100 Essential Things You Didn't Know You Didn't Know by John D. Barrow
Need a Christmas present for someone who likes interesting facts, with a mathematical flavour? Then this is the book. John D. Barrow is a mathematician/physicist at Cambridge University, who has given us a pot-pourri of intriguing things, with something for everyone who likes elementary physics, or is intrigued by various ways of counting.
In 100 short chapters, he covers plenty of ground, some of it in more than one way. He’s at home with different schemes for deciding the winner of an election, and in one case shows how an obvious loser under a preferential voting scheme wins under a suitably contrived counting system. If you prefer purer knowledge, he gives a proof of Pythagoras’s theorem devised by the US President James Garfield. And if you prefer more practical things, he gives a far more efficient method of boarding a plane than the one to which we are used.
Among my favourites is the chapter about why a tight-rope walker carries a long pole. I used to think it was because it lowered the centre of gravity, but not at all. As Barrow explains it’s all to do with inertia, and in this context he gives the example of two balls of the same diameter and weight. In one the mass is evenly distributed, while the other is hollow and the mass is all concentrated near the surface. Which one rolls more easily down an incline? The first person I asked, who has a degree in mechanical engineering, got the wrong answer.
Here is another favourite, this one about pure physics, or even philosophy. If some modern theories of the universe are correct, we live not in a single universe, but a “multiverse”. Some of the universes of this multiverse will contain beings more intelligent than us. While we can use computers to simulate things such as the weather, or the formation of galaxies, they might simulate a whole universe. How do we know we are not simply occupants in one of their simulations?
If you want to keep your feet more firmly on the ground, did you know that Olympic high-jumpers clear such high bars by getting their bodies over while the centre of gravity goes under? Sounds impossible, but Barrow explains and gives the historical context. If you like sport, there is plenty more where this comes from, including a 1994 football match between Grenada and Barbados that turned into a challenge to score own goals just before the 90th minute, in order to obtain, or obviate the need for, extra time.
However, if you prefer simple things you can test at home, why does spaghetti break in at least three pieces when you snap it? How is a diamond cut to give it such brilliance? And what happens if you toss a tennis racket in the air so it does a somersault through 360 degrees? Make a chalk mark on the top side and you’ll find it flips from top to bottom. Amazing? But it’s told in connection with the very serious problem of how to stabilise the international space station that was knocked into a spin while docking with a Russian supply craft. My only complaint is the word essential in the title; perhaps not essential, but certainly fun.