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Chance, Logic and Intuition - Steven Tijms ****

This is very much a book of two halves, the first a history of the development of probability theory and the second examples of where probability goes wrong and an attempt to explain why we're so bad intuitively at estimating chances. Steven Tijms has a rather old-fashioned writing style, which made me think this was a reprint of a book from the 1960s until I hit an entry on Covid-19. This means that the historical section is sometimes a little dry - but strangely, for me, this first half was by far the best part.

The main reason for my preference was originality. Although the 'where probability goes wrong' section is arguably the reason books on probability are so much fun, whether it's dealing with the gambler's or prosecutor's fallacy - or the inevitably Monty Hall problem - Tijms was mostly treading very familiar ground here. However, there were parts of the the history section covering aspects that I've rarely seen before in a popular mathematics text. For example, it's common to start such a history with Cardano, but Tijms gives us the thirteenth century Richard de Fournival, the probable author of a poem originally falsely attributed to Ovid, which includes a description of the probabilities of getting different throws with three dice.

As well as some historical novelties, Tijms gives a lot more focus to the law of large numbers and how we tend to misunderstand it than is usual (not appreciating that large numbers have to be really large in this context - or that a sequence of, say, heads and tails can have a distinct preponderance of one or the other despite the averages tending to 50:50). For me, this was a powerful guide to understanding why we tend to get probability wrong that I have not seen elsewhere.

The book felt like it could have had a better edit - several times it referred to something that had already been covered as if it were a new point - and could have been more engaging in places. I didn't like the way the historical material was described in the present tense. It's also wildly overpriced, so it's one to get from the library. But I think this is a genuinely useful addition to the popular maths coverage of probability.

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Review by Brian Clegg
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  1. Steven Tijms4 September 2021 at 06:24

    For those who find the hardcover too pricey: an affordable paperback version of the book has recently been released as well.

    ReplyDelete

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