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A Mathematician Reads the Newspaper by John Allen PaulosA Mathematician Reads the Newspaper, John Allen Paulos (Penguin 1996)

Ah, unrequited love. I love maths, but maths doesn’t love me. Still, it likes me enough for me to learn a lot from books like this. And I, like most people, do need to learn a lot about maths, because not knowing about it can lead you to make all sorts of mistakes and fall into all kinds of misunderstandings.

So we need more writers like the mathematician John Allen Paulos, who knows a lot about maths and can express what he knows simply and entertainingly. This book is one of those that divide your life into BR and AR – Before Reading and After Reading – because it changes the way you look at the world.

Take politics and important questions like the way we vote and the way power blocs work. Paulos examines all sorts of paradoxes and contradictions in both and you should come out of that section understanding the imperfections and dangers of democracy a lot better. You’ll also know that it’s possible to create a set of four dice, A, B, C, and D, in which A beats B, B beats C, C beats D, and D beats A. Impossible? No, it’s very simple – once you know how.

Or take the horrors of discrimination in terms of issues around race and gender. Women are about 50% of the British population and non-whites are about 10% and you should therefore expect them to be 50% and 10%, respectively, of MPs or judges or disc-jockeys or senior managers in confectionery factories, shouldn’t you? And if they aren’t, that’s clear proof of discrimination, isn’t it?

Paulos’s answers are, respectively, no, not necessarily, and no, not necessarily. What is true of a general population is not always true of its extremes:

As an illustration, assume that two population groups vary along some dimension – height, for example. Although it is not essential to the argument, make the further assumption that the two groups’ heights vary in a normal or bell-shaped manner. Then even if the average height of one group is only slightly greater than the average height of the other, people from the taller group will constitute a large majority among the very tall (the right tail of the curve). Likewise, people from the shorter group will constitute a large majority among the very short (the left tail of the curve). This is true even though the bulk of the people from both groups are of roughly average stature. Thus if group A has a mean height of 5’8” and group B has a mean height of 5’7”, then (depending on the exact variability of the heights) perhaps 90 percent or more of the those over 6’2” will be from group A. In general, any differences between two groups will always be greatly accentuated at the extremes.

Discrimination undoubtedly exists, but where it exists, who it’s being exercised against and how much of an effect it has are not questions that can always be answered in simple ways. Paulos even describes how taking measures against discrimination can make its supposed effects worse.

Look before you leap, in other ways, and look with mathematically trained eyes. It will help you in all sorts of ways, from not being taken in by fallacious political arguments to not being ripped off. Suppose, Paulos asks, a pile of potatoes is left out in the sun. It’s 99% water and weighs 100 pounds. A day later, it’s 98% water. How much does it weigh now?

If you can’t work out the answer then you might be on your way to losing a lot of money if a conman looks after your money or investments. Paulos explains the answer – which, surprisingly (or not), is 50 pounds – very clearly and simply, the way he explains the answers of all the other little puzzles he drops into the text as he discusses gossip, celebrity, cooking, bargains, infectious disease, and a host of other subjects that maths can either illuminate or obfuscate, depending on how well you understand it and the logic that underlies it.

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The talkSPORT Book of Premier League Legends, Bill Burrows with Derek Hammond

I’m interested in art, I’m interested in maths, I’m interested in biology. How could I not be interested in football? Easily. But I am interested in football and I enhance my appreciation by looking for aesthetic, mathematical, and biological patterns in the game. Sometimes they’re easy to see: the curve of a Beckham cross combines both art and maths; the under- and over-representation of blacks as goalkeepers and forwards, respectively, says something interesting about human biology. So, less obviously, do football’s origins in the rule-worshipping, world-conquering folk of nineteenth-century Britain. Football and English are Britain’s two most popular exports, though if football spoke English it would have an odd accent, sounding as much Celtic as Saxon and more European than either. This book reflects that: the top ten legends in an English league consist of a Scot, a Welshman, a Dutchman, an Italian, two Frenchmen, and four Englishmen, at least one of whom has Irish ancestry. That’s discarding the Russian at number 7, Chelsea’s billionaire owner Roman Abramovich, who isn’t a player or a manager. And hasn’t necessarily been good for the game. Fernando Torres, the Spanish legend at 77, is a good player, but was he worth £50m of Mr Abramovich’s hard-insider-dealt cash?

More pertinently, is Torres a legend? I wouldn’t say so, but hype is a keyly core, and corely key, component of modern football. “Premier League” is marketese for “First Division”, after all, and talkSPORT is a commercial radio station. I’ve barely listened to it, but the impression I got made me pick up this book expecting a lot of exclamation marks and a lot of illiteracy. I didn’t get either: the potted biographies of the legends, both for the league as a whole and for individual clubs, are well-written and interesting, though Borrows or his simul-scribe should learn what a hanging participle is. There are blasts from the past, like Georgie Kinkladze of Manchester City, who were then dosh-dry, not dosh-drenched, and current comets, like Wayne Rooney of Manchester United, who have been dosh-drenched for decades. Kinkladze was Georgian, Rooney is Anglo-Irish, and both challenge the genetic theory that links athletic ability to symmetry and symmetry to attractiveness. In fact, Rooney’s challenge threatens to break both its legs: he plays like an angel and looks like an orc. But I think his body, if not his face, would support the theory and biology is about tendencies, not absolutes. For example, men are taller than women, on average, and that has great biological significance. The significance doesn’t disappear because some women are a lot taller than some men.

