Skip to main content

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.
Paperback:  
Review by Brian Clegg

Comments

Popular posts from this blog

Rockets and Rayguns - Andrew May ****

The Cold War period saw dramatic developments in science and technology, coinciding with the flourishing of the science fiction genre. In Rockets and Rayguns, Andrew May draws on the parallels between reality and fiction, each influencing the other.

Inevitably a major Cold War theme was the threat of nuclear war, and May opens with the bomb. It's fascinating that fiction got there first - nuclear weapons were featured in science fiction when many physicists were still doubting the practicality of using nuclear energy. Of course, it's a lot easier to simply take a concept and dream up a weapon than it is to make it for real - for example, H. G. Wells' prophetic nuclear bombs from his 1914 The World Set Free were nothing like the real thing. And some science fiction devices concepts - notably ray guns and force fields - came to very little in reality. However this doesn't prevent the parallels being of interest.

May gives us a mix of the science - describing how nuclear we…

Galileo Galilei, the Tuscan Artist – Pietro Greco ****

Near the beginning of John Milton’s epic poem Paradise Lost, he refers to a ‘Tuscan artist’ viewing the Moon through an optic glass. He’s talking about Galileo – one of history’s greatest scientists, but not the most obvious person to slap an ‘artist’ label on. Yet Galileo lived at a time – the Renaissance – when it was fashionable to dabble impartially in both the arts and sciences. Look up ‘Renaissance man’ on Wikipedia and you’ll see Galileo’s picture right there underneath Leonardo da Vinci’s. It’s a less well-known side to his life, but it crops up again and again – interspersed among his many scientific achievements – in this excellent new biography by Pietro Greco.

If you’re looking for interesting trivia, you’ll find plenty in this book. Galileo’s father was a musician with scientific leanings, who carried out some of the first experiments on musical acoustics – which Galileo may have assisted with. As a young professor of mathematics, Galileo delivered a couple of lectures on …

The Ultimate Interplanetary Travel Guide - Jim Bell **

Not too long ago, NASA brought out a series of spoof ‘space tourism’ posters for various destinations in the Solar System. For people like me, who have watched NASA depressingly fail to send humans to the other planets for decade after decade, it was just another painful twist of the knife. On the other hand, the posters probably have more appeal for younger and less cynical minds, by presenting familiar astronomical objects in a new and engaging way. There may even be scope for a whole book along these lines – and that’s what Jim Bell has attempted here.

The main thing I learned from it is that my brain is programmed to read either fiction or non-fiction, and can’t handle a 50:50 mix of the two – which is what this book is. It drove me mad –  not least because I could see that the same material, presented as straight non-fiction, could have made a really excellent book. Using the NASA posters as a starting point, he could have enumerated the potential ‘tourist sights’ at each location…