts of this narration ring slightly false, that the author here seems to burst through the voice of the narrator like a small child who wishes to tell us something, and that those of us who look for solutions in maths, rarely dare to hope for simplicity.

My girlfriend got this book for Christmas but hasn't read it, so I can't really comment on the story or storytelling, but I am pretty familiar with the uproar over the Monty Hall problem. It's pretty strange, really. I mean, it's easy to get the solution to the problem wrong when you're just idly thinking about it, but once you see a 'mathematical' (conditional probability and Baye's Theorem and whatnot) explanation, it makes perfect sense.

So, to summarize, there's no shame in not getting it write, even if you're a mathematician, but once it's explained (mathematically) to a mathematician, there should really be no doubt. I just fail to see how there was, like, almost a civil war just because Marilyn vos Savant (it was her column, right?) is a jerk and so are some mathematicians.

--Mike Sheffler
... turning to the 3-D map, we see an unmistakable cone of ignorance
true say.
the 'controversy' is bollocks. the question is only interesting until you understand it, then it becomes trivial.
the only interest to the story is that if you didn't already know that maths professors and such like sometimes make obvious mistakes: well they do.
what i found strange is that the narrator of this story would want to make such a point.
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