FROM THE GUARDIAN
Alex's Adventures in Numberland
by Alex Bellos
448pp,Bloomsbury,£18.99
Alex's Adventures in Numberland by Alex Bellos
Joan Brady is delighted to discover that if you can throw a ball or read a map, you can do maths
Half a century ago, girls didn't do either subject, especially since back then philosophers were trying to reduce philosophy to maths. I was shocked: all the fundamental questions of life turned into equations? Ridiculous. It wasn't until years later that I realised I should have dumped philosophy, where there's little beyond long-winded uncertainty, and pressed harder at mathematics where answers abound.
What stopped me was simple: I'm hopeless with numbers. When people say "I can't do maths," that's usually what they mean: no good at arithmetic. But why are we so bad at it? Alex Bellos in Alex's Adventures in Numberland gives me the first real clue I've ever had: arithmetic just doesn't come naturally; Bellos says that little kids and aboriginals think of 1, 2, 3, 4 as stretching off into the distance like telephone poles down a country road. Poles near us look far apart; ones further away look closer together. To add and subtract we have to break this intuitive grasp and see numbers as equally spaced dots along a line. Such mind-bending calls for brilliant teachers, and brilliance of any kind is rare. No wonder we have trouble getting the hang of it.
It's not just non-mathematicians who have such difficulties, either. Years after I graduated, I read about a great mathematician whose laundress felt sorry for him because he couldn't add up his laundry list. That was the encouragement I'd needed all along. I enrolled in an Open University course. What joy to find out that I could manage the meat of mathematics even though I remain as lousy at numbers as ever.
The guy who taught the course told me that if you're looking for aptitude, the crucial question is: "Can you pack your bags in the boot of your car?" If the answer is "yes" then you've got some mathematical gift. It's independent of numbers. If you can quilt or read a map or throw a ball to somebody, you're actually doing maths. Take that toss of a ball: elementary calculus in school shows you how to describe it and then tells you that Archimedes used the same principle to smash Roman ships with a massive catapult – a familiar, ordinary, everyday activity abstracted by one man into a killing machine.
It wasn't numbers that got him to see that his catapult could work or even how it might work. It was the pattern of the thing. And any pattern can have the same effect. Bellos meets an Australian mathematician fascinated by juggling. "Maths is not sums, calculations and formulae," the Australian says. "It is pulling things apart to understand how things work." He says his juggling rules make up "a language" people can use "to talk about problems". The same principle applies to numbers: they're a language, one way of telling other people how something works when you've figured it out.
Imagine the jolt of satisfaction when Archimedes realised that something so ordinary could be scaled up – patterned up – to something powerful enough to destroy an enemy fleet. Bellos touches on this well-hidden delight of the mathematics world; he says there's an "almost physical pleasure" that comes when "suddenly everything makes sense". It's interesting how coy even he is about this. I've experienced it myself, and there's no "almost" about it. It's definitely physical. Feel it once and you really want it again. Orgasm isn't quite right, but the two sensations – that flood of intensity through the body and the release of tension that comes after it – are all too alike: not subjects for discussion in polite company, and ones that only raise a giggle alongside words like "nerd" and "geek".
Bellos catches many mathematicians looking for patterns in things as unexpected as juggling, and his cast includes characters who could fit comfortably into his book's namesake, Alice's Adventures in Wonderland: collections of ancients with wispy beards all het up over remains of felt at a hat-maker's; a blank-faced chimpanzee who's spent years eagerly tapping number sequences into a computer eight hours a day, seven days a week, never bored, never distracted; and many more.
But Bellos's book isn't just about strange creatures, human or otherwise. A better way to see it is as a kaleidoscope of delightful toys from a field most people don't think of as "delightful" at all. Bellos tells you how numbers struggled into life long ago, learned to jump through hoops and finally arrived at today's scary-movie weirdness. Along the way, he provides a Cook's tour of the kinds of maths that touch our lives – everybody's life – each discipline wrapped up in its own anecdotes. Much of this is fun as well as informative. Who would have thought that the geometry of the 50p coin so enraged people that a colonel from Derbyshire led militant protests in the streets against the "monstrosity" that "insults our Queen"? Now it's a classic of British design, and Bellos explains why its seven sides make it the most "thought-provoking" coin in circulation. And who would have guessed that position of a beautiful woman's belly button in relation to her height is the same as the crossbars on the devil's pentagram?
