Contents
Preface
Pylon of the Month
A Sense of Balance
Monkey Business
Why Does the Other Queue Always Move Faster?
I Do Not Believe It!
Financial Investment with Time Travellers
A Thought for Your Pennies
Your Number’s Up
The Most Infamous Mathematician
How to Win the Lottery
A Truly Weird Football Match
The Gherkin
Packing Your Stuff
The Madness of Crowds
The Three Laws of Robotics
Testing Spaghetti to Destruction
All Aboard
The Global Village
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Epub ISBN: 9781407073668
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Published by The Bodley Head 2010
Copyright © John D. Barrow 2008
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First published in hardback in Great Britain in 2008 under the title 100 Essential Things You Didn’t Know You Didn’t Know by The Bodley Head
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ISBN 9781407073668
About the Author
John D. Barrow is Professor of Mathematical Sciences and Director of the Millennium Mathematics Project at Cambridge University, Fellow of Clare Hall, Cambridge, a Fellow of the Royal Society, and the current Gresham Professor of Geometry at Gresham College, London. His previous books include The Origin of the Universe, The Universe That Discovered Itself, The Book of Nothing, The Constants of Nature: From Alpha to Omega, The Infinite Book: A Short Guide to the Boundless, Timeless and Endless and, most recently, Cosmic Imagery: Key Images in the History of Science. He is also the author of the award-winning play Infinities.
To David and Emma
Preface
This is a little book of bits and pieces – bits about off-beat applications of mathematics to everyday life, and pieces about a few other things not so very far away from it. They are presented here in no particular order, with no hidden agenda and no invisible thread. Sometimes you will find only words, but sometimes you will find some numbers as well. Maths is interesting and important because it can tell you things about the world that you can’t learn in any other way. When it comes to the depths of fundamental physics or the breadth of the astronomical universe we have almost come to expect that. But I hope that here you will see how simple ideas can shed new light on all sorts of things that might otherwise seem boringly familiar or just pass by unnoticed.
John D. Barrow
I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours. I found it quite enthralling.
Agatha Christie
BY THE SAME AUTHOR
Theories of Everything
The Left Hand of Creation
(with Joseph Silk)
L’Homme et le Cosmos
(with Frank J. Tipler)
The Anthropic Cosmological Principle
(with Frank J. Tipler)
The World within the World
The Artful Universe
Pi in the Sky
Perchè il mondo è matematico?
Impossibility
The Origin of the Universe
Between Inner Space and Outer Space
The Universe that Discovered Itself
The Book of Nothing
The Constants of Nature:
From Alpha to Omega
The Infinite Book:
A Short Guide to the Boundless,
Timeless and Endless
Cosmic Imagery:
Key Images in the History of Science
and most recently 100 Essential Things You Didn’t Know You Didn’t Know
He is also the author of the award-winning play Infinities
ESSENTIAL THINGS YOU DIDN’T KNOW
YOU DIDN’T KNOW BRAIN SHOT
John D. Barrow
LONDON
Pylon of the Month
Like Moses parting the waves, National Grid Company PLC’s 4YG8 leads his fellow pylons through this Oxfordshire housing estate towards the ‘promised land’ of Didcot Power Station.
Pylon of the Month, December 1999
There are some fascinating websites about, but none was more beguiling than the iconic Pylon of the Month, (www.pylonofthemonth.org) once devoted to providing monthly pin-ups of the world’s most exciting and seductive electricity pylons. Alas, Pylon of the Month now seems to have become a cobweb site, but there is still something to learn from it, since, for the mathematician, every pylon tells a story. It is about something so prominent and ubiquitous that, like gravity, it goes almost unnoticed.
Next time you go on a train journey, look carefully at the pylons as they pass swiftly by the windows. Each is made of a network of metal struts that make use of a single recurring polygonal shape. That shape is the triangle. There are big triangles and smaller ones nested within them. Even apparent squares and rectangles are merely separate pairs of triangles. The reason forms a small part of an interesting mathematical story that began in the early nineteenth century with the work of the French mathematician Augustin-Louis Cauchy.
Of all the polygonal shapes that we could make by bolting together straight struts of metal, the triangle is special. It is the only one that is rigid. If they were hinged at their corners, all the others can be flexed gradually into a different shape without bending the metal. A square or a rectangular frame provides a simple example: we see that it can be deformed into a parallelogram without any buckling. This is an important consideration if you aim to maintain structural stability in the face of winds and temperature changes. It is why pylons seem to be great totems to the god of all triangles.
If we move on to three-dimensional shapes then the situation is quite different: Cauchy showed that every convex polyhedron (i.e. in which the faces all point outwards) with rigid faces, and hinged along its edges, is rigid. And, in fact, the same is true for convex polyhedra in spaces with four or more dimensions as well.