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Numbercrunch - Oliver Johnson ***

A classic curate's egg of a book. Some aspects of it are brilliant, but there is enough that isn't to make it frustrating. Wisely, Oliver Johnson decided to do a book on very practical aspects of maths - applications that are a wonderful counter to the old moan at school of 'but what use is it to me?' This is great, but two aspects are less positive. One is that this would be a sensible argument if we taught school students this stuff. Just as I think we should teach interesting physics, this is genuinely interesting maths that doesn't necessarily involve more work to learn the basics. But we don't. The second issue is that Johnson decided to do maths without formulae and equations.

This is a common enough practice in popular science, where you can often get away without the mathematics, but in popular maths it is a real stumbling block. When, for example, Johnson is telling us about Bayesian methods - really useful stuff - rather than presenting us a with a very straightforward formula we have to deal with hard-to-grasp wording like using 'the "top divided by bottom-minus-top" rule'. I admit I'm comfortable with mathematical symbols, but getting my head round this kind of presentation was far too like hard work.

Despite this, there's a lot of good material covered. I particularly enjoyed the section looking at gambling odds - I understand probabilities, but I've never been able to get my head round a presentation of these like '3 to 1 on', and Johnson makes this approach clear, pointing out some of its uses (though I still find it less transparent that a straightforward probability). Another example where I got something useful out of it is an exploration of where using logarithmic plots is more effective than straightforward presentation of the numbers. Johnson demonstrates this well, though I feel he is so enamoured with log presentation, that he didn't seem aware of examples such as Moore's law, where the data is almost always presented logarithmically and I think this hides away just how dramatic the growth has been.

We get some good material on the way we struggle with randomness (and its implications), the basics of information theory and the usefulness of understanding Markov chains, the effectiveness of estimation in some cases (and the dubious nature of over-precise numbers) and significantly more. In all this, a little relaxation of the urge to avoid any mathematical representation would have helped.

I did have a couple of other issues that were personal and others might not have found them a problem. Johnson worked mathematically on the COVID pandemic and in all his main topics this features heavily. I find this a particularly unhelpful example to explain the maths because it is so out of or ordinary experience (and feels like a dream world now). The whole point of the book is to illustrate 'what use is it to me?' - it certainly was useful to Johnson and his colleagues in the pandemic, but less so to the rest of us. Of course, we all experienced the pandemic, but not in a way that can be seen as relating to everyday life. Johnson also used a number of sporting examples, which I find off-putting in the extreme - but I appreciate that there are plenty of potential readers who would find them entertaining.

Overall it's a great idea for a book, the areas Johnson cover are fascinating, and he knows his stuff. The book is worth having. But it would have benefited from more awareness of what makes a piece of popular maths writing a good read.

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