Such baubles aren't the whole of it either. There are very few books that aim at exposing the pleasures of maths to non-mathematicians simply because they're so difficult to write that hardly anybody has the guts to try. I read as many as I could get hold of when I was starting my Open University course. Most of them made me feel a complete dim-wit. I didn't understand Lancelot Hogben's famous bestseller from the 1930s, Mathematics for the Million: How to Master the Magic of Numbers, just as, years later, I couldn't understand the work of Ian Stewart, the eminent mathematician and populariser who praises Bellos on the back of Alex's Adventures in Numberland. Another guy on the back jacket, Martin Gardner, is fun to read, but he's never attempted anything as ambitious as this.
At first glance the numbers in Bellos's book might seem a little off-putting, and yet every day we pore over strings of numbers more daunting than any he presents: grocery receipts, bank statements, telephone numbers. If his start getting too heady, just skip to the next section. The heart of the book isn't going to be lost. Numbers or no numbers, it will spark an interest in maths or fuel one that's already there. Any reader will come away with a feel for what mathematicians are like as people, a taste of what they do for a living and an insight into why it excites them.
Bellos also lets us see how deeply dependent we are on mathematics. Those daily lists, every mechanical or electronic device we use, every financial move we make or that bankers make in robbing us: all this stuff relies on maths, wouldn't happen without it. And yet the view persists that we really don't have to bother with the subject. Why should we stay so blinkered? Especially when Bellos's book offers us such an exciting way to take a look? Its subtitle is "dispatches from the world of mathematics". A good description. For a number-challenged reader like me it is perfect to dip into. Pick it up, look anywhere and there's something as pleasing as you'll find in any collection of aphorisms. But Bellos's dispatches add up to much more: a travelogue through a bizarre and beautiful country that rules us all but which too few of us have had the chance to visit.
Joan Brady's Venom is published by Simon & Schuster
Alex's Adventures in Numberland
by Alex Bellos
448pp,Bloomsbury,£18.99
Alex's Adventures in Numberland by Alex Bellos
Joan Brady is delighted to discover that if you can throw a ball or read a map, you can do maths
Half a century ago, girls didn't do either subject, especially since back then philosophers were trying to reduce philosophy to maths. I was shocked: all the fundamental questions of life turned into equations? Ridiculous. It wasn't until years later that I realised I should have dumped philosophy, where there's little beyond long-winded uncertainty, and pressed harder at mathematics where answers abound.
What stopped me was simple: I'm hopeless with numbers. When people say "I can't do maths," that's usually what they mean: no good at arithmetic. But why are we so bad at it? Alex Bellos in Alex's Adventures in Numberland gives me the first real clue I've ever had: arithmetic just doesn't come naturally; Bellos says that little kids and aboriginals think of 1, 2, 3, 4 as stretching off into the distance like telephone poles down a country road. Poles near us look far apart; ones further away look closer together. To add and subtract we have to break this intuitive grasp and see numbers as equally spaced dots along a line. Such mind-bending calls for brilliant teachers, and brilliance of any kind is rare. No wonder we have trouble getting the hang of it.
It's not just non-mathematicians who have such difficulties, either. Years after I graduated, I read about a great mathematician whose laundress felt sorry for him because he couldn't add up his laundry list. That was the encouragement I'd needed all along. I enrolled in an Open University course. What joy to find out that I could manage the meat of mathematics even though I remain as lousy at numbers as ever.
The guy who taught the course told me that if you're looking for aptitude, the crucial question is: "Can you pack your bags in the boot of your car?" If the answer is "yes" then you've got some mathematical gift. It's independent of numbers. If you can quilt or read a map or throw a ball to somebody, you're actually doing maths. Take that toss of a ball: elementary calculus in school shows you how to describe it and then tells you that Archimedes used the same principle to smash Roman ships with a massive catapult – a familiar, ordinary, everyday activity abstracted by one man into a killing machine.
