Much Ado About Numbers E-Book

Rob Eastaway

• Herausgeber: Allen & Unwin
• Kategorie: Geisteswissenschaft
• Sprache: Englisch
• Veröffentlichungsjahr: 2024

Seitenzahl: 261

Beschreibung

"A spectacular journey... Highly recommended!" Dr Simon Smith, The Shakespeare Institute "A fascinating and hugely entertaining guide to Shakespearean mathematics." ProfSarah Hart, author of Once Upon A Prime "A playful and engaging book ... bound to excite the appetite of all Shakespeare junkies." Patrick Spottiswoode, Founder, Shakespeare's Globe Education 'Instead of cleaving maths and English in twain, Eastaway brings them together to surprise and delight the reader.' Dr Rebecca Fisher, The English Association A fascinating new take on the world of Shakespeare. What's the connection between Shakespeare and maths? A lot, as it turns out! Shakespeare grew up in a time of remarkable mathematical innovation. From astronomy to probability, music to multiplication, new mathematical ideas were taking off - and much of this was reflected in his work. In this highly engaging book, award-winning author Rob Eastaway explores the surprising and entertaining ways that maths and numbers crop up in Shakespeare's plays. Find out how Tudors multiplied, why Shakespeare never ended a line with the word orange, and why dice-playing was a serious hazard for the unwary. With historical asides about games, optics, astronomy, music and magic, you will never think about maths, history or Shakespeare the same way again.

Leseprobe

Published in hardback in Great Britain in 2024 by Allen & Unwin, an imprint of Atlantic Books Ltd.

Copyright © Rob Eastaway, 2024

The moral right of Rob Eastaway to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act of 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of both the copyright owner and the above publisher of this book.

The picture acknowledgements on p. 205 constitute an extension of this copyright page.

Every effort has been made to trace or contact all copyright holders. The publishers will be pleased to make good any omissions or rectify any mistakes brought to their attention at the earliest opportunity.

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A CIP catalogue record for this book is available from the British Library.

Hardback ISBN: 978 1 80546 027 5

E-book ISBN: 978 180546 028 2

Printed in Great Britain

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CONTENTS

PROLOGUE

1.   SHAKESPEAREAN NUMBERS

A Playfulness with Numbers

Huge Numbers

Much Ado About Nothing

2.   SCHOOL LIFE

Maths at Grammar School

The Book of Arithmetic

The Seven Liberal Arts

Girls and Maths

3.   SPORT AND GAMES

Anyone for Tennis? Or Football?

Hazard and Risk

Nine Men’s Morris

Noddy, Primero and other Card Games

4.   MONEY

Shakespearean Currency

Shakespeare the Accountant?

Borrowing, Lending and Interest

5.   MEASURE FOR MEASURE

An Era of Imprecise Measurements

Length and Distance

Telling the Time

Navigation and Maps

6.   MUSIC, RHYTHM AND DANCE

The Measure of Dance

Patterns of Verse

Rhyming Patterns

Music As a Mathematical Subject

The Music of the Spheres

7.   ASTRONOMY AND ASTROLOGY

Telescopes and Horoscopes

Ruled by the Seven Planets

The Science of Astronomy

The New Calendar

8.   COLOURS AND THE RAINBOW

Rainbows in Shakespeare’s World

Shakespeare’s Colours

The Emerging Maths of Colour

9.   PUTTING INK TO PAPER

Writing with a Quill

Writing with Ink

Arrival of the Pencil

Printing and Publishing

10.   MATHEMATICS, MAGIC AND WITCHCRAFT

John Dee, Mathematician and Magician

The Book of Magic

Think of a Number

11.   CODES AND CONSPIRACY

Secret Messages and Chronograms

Acrostics and other Hidden Words

Numerology and Codes

Shakespeare’s Calculator

APPENDIX: MATHEMATICAL ASIDES

Tactics for Winning at Three Men’s Morris

The Pythagorean Octave and Dorian Mode

Shakespeare, Orange and Sir Isaac Newton

Philip Henslowe’s Diary

Francis Bacon’s Cipher System

A Shakespeare/Historic Event Timeline

Timeline of Shakespeare’s Plays and Poems

Bibliography

Acknowledgements

Picture Credits

Index

PROLOGUE

The idea for this book was sown in Stratford-upon-Avon. Where else? The British Mathematical Association, an august body that has represented teachers and general mathematicians for over a hundred years, had decided to hold its 2022 annual conference in William Shakespeare’s hometown. And that gave me the germ of an idea.

