Thursday, 19 October 2006

Coincidences, Chaos and all that Math Jazz – Edward B. Burger & Michael Starbird ****

It’s not often someone manages to write a book on the topic of maths and makes it light, easy going and fun – yet Edward Burger and Michael Starbird have done just that.
In a relatively slim volume, the authors manage to cover a whole host of topics, without ever becoming terrifying. It’s not just the probability and chaos theory suggested by the title – though of course they make an appearance – but much more. Often, without resorting to formulae, there are simple, clear examples – for example, when dealing with chaos there is a demonstration of how easily number sequences can deviate that uses Excel as the generator of the chaotic sequence.
Again, series are illustrated using a wonderful physical example involving stacking playing cards that seems absolutely impossible if seen through the eyes of common sense – as often is the case with good popular maths, common sense, which is hopeless at maths, takes a battering. There’s a good section on topology too, a subject that is rarely well explained in popular books which tend to make confusing statements like telling the reader that a doughnut is the same topologically as a tea cup without explaining why, or spotting that this is only true of some doughnuts and some cups. Burger & Starbird manage to get the message across while maintaining the precision required for maths.
I do have one hesitation about this book. Because it has such a breezy manner, and speeds through topics so lightly, it can sometimes oversimplify. Sometimes surprising mathematical results are just stated plonkingly, without explaining why it’s the case. Elsewhere, the high speed delivery results in information that is only partially true. Take the example of airline safety. After pointing out how easy it is to misuse statistics, this is arguably what the authors proceed to do. They compare deaths per passenger mile by plane and deaths per passenger mile by car. But this overlooks the fact that more fatal crashes take place in the take off/climb and descent/landing parts of the journey than do in the cruise segment – distance isn’t the issue with airline crashes, it’s number of take-offs and landings.
If, instead, you make a comparison of the chance of being killed on a single journey in a plane with the chance of being killed on a single journey in a car (and most people want to know “will I survive this journey?”), then the car is actually safer. Taken over a year, of course, there are many more car journeys, so the plane becomes safer – but the difference between the two modes of transport is much less significant than basing the comparison on deaths per mile. The authors also take a rather parochial view, arguing that if people didn’t fly they would drive. This may be true in the US, but in most of the world, the long distance alternative is likely to be don’t go at all, or go by train. Try driving from London to New York. This, then, was an unfortunate example to use, because it hides a huge can of worms.
Such problems, though, are few and far between. This a great across-the-board intro to the fun of maths. Having read it, I would then recommend the reader to find a good popular book to get more depth on any topics of interest (for instance, my own A Brief History of Infinity inevitably goes into a lot more than is possible in this book’s short dabble with infinity) – but do start here.
Review by Brian Clegg

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