It wasn't numbers that got him to see that his catapult could work or even how it might work. It was the pattern of the thing. And any pattern can have the same effect. Bellos meets an Australian mathematician fascinated by juggling. "Maths is not sums, calculations and formulae," the Australian says. "It is pulling things apart to understand how things work." He says his juggling rules make up "a language" people can use "to talk about problems". The same principle applies to numbers: they're a language, one way of telling other people how something works when you've figured it out.
Imagine the jolt of satisfaction when Archimedes realised that something so ordinary could be scaled up – patterned up – to something powerful enough to destroy an enemy fleet. Bellos touches on this well-hidden delight of the mathematics world; he says there's an "almost physical pleasure" that comes when "suddenly everything makes sense". It's interesting how coy even he is about this. I've experienced it myself, and there's no "almost" about it. It's definitely physical. Feel it once and you really want it again. Orgasm isn't quite right, but the two sensations – that flood of intensity through the body and the release of tension that comes after it – are all too alike: not subjects for discussion in polite company, and ones that only raise a giggle alongside words like "nerd" and "geek".
Bellos catches many mathematicians looking for patterns in things as unexpected as juggling, and his cast includes characters who could fit comfortably into his book's namesake, Alice's Adventures in Wonderland: collections of ancients with wispy beards all het up over remains of felt at a hat-maker's; a blank-faced chimpanzee who's spent years eagerly tapping number sequences into a computer eight hours a day, seven days a week, never bored, never distracted; and many more.
But Bellos's book isn't just about strange creatures, human or otherwise. A better way to see it is as a kaleidoscope of delightful toys from a field most people don't think of as "delightful" at all. Bellos tells you how numbers struggled into life long ago, learned to jump through hoops and finally arrived at today's scary-movie weirdness. Along the way, he provides a Cook's tour of the kinds of maths that touch our lives – everybody's life – each discipline wrapped up in its own anecdotes. Much of this is fun as well as informative. Who would have thought that the geometry of the 50p coin so enraged people that a colonel from Derbyshire led militant protests in the streets against the "monstrosity" that "insults our Queen"? Now it's a classic of British design, and Bellos explains why its seven sides make it the most "thought-provoking" coin in circulation. And who would have guessed that position of a beautiful woman's belly button in relation to her height is the same as the crossbars on the devil's pentagram?
Such baubles aren't the whole of it either. There are very few books that aim at exposing the pleasures of maths to non-mathematicians simply because they're so difficult to write that hardly anybody has the guts to try. I read as many as I could get hold of when I was starting my Open University course. Most of them made me feel a complete dim-wit. I didn't understand Lancelot Hogben's famous bestseller from the 1930s, Mathematics for the Million: How to Master the Magic of Numbers, just as, years later, I couldn't understand the work of Ian Stewart, the eminent mathematician and populariser who praises Bellos on the back of Alex's Adventures in Numberland. Another guy on the back jacket, Martin Gardner, is fun to read, but he's never attempted anything as ambitious as this.
At first glance the numbers in Bellos's book might seem a little off-putting, and yet every day we pore over strings of numbers more daunting than any he presents: grocery receipts, bank statements, telephone numbers. If his start getting too heady, just skip to the next section. The heart of the book isn't going to be lost. Numbers or no numbers, it will spark an interest in maths or fuel one that's already there. Any reader will come away with a feel for what mathematicians are like as people, a taste of what they do for a living and an insight into why it excites them.
Bellos also lets us see how deeply dependent we are on mathematics. Those daily lists, every mechanical or electronic device we use, every financial move we make or that bankers make in robbing us: all this stuff relies on maths, wouldn't happen without it. And yet the view persists that we really don't have to bother with the subject. Why should we stay so blinkered? Especially when Bellos's book offers us such an exciting way to take a look? Its subtitle is "dispatches from the world of mathematics". A good description. For a number-challenged reader like me it is perfect to dip into. Pick it up, look anywhere and there's something as pleasing as you'll find in any collection of aphorisms. But Bellos's dispatches add up to much more: a travelogue through a bizarre and beautiful country that rules us all but which too few of us have had the chance to visit.
Joan Brady's Venom is published by Simon & Schuster
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