Stratford is of course still steeped in Shakespeare. Dominating the town is the huge Royal Shakespeare Theatre looking out towards the River Avon. The river is spanned by the fourteen-arch Clopton Bridge that Shakespeare would have traversed many times on his travels. Several half-timbered buildings survive from the sixteenth century, including the house in Henley Street where Shakespeare was born.

My friend Andrew Jeffrey and I had put ourselves forward to run a joint workshop at the teacher conference, as we have often done in the past. It would be our usual hour of light-hearted pick-and-mix mathematical curiosities.

But the location caught my imagination. Following the old rule that you’re more creative if you put a constraint on yourself, I suggested that we theme our workshop on Shakespeare. Why not pick out Shakespearean quotes and link them to mathematical concepts? We could do a slot about the use of zero and call it Much Ado About Nothing, another one about fractions called Henry the Fifth (aka Henry the 20%), and dotted throughout there could be a Comedy of Maths Errors. Cheesy, yes, but we knew our audience.

The curious thing, however, was that the more I hunted for superficial links between Shakespeare and mathematics, the more I realized that Shakespeare’s world was filled with much deeper mathematical ideas, and that many of them are reflected in his plays.

If you’d asked me about maths and Shakespeare before I started investigating it, I’d have dragged up hazy recollections about rhyming patterns in his verses, and also a mathematical rhythm in the way his lines were spoken, known as iambic pentameter. But it turns out that this is just the start of it. I have since uncovered numerous mathematical connections. As a result, a whimsical joke about Shakespearean maths that was originally intended for teachers at a conference has ended up as this book.

I have been told by many people that in writing a book about Shakespeare I am stepping into a lion’s den. There are thousands of academics, theatre producers, actors and historians across the world who have spent their lives studying Shakespeare, and there are countless books about him. His work has been analysed from just about every conceivable angle. Pick any topic – from horticulture to Harry Potter – and you’ll find somebody who has investigated its connection with Shakespeare. I might, however, be the first to have looked at his life and work through the prism of maths.

Before I embarked on this book, my knowledge of Shakespeare was typical of somebody who studied him at school (Richard III was my O Level play – I loved it) and who has then seen a couple of dozen productions on stage or screen, dotted through my adult life.

Happily, I now know considerably more about Shakespeare than I did when I started writing this book. It has been a joyful adventure. My research has taken me to the Royal Observatory in Greenwich, the real tennis court at Hampton Court, to the graphite mines of Cumbria, the inner sanctum of Oxford’s Bodleian Library and the salvaged wreck of the Mary Rose ship in Portsmouth. I’ve spoken to historians of musical instruments, glove-making, taxation, art restoration, astronomy, stationery, card games and magic. And, of course, I have read plenty of books and spoken to plenty of Shakespeare experts too.

It is worth pointing out that, aside from the plays and poems that he wrote, we know remarkably little about Shakespeare the man, and what he studied or said. This lack of biographical detail means it is very easy to make wild speculations. I could, for example, claim that Shakespeare used to practise his times tables at breakfast, spend lunchtime totting up the accounts for the Globe theatre, and spend the evening winning money with loaded dice, in the confidence that nobody can be certain that I’m wrong. I will avoid such speculation, but, as you’ll see, there is plenty of evidence that Shakespeare was aware of many of the mathematical ideas that were circulating in his lifetime, and that he incorporated many of them in his work.

