Rob Eastaway - Maths on the Back of an Envelope - Clever ways to (roughly) calculate anything

HarperCollins Publishers 1 London Bridge Street London SE1 9GF

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First published by HarperCollins Publishers 2019

FIRST EDITION

© Rob Eastaway 2019

Cover design by Andrew Davis © HarperCollins Publishers Ltd 2019 Cover photograph © Shutterstock.com

A catalogue record of this book is available from the British Library

Rob Eastaway asserts the moral right to be identified as the author of this work

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Source ISBN: 9780008324582

Ebook Edition © September 2019 ISBN: 9780008324599

Version 2019-08-30

1 Cover

2 Title Page

3 Copyright Copyright HarperCollins Publishers 1 London Bridge Street London SE1 9GF www.harpercollins.co.uk First published by HarperCollins Publishers 2019 FIRST EDITION © Rob Eastaway 2019 Cover design by Andrew Davis © HarperCollins Publishers Ltd 2019 Cover photograph © Shutterstock.com A catalogue record of this book is available from the British Library Rob Eastaway asserts the moral right to be identified as the author of this work All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the nonexclusive, non-transferable right to access and read the text of this e-book on screen. No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins e-books. Find out about HarperCollins and the environment at www.harpercollins.co.uk/green Source ISBN: 9780008324582 Ebook Edition © September 2019 ISBN: 9780008324599 Version 2019-08-30

4 Prologue: How Many Cats?

5 THE PERILS OF PRECISION

6 TOOLS OF THE TRADE

7 EVERYDAY ESTIMATION

8 FIGURING WITH FERMI

9 LAST WORD: WHEN THE ROBOTS TAKE OVER

10 Appendix

11 Answers and Tips

12 Endnotes

13 Acknowledgements

14 About the Author

15 About the Publisher

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1 Cover

2 Frontmatter

3 Begin Reading

4 Table of Contents

A few years ago, at a school event, I asked the audience of teenagers to submit some estimation questions that I would then attempt to answer live on stage. One pupil posed this simple question: ‘How many cats are there in the world?’

Cats are always a popular topic, so I took it on.

My thinking went like this:

Let’s assume that most cats are domestic.

Some people have more than one cat, but usually a household has only one cat, if any at all.

In the UK, and thinking of my own street as an example, it seems reasonable to suppose that there might be one cat in every five households.

And, if a household contains on average two people, that means there is one cat for every 10 people.

So, with 70 million people in the UK, let’s say that there are, perhaps, seven million cats in the UK.

So far, so good. But what about the number of cats in the rest of the world? It seems unlikely that cats are as popular in countries like India or China as they are in the UK (although what would I know? Remember, this is purely guesswork on my part), therefore, I’d expect the ratio across the world to be smaller than it is in the UK – maybe one cat for every 20 people?

So, with eight billion people in the world, that suggests there are maybe:

8 billion ÷ 20 = 400 million cats.

It doesn’t seem an outrageous number.

That was the figure I suggested, anyway.

A member of the audience put his hand up.

‘The real number is 600 million,’ he said.

‘Really – how do you know?’

‘I just looked it up online.’

So that’s it: no need to come up with an answer; it’s already been done.

If it’s really that simple, we can forget about doing estimations altogether. With just a few clicks on Google you will probably find a statistic to answer every question you could possibly think of.

Except for one crucial thing.

Where did the person who published that figure of 600 million online get their number from? No one, I’m quite sure, has gone around the world doing a census of cats. The figure of 600 million is an estimate. It might be an estimate that is based on a slightly more scientific method than mine, using rigorous surveys and cross-checks, but it’s just as likely that the figure cited online came from somebody who did a back-of-envelope calculation like the one I just described. Or, perhaps they simply invented a figure that suited their agenda. There’s no reason to believe that their number is more reliable than mine – indeed, it might be less reliable.