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Sixteen year old Will Sterling is the protagonist of this "coming of age story" that throws just a little math in with the usual teenangst and sexual exploration. The author is very good at letting you get inside Will's thoughts. Clearly, Will thinks he is "broken". He describes himself as a "COD" (Children of the Dead) because his father died when he was young and feels a special affinity for others who have lost a parent. Among his other difficulties, he has to deal with his mother's own insecurities as a lonely widow. However, Will does not seem to be very unusual at all. His descriptions of friends, of school, of his relationships with girlfriends (including a flirtatious relationship with a married older woman) all seem quite ordinary to me. Perhaps it was to add some interest and to differentiate him from other young men that Stein chose to emphasize his interest in mathematics. Presumably, Will's interest in probability is somehow linked to an attempt to stay connected to his father, who had taught the subject. But, it becomes something that Will thinks about and mentions in all sorts of circumstances. Sometimes I like the resulting prose (such as this discussion of his colleagues in the advanced math class):
At other times, I think he gets lost in his attempt at a mathematical metaphor:
Will is able to impress some of the adult characters with his mathematical ability (such as when he is able to determine the number of possible radio station call letters for his mother's boyfriend), but usually the math is just his own internal way of thinking about the world. Unlike some books in which the author is trying to teach the reader something about math, here I think it merely serves the purpose of creating an impression about the character of Will. There is, however, one point in the book where it takes a didactic tone. Towards the end, Will is explaining how statistics is used in experimental science to determine whether something really had an effect. (In other words, when the null hypothesis can be rejected, although he does not use this terminology.) The particular example involves attracting mosquitos, but that doesn't matter. The point is that it is 20 repeated trials of an experiment for which the null hypothesis is that either of the two possible outcomes are equally likely. Will writes that the "geniuses" in his class would use the binomial distribution to work out the probability that the result would be 17 of one outcome to 3 of the other, and correctly concludes that the value is "about" 0.001. Since this seems very unlikely, it is reasonable to conclude that there was something causing the outcome to go one way rather than the other way (although the fact that the probability is positive means that in some rare instances it will turn out to be this way just by chance anyway.) Unforunately, the formula printed in the book is not quite right (the binomial coefficient which is supposed to represent the number of ways of choosing x items out of 20 instead looks like the fraction 20/x) and it actually computes the probability of at least 17 occurrences of one outcome (since it is a sum of the probabilities for 17, 18, 19, and 20...although the latter three are so small that the statement that it is "about 0.001" is true regardless). But the thing that seemed least believable to me is that Will or the geniuses would say "(.5)^{x}(.5)^{20x}" as he does here since this is just (.5)^{20}. But, I wonder, am I missing some big point? This discussion of the mosquito experiment seems to relate back to the earlier quote about "large effects" and "chance" quoted above. He seems to be explaining how you can tell that something did not happen by chance. Speaking mathematically, I would have to say that it is not reasonable to try to apply this idea to the events in your life. Even if the probability of something happening to someone is very small, since there are so many people, there is a good chance that it will happen to someone. (Otherwise, nobody would ever be hit by lightning or win the lottery!) It is different from the experiment situation because you are not looking at the whole population and counting how many times it occurs...you're just looking at yourself (a single trial) and there is nothing you can conclude from that. But, as a reader, I'm wondering if I am missing some big point the author is trying to make. Lots of things happen to Will in the course of the book:his mother finds new boyfriends, he breaks up and makes up with girlfriends, a classmate dies, etc. Are we supposed to conclude that some of these things are the consequence of some identifiable cause? If so, I don't know what it is...and if not then I'm not sure why these discussions appear in the book. Also of possible interest to fans of mathematical fiction is the cover of the book, which shows a cute (feel free to interpret that word as being positive or negative) picture of a face made out of mathematical symbols. Anyway, I agree with the other reviewers that this book does a great job of making you feel like you are Will's true confidant. He shares with you raw details of his life and world view. However, I am not personally a fan of the "coming of age" novel. If, on the other hand, you are the sort of person who enjoys reexperiencing the "joys" of puberty in fictional form and like mathematics besides, then you should definitely give Probabilities a chance. (And when you do, please write in with your own opinions and comments so that I can post them here.)

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