You might ask ‘Is this mainly a maths book or a Shakespeare book?’ I would reply that arguably it is a history book. Or maybe a science book. Or even a book about language, music and the arts. The truth is that it is a bit of all of them, because they are all connected. In the modern world, anyone who takes an interest in arithmetic or algebra might be described as a maths person. But that is partly because we live in a binary world, where you are assumed to be interested in either the mathematical subjects or the arts, not both. In Elizabethan times, things were different.

The fact that leading mathematicians of that period, such as John Dee and Thomas Harriot, also experimented with optics, chemistry, map-making, seafaring and other diverse activities shows how blurred the edges were between different fields that are now distinct areas of study. It was a time when curiosity was rewarded because there were so many things still to be discovered and explained. This was the English Renaissance, and these were Renaissance men, living (for much of their lives) under a queen who was a Renaissance woman.

Shakespeare was born in 1564, at a time when there were huge advances happening in just about every sphere of life – in science, in the arts and of course in maths itself. The radical astronomical ideas of Copernicus, who had suggested that the universe was centred around the sun rather than the earth, were a matter of huge religious and public debate in the late 1500s; arithmetic was becoming an essential skill for anyone involved in trade or business, be that manufacturing gloves (as Shakespeare’s father did) or running a theatre; and music, regarded at the time as being a mathematical subject, was in the middle of its own revolution.

On the high seas, Walter Raleigh was one of the many adventurers opening up the world for exploration, which required increasingly advanced navigation skills. There was a huge growth in international trade as England developed a taste for exotic foods and spices; and at home the growth of mining and textiles was building the foundations for the Industrial Revolution that would finally explode a few generations later. Recreation was also taking off, with the invention of a plethora of sports and games, many of which provided a popular vehicle for gambling, which had a mathematics all of its own.

In this book I will be reflecting on the mathematics of Shakespeare’s world as much as maths in his plays: from games to astronomy, and from measurement to magic. In 1592, the playwright Robert Greene, who famously described William Shakespeare as an ‘upstart crow’, also called him a ‘Johannes factotum’. That second description was particularly snide, as it is a variant of ‘Jack of all trades’.

My sense of Shakespeare, however, is that he was an all-rounder in the best sense of the word, who was knowledgeable and curious about the world around him. And, while he wasn’t necessarily a mathematician, he had a particular aptitude for numbers, and a mathematical mind.

A rounded education was assumed to include an in-depth understanding of the classics but also of mathematics. If you were interested in history, the sciences, languages or music, you were free to explore them, and to serendipitously find connections between them. That is the spirit in which I have written this book.

MATHEMATICAL INFLUENCES ON SHAKESPEARE

CHAPTER I

SHAKESPEAREAN NUMBERS

A PLAYFULNESS WITH NUMBERS

They doubly redoubled strokes upon the foe.

MACBETH

The notion that Shakespeare’s work might have any links at all with maths might come as a surprise. In an era of Spanish Armadas, the arrival of tobacco, and the suppression of Catholics, you might think that maths would have been the last thing on people’s minds.

Yet what is striking is that Shakespeare’s plays and poems are full of mathematical ideas, and in particular numbers. He quantifies just about everything: hours, years, distances, the size of an army: you name it, if Shakespeare can put a number to it, he generally does.

The more I’ve investigated the numbers he uses, the more impressed I’ve been by just how creative he is in expressing them. And, as you might expect, he is often poetic with numbers, too. One of my favourite examples appears in Othello, a tragic play about love and jealousy. In Act 3 Scene 4, Bianca is sorry that her lover Cassio has been away for a week. She begins:

What, keep a week away? Seven days and nights?

OK, we get it. But she decides to ram it home with another way of expressing just how long a week is:

Eight score eight hours?

Of course it’s not Bianca who does this calculation; it’s Shakespeare who has figured it out and then put the words into Bianca’s mouth.