Some women are also a lot better at running and jumping than some men, but that doesn’t change the statistics. At the extremes – the far tails of the bell-curve – one sex can hugely outnumber another and this book is about human beings who have exceptional athletic ability. Accordingly, although the average man is not hugely more athletic than the average woman, the only woman who turns up here is Delia Smith, the TV-chef and Norwich City benefactrix who clocks in as legend no. 99. But, just as cooking involves more than a sensitive palate, football involves more than athleticism. A footballer’s brain has to deal with much more than a sprinter’s, so running ability isn’t all a footballer needs. Sometimes he can do without it: legend no. 6, David Beckham, wasn’t known for his speed. He doesn’t challenge the symmetry-and-attractiveness theory either: he’s famously good-looking. And famously well-rewarded for it: the Beckham photo chosen by the authors shows him in a room crowded with photographers as he promotes an aftershave. But Beckham, often mocked for his verbal indexterity, does challenge the theory that football requires intelligence. I’m sure, though, that, despite his clumsy way with words, he does have an above-average IQ. I’m also sure that his brain is above average in other ways. All the brains in this book must be, including those of Roman Abramovich and Delia Smith. You need an above-average brain to be successful in a field that doesn’t depend purely on luck. Business and cookery don’t, and neither does football.

But luck is a big part of what makes football interesting: the book is full of might-have-beens. How high would legend no. 79, Darren Anderton of Tottenham Hotspurs, have gone without all the injuries? And what would have happened to legend no. 8, Sir Alex Ferguson, if, as seemed more likely than not, Manchester United had sacked him in 1990, “following defeat against [Nottingham] Forest in the third round of the FA Cup”? But the defeat didn’t happen: a late goal by Mark Robins saved Fergie’s job and started the avalanche of silverware that means Manchester United are now the most successful club in British football. The might-have-beens of legend no. 15, Matthew le Tissier of Southampton, are different: it wasn’t injury that stopped him moving to a bigger club, it was loyalty and laidbackness. As he himself says here: “Perhaps I’m in the nought point one per cent of footballers who don’t give a toss about unlimited money.”

He was another player who wasn’t good to look at, but was good to watch. Very good: his goals, like Beckham’s passes and crosses, were things of beauty. The aesthetics of football appeal even to the most lumpish fans, but le Tissier the aesthetician belongs with legend no. 10, Dennis Bergkamp of Arsenal, not with Beckham or legend no. 16, Cristiano Ronaldo. Beckham and Ronaldo are wonderful to watch, but they perform off the field too and bring the tedious worlds of fashion and celebrity into their footballing careers. Le Tissier and Bergkamp didn’t, which makes them my favourite players in the book. My favourite manager is legend no. 13, Arsène Wenger of Arsenal, but the most interesting manager, or even most interesting man, who appears here, Brian Clough of Nottingham Forest and Derby County, isn’t one of the legends. He’s discussed in the section devoted to legend no. 61, the manager Martin O’Neill, who played for Clough at Nottingham Forest. Clough himself never managed a team in the Premier League, but he did achieve remarkable things with medium-sized clubs in the old First Division. He also achieved remarkable things as a player, scoring 63 goals in 74 games for Sunderland in the early 1960s, before breaking his leg and having to retire young.

What might have been there? Clough’s goal-rate is reminiscent of the prodigious run-rate of the Australian cricketer Donald Bradman and, like Bradman’s, it doesn’t seem to have been a statistical fluke. Legend no. 56, Kevin Phillips, also scored at a remarkable rate for Sunderland, but after 30 goals in 36 games during his first season, he reverted to the mean and ended his career with a unexceptional 92 goals in 259 games. He was another good player who doesn’t genuinely count as a league legend, but his place in the section on club legends is taken by Kevin Ball. If you’re thinking “Who?”, join the club. Burnley’s club legend isn’t even a player: it’s the “super-fan” Dave Burnley, who has clocked up 480,000 miles following every Burnley game since 1974 and who named his daughter “Clarette in honour of the team’s colours”. Another exceptional person in a book about exceptional people. The book itself isn’t exceptional, but it is entertaining and unhysterical. The premier league gets only the first of those right. Crowds in the German Bungesliga are bigger and the skill in the Spanish league is greater, but the international audience for Fußball and futbol is much smaller. English football, though increasingly less English, is the most popular in the world. That is proved by trivial mathematics, but more subtle and powerful mathematics, which governs the movement of rocky spheres in the heavens, also governs the movement of airy spheres on football fields. Those spheres can still create music at the feet of men like le Tissier and Bergkamp, and the muzak of hype and hysteria doesn’t drown it. That’s what makes this book worth reading through and reminiscing over.

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