Maths made interesting, even for the number-phobic
Alex Through the Looking Glass, by Alex Bellos, Bloomsbury, £18.99 (ebook, £16.99)
What is your favourite number? Statistically, it is likely to be 7, according to research by Alex Bellos, the author of this follow-up to his popular book on maths, Alex in Numberland.
There are various reasons for this but the Jews played their part with the invention of the seven-day week. There are also the seven deadly sin, the seven seas and the seven dwarfs. Odd numbers are psychologically more attractive to many of us and in certain cultures they dominate — you will look in vain for a plate with an even number of sushi in a Japanese restaurant.
However, the significance of numbers, and their order, goes well beyond the psychological. If you look at any data, from the Domesday Book to stats in the FT, you will see that 1 is the most common number, 2 is the second most common, 3 the third most common.
Not only that but their ratio is pretty much constant: 1 will occur around 30 per cent of the time, 2 around 18 per cent and so on. This, I discovered, was Benford’s Law and has applications in forensic accounting. If the numbers in a financial report are out of synch, it is a pretty good guess that someone is fiddling the books. This is the first “wow” moment in the book but by no means the last.
For example, there is the story of Eratosthenes who, by using a staff to measure the shadow of the sun, then measuring its distance from a famous well in Cyrene, drew a triangle which enabled him to measure the circumference of the world. He was ultimately only about 1,000 miles out with his calculations — not bad for an ancient Greek without GPS. The same principle of trigonometry has enabled us to measure entire countries and calculate the height of Everest.
Bellos writes in an engaging, journalistic style which draws in even those of us who are maths-phobic.There is a point in most chapters when I was faced with a page packed with equations, bringing back the dread of O-Level maths but, even for the most dyscalculic, there are plenty of examples that bring mathematics to life.
For example, to explain the concept of exponential growth, Bellos advises you to start folding a piece of paper. Each fold doubles the thickness. After only seven folds, the paper will be the thickness of a 256-page book and it would be physically impossible to fold it further. But, if you could continue, 12 folds later it would reach 3km into the sky. The paper reaches the moon after 42 folds. No maths teacher ever told me this. Why not?
And for those of us who have sometimes found numbers boring, Bellos demonstrates this not to be the case in his chapter on mathematical proof. If numbers are not interesting, he reasons that there must be a smallest boring number — and this would be interesting just because it is the smallest boring number.
Of course, some chapters are more accessible than others for the numerically challenged. Despite having read the chapter on calculus, I still have only the vaguest idea what it is. And, even if the book’s title is somewhat contrived — Alex in Numberland 2 might have been more appropriate — Bellos remains the best maths teacher I never had.
Simon Round is a freelance writer who failed his Maths O-level