Did you already know that there are 168 hours in a week? I certainly didn’t, until I worked it out. This would have been just as obscure a number fact in Shakespeare’s time as it is today. It takes some mental agility to both calculate the number of hours in a week and then express it in a poetic turn of phrase. ‘Eight score eight’ sounds so much more elegant than ‘one-hundred and sixty-eight’.

‘Score’ (meaning twenty) was one of Shakespeare’s favourite numbers. The word comes from the Old Norse word skor meaning a mark or notch. One theory for why it came to represent twenty is that it was used for counting large numbers of, for example, sheep and making a notch in a stick for every twenty. Its meaning slowly changed to cover a reckoning or total amount, and by 1670 it had become a mark made to record a point in a game, which continues to this day.

The words ‘sixty’ and ‘eighty’ were very much in use in Shakespeare’s time, but he hardly uses them, opting for ‘three score’ and ‘four score’ instead (sometimes hyphenated, sometimes a single word).

Keeping score

Use of the word ‘score’ (meaning 20) in Shakespeare.

No. of appearances

Half a score (10)

1

One score (20)

6

Two score (40)

None

Three score (60)

6

Three score and ten (70)

2

Four score (80)

13*

Five score (100)

2

Six score (120)

1

Eight score (160)

2

Nine score (180)

2

Twelve score (240)

3

*’Four-score’ also appears in The Winter’s Tale, as ‘Wednesday the fourscore of April’. In this case, rather confusingly, ‘four-score’ is being used to mean twenty-four (4 + 20), not eighty (4 × 20). It’s the only time Shakespeare uses ‘four-score’ to mean 24 and in other contexts it might have caused confusion. However, since April has only 30 days, the context here makes it clear that it must mean 24, not 80.

This use of multiples of twenty to express numbers was particularly popular in Elizabethan times. It’s an idea that still lives on in the French numbering system. You may recall that once French counting goes past 69 it becomes eccentric. The French 70 is ‘sixty-ten’ (soixantedix) and 80 is ‘four twenties’ (quatre-vingts). Four score is the English equivalent of quatre-vingts.

Curiously, the French don’t seem historically to have referred to 70 as ‘three-twenties-ten’ – but the English did. Shakespeare himself does so in Macbeth when the nameless ‘Old Man’ declares that he can remember ‘three score ten’ years of his life.

Shakespeare would have been well versed in the Bible and was no doubt familiar with Psalm 90, which includes the famous line that dictates the natural lifespan of an adult, the so-called allotted span. The King James Bible, published in 1611 (late in Shakespeare’s career), puts it this way:

The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away.1

In other words, you can expect to live to 70, and if you somehow make it to 80, you’ll be shuffling off your mortal coil pretty soon afterwards. Thankfully in modern times we’ve pushed a bit further beyond these limits.

There’s plenty more number-play to be found in Shakespeare if you search for it. This includes, for example, referring to ten as ‘half a score’ (The Taming of the Shrew), and ‘twice five’ (in three plays). He also expresses fifty as ‘half a hundred’ (Coriolanus).

Shakespeare was also fond of compounding numbers and leaving the audience to imagine how big the result would be. In The Tempest, instead of describing himself as a complete idiot, Caliban says he is a ‘thrice-double ass’. Thrice-double is six. Shakespeare does something similar in The Merchant of Venice, but on a bigger scale, when Portia suggests that a payment should be ‘double six thousand and then treble that’, which ends up as 36,000.

And there’s also what I would call exponential wordplay, which exploits the fact that if you keep doubling a number you reach a vast total very quickly. In Macbeth, a wounded captain is reporting how he saw Macbeth and Banquo fighting on the battlefield. He tells how

they doubly redoubled strokes upon the foe

That sounds like a lot, but just how much is it? Double one cannon ball and you have two. Redouble and you have four. If you doubly redouble, you redouble twice, and four doublings means multiplying by sixteen. Shakespeare clearly liked this phrase because he’d used it before in the play Richard II, when John of Gaunt encourages Henry Bolingbroke to ‘let thy blows doubly redoubled fall. . . on thy enemy’.

