Alex Through the Looking-glass

362 Pages·2014·28.4 MB·English

by  Alex Bellos

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For Nat
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Contents
Introduction
CHAPTER ONE
Every Number Tells a Story
CHAPTER TWO
The Long Tail of the Law
CHAPTER THREE
Love Triangles
CHAPTER FOUR
Coneheads
CHAPTER FIVE
Bring on the Revolution
CHAPTER SIX
All About e
CHAPTER SEVEN
The Positive Power of Negative Thinking
CHAPTER EIGHT
Professor Calculus
CHAPTER NINE
The Titl of This Chapter Contains Three Erors
CHAPTER TEN
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Cell Mates
GLOSSARY
APPENDICES
ASSUMPTIONS, CLARIFICATIONS, REFERENCES AND NOTES
PLATE SECTION
PLATE SECTION PICTURE CREDITS
PICTURE CREDITS
ACKNOWLEDGEMENTS
A NOTE ON THE AUTHOR
BY THE SAME AUTHOR
eCopyright
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Introduction
Mathematics is a joke.
I’m not being funny.
You need to ‘get’ a joke just like you need to ‘get’ maths.
The mental process is the same.
Think about it. Jokes are stories with a set-up and a punch line. You follow
them carefully until the payoff, which makes you smile.
A piece of maths is also a story with a set-up and a punch line. It’s a
different type of story, of course, in which the protagonists are numbers,
shapes, symbols and patterns. We’d usually call a mathematical story a
‘proof’, and the punch line a ‘theorem’.
You follow the proof until you reach the payoff. Whoosh! You get it!
Neurons go wild! A rush of intellectual satisfaction justifies the initial
confusion, and you smile.
The ha-ha! in the case of a joke and the aha! in the case of maths describe
the same experience, and this is one of the reasons why understanding
mathematics can be so enjoyable and addictive.
Like the funniest punch lines, the finest theorems reveal something you
are not expecting. They present a new idea, a new perspective. With jokes,
you laugh. With maths, you gasp in awe. It was precisely this element of
surprise that made me fall in love with maths as a child. No other subject so
consistently challenged my preconceptions.
The aim of this book is to surprise you, too. In it, I embark on a tour of my
favourite mathematical concepts, and explore their presence in our lives. I
want you to appreciate the beauty, utility and playfulness of logical thought.
My previous book, Alex’s Adventures in Numberland, was a journey into
mathematical abstraction. This time I come down to earth: my concern is as
much the real world, reflected in the mirror of maths, as it is the abstract
one, inspired by our physical experiences.
Firstly, I put humans on the couch. What are the feelings we have for
numbers, and what triggers these feelings? Then I put numbers on the couch,
individually and as a group. Each number has its own issues. When we engage
with them en masse, however, we see fascinating behaviour: they conduct
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themselves like a well-organized crowd.
We depend on numbers to make sense of the world, and have done so ever
since we started to count. In fact, perhaps the most surprising feature of
mathematics is how extraordinarily successful it has been, and continues to
be, in enabling us to understand our surroundings. Civilization has progressed
as far as it has thanks to discoveries about simple shapes like circles and
triangles, expressed pictorially at first, and later in the vernacular of
equations.
Maths, I would argue, is the most impressive and longest-running
collective enterprise in human history. In the following pages I follow the
torch of discovery from the Pyramids to Mount Everest, from Prague to
Guangzhou, and from the Victorian drawing room to a digital universe of
self-replicating creatures. We will meet swashbuckling intellects, including
familiar names from antiquity and less familiar names from the present day.
Our cast includes a cravat-wearing celebrity in India, a gun-toting private
investigator in the United States, a member of a secret society in France, and
a spaceship engineer who lives near my London flat.
As we roam across physical and abstract worlds, we will probe well-known
concepts, like pi and negative numbers, and encounter more enigmatic ones,
which will become our confidantes. We will marvel at concrete applications
of mathematical ideas, including some that actually are made of concrete.
You don’t need to be a maths whizz to read this book. It’s aimed at the
general reader. Each chapter introduces a new mathematical concept, and
assumes no previous knowledge. Inevitably, however, some concepts are
more stretching than others. The level sometimes reaches that of an
undergraduate degree, and, depending on your mathematical proficiency,
there may be moments of bewilderment. In these cases, skip to the beginning
of the next chapter, where I reset the level to elementary. The material might
make you feel a bit dizzy at first, especially if it is new to you, but that’s the
point. I want you to see life differently. Sometimes the aha! takes time.
If all this sounds a bit serious, it isn’t. The emphasis on surprise has made
maths the most playful of all intellectual disciplines. Numbers have always
been toys, as much as they have been tools.
Not only does maths help you understand the world better, it helps you
enjoy it more, too.

Alex Bellos
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January 2014
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CHAPTER ONE
Every Number Tells a Story
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