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Review - Chaos: A Very Short Introduction - Leonard Smith

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Chaos theory is one of those subjects that pretty well everyone has a vague idea about, but few understand what it really does. Most of us will think "butterfly flaps wings and causes storm the other side of the world" or "Jeff Goldblum as crazy mathematician in Jurassic Park watching water ripples caused by T. Rex stomping"... but don't really have a good picture of what chaos is all about. It's great to see this book because it really fills in the final segment of a four part jigsaw of the understanding of chaos theory for beginners (as far as I'm concerned).

If you are a chaos virgin and want to find out more, I'd recommend the following path to enlightenment. First read the weird and wonderful Introducing Chaos. You won't get any great insights from this book, but it will lay a little groundwork and acts as a brilliant teaser for reading further. Then read Chaos by James Gleick. This is a biography of the opening up of chaos theory with a brilliant portrayal of the key characters involved. Then move on to Cohen & Stewart's The Collapse of Chaos, which illustrates why the initial bright hopes for chaos theory weren't to be resolved, and why complexity is, erm, less complex than chaos. Finally, the subject of this review, Leonard Smith's Chaos (part of the Oxford Very Short Introduction series) will give you the clearest (but not too painful) idea of the maths involved and explores the practical uses of chaos theory, particularly in weather forecasting and astronomy.

That's the ideal research route - but if you want to cut it down a little, I'd still start with Introducing Chaos if possible, because that book does a better job of introducing the nature of chaos in a "wow, gee-whiz" way, where Smith's book is more matter-of-fact and down to earth. In fact just the sort of book you'd expect to come out of the British school of weather forecasting: sober, slight twinkle in the eye, but largely conservative with a small C. There's a lot packed into this little book, and for such a technical exploration it's surprisingly readable and enjoyable - I really wanted to keep turning the pages.

I do have a few small points of advice for any future books along this line. Drop the irritating schema of putting keywords in bold, indicating they should be looked up in the glossary. Only badly written books need glossaries. Be careful of how you use technical jargon. If the jargon makes sense in English, that's fine. So words like series and sequence can be used without harm. But if the word has a different meaning in English, avoid it. Use an alternative, even if it doesn't have quite the right mathematical fit. So, for instance, Smith regularly uses the word "ensemble". This has very specific meanings in normal English which don't fit with the mathematical use, so it should have been avoided. Finally, Smith has clearly heard that you lose some percentage or other of readers for every equation in a book, so avoids them. This is fine, but if you are going to take this approach you should go the whole hog and avoid equations (and the evil X's, i's, alpha's and the like) in any form. Smith adopts a strange hybrid where he does use equations, but writes them out in English (for example: "X squared multiplied by 1 minus a random number selected from a bell curve") which is, frankly, more confusing than just about any alternative.

Because of these foibles it does help to have a little mathematical knowledge to cope with this book, but even so I would strongly recommend it for anyone who wants to get a better feeling for chaos theory, and particularly its relevance to the real world. Smith also has some excellent words of wisdom about common misunderstandings of chaos theory, like the old chestnut that it's impossible to describe a chaotic system mathematically, or to make effective forecasts where chaos is involved. One of the best books so far in this useful and informative series.

Only in paperback.

Schema: A theoretical construction and hence a pseudo-intellectual and unnecessary way to refer to a printing style or convention in a book.

Reviewed by Brian Clegg

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Last update 05 June 2007