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The Fate of Schrodinger's Cat - James Stein ***

This is a difficult book to pin down. It covers a topic I find fascinating - probability and statistics, and specifically applications where these become counter-intuitive. Much of the book focuses on a particular kind of probabilistic outcome where introducing an extra, apparently irrelevant, factor makes seemingly impossible results occur (more on the specifics in a moment). There is no doubt that the result is mind-boggling, yet the way it is presented makes it difficult to get your head around. James Stein is a retired maths professor, and though he makes it clear he is a relative newcomer to statistics, he probably doesn't really understand just how opaque a mathematical discussion can be to the general reader.

The book starts with an old favourite, the Monty Hall problem. The problem itself is well covered by Stein, but he misses an opportunity to give it more bite by bringing in the controversy when Marilyn vos Savant brought this up in Parade Magazine in 1990 and a whole string of PhDs (almost entirely male) told her how wrong she was with her (correct) solution. Stein makes the outcome sound obvious, which it is when you are familiar with it, but most coming to the problem afresh still find it very challenging to get their head around.

With the Monty Hall problem, it is very easy to see what the proposition is, even though many have struggled to accept that it's true. But once Stein gets onto the core problem of the book, which will go on to appear in a range of variants (including the Schrödinger's cat example of the title), the proposition itself could have been explained more clearly. In the problem (Blackwell's bet) you are shown two envelopes with different amounts of money in them. You open one and then are given the opportunity to exchange the amount for the amount (unseen) in the other envelope. The surprising result is that, by comparing the contents of the envelope with an independent random number, such as the temperature, it is possible to make the decision on which envelope to choose and be right more than 50 per cent of the time.

Stein makes it clear that the maths involved to prove this outcome only requires high school algebra - it does - but in reality, getting your head around what the maths is doing, particular as more detail is added for the variants of the problem, is far beyond simple high school level. 

I absolutely love one aspect of this book. Stein makes a very strong argument as to why we should teach students simulation techniques (which are used several times in the book to demonstrate an outcome) rather than algebra. As he says 'Why so much emphasis on teaching something that's basically useless for most people, when learning how to construct models and program computers that teaches them equivalent skills, is far more useful and is about three orders of magnitude more fun.'

A smaller issue I have with a book is that a lot of the examples are taken from sport (which mostly means sports that only Americans play) and if you have no interest in sport, and particularly American sport, it rather puts a dampener on things. Half the time, I had no clue what the sports terminology meant.

Overall, rather too much of the book is focused on variants of the same thing, where I would have liked to see a broader range of challenges. Even so, there's no doubt that Blackwell's bet and its derivatives are truly fascinating, I just wish that they could be appreciated by a wider audience.

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Review by Brian Clegg
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