Ne’er the twain shall meet

Shakespeare mentioned the number two nearly 700 times, but he sometimes looked for creative alternatives, just as modern football reporters do. In the same way a journalist will say that a striker scored a ‘brace’ of goals, Shakespeare talks about a brace of greyhounds, or courtesans, or harlots. He also refers to a ‘couple of pigeons’. But he had another word in his armoury that has disappeared from modern journalism: ‘twain’, an old English word for two. He uses it 47 times, including the line ‘O Hamlet, you have cleft my heart in twain’. The word largely died out over the next 300 years, though in nineteenth-century Mississippi, boatmen measuring the river depth would shout a warning if the river was shallower than two fathoms, with the cry ‘mark twain’. When the American writer Samuel Clemens was looking for a pseudonym, he decided to borrow this boating call.

And Shakespeare wasn’t averse to a little numerical sleight of hand. Here is the Fool addressing King Lear:

. . . Leave thy drink and thy whore,

And keep in-a-door,

And thou shalt have more

Than two tens to a score.

In other words, live wisely and carefully, and you’ll end up in profit, and two tens will end up being worth more than twenty. That’s creative accounting for you.

HUGE NUMBERS

Ay, sir. To be honest, as this world goes, is to be one man pick’d out of ten thousand.

HAMLET

As well as being playful with numbers, Shakespeare also used them for dramatic effect. The more I’ve explored his plays, the more I’ve come to appreciate how he clearly loved the theatrical power of big numbers. His plays are full of them. The word ‘thousand’ appears over three hundred times in his work, most famously in his mention of the ‘thousand natural shocks that flesh is heir to’ in Hamlet’s ‘To be or not to be’ speech. But that’s small fry compared to some of the numbers he uses.

Before we go any further, it’s worth considering what would have been viewed as a ‘huge number’ in Shakespeare’s time. These days we get first-hand experience of big numbers all the time. We are used to travelling thousands of miles on holidays, we see crowds in the tens or even hundreds of thousands at football matches and rock concerts, and we routinely hear about houses valued in the millions. On top of that the government routinely spends billions and astronomical distances are often in the trillions (it’s 23 trillion miles to Alpha Centauri). But the numbers in Shakespeare’s world were much smaller. Few people would have had any experience of a distance of more than a hundred miles, and for most people an income of more than £100 per year would have been unheard-of riches. The population of London in 1600 was around 200,000 – roughly the capacity of two Wembley stadiums – but of course they’d never have all assembled in the same place.

The most tangible sense of a huge number would have been witnessing crowds of people. The biggest crowd gatherings would probably have been for the gruesome spectacle of public hangings. In London most public hangings took place at Tyburn, close to where Marble Arch is today. There were no officials tasked with counting the number in the crowd, but there are credible claims that several thousand would have turned up to watch the hanging of a notorious convict such as Sir Brian O’Rourke of Ireland. On 3 November 1591 (a Wednesday) he was found guilty of treason and towed through the streets to Tyburn. There, in front of a large crowd, he suffered the routine punishment of the age. First he was hanged and then (while still alive) cut open to have his bowels removed and thrown on a fire, before being beheaded and then having his body cut into quarters. Shakespeare was familiar with this ghoulish form of execution, because he refers to it in King John when Lewis, the French prince, is described as being so intensely in love that it has ‘hanged drawn and quartered’ him. Perhaps the 27-year-old Shakespeare was even in the Tyburn crowd that November day to see O’Rourke’s execution.

The so-called Tyburn Tree, first erected in 1571, was used to carry out multiple executions. Hangings of notorious people are believed to have attracted crowds of several thousand.

But would a Tyburn spectator have been able to see how big the crowd was? I took the tube to Marble Arch to find the spot where the Tyburn Tree used to stand. The ground around there is actually quite flat, so you’d have needed to be on an elevated platform to get a real sense of what a crowd of thousands looked like. And the only people on an elevated platform were the hangman and the person he was about to execute, who probably had other things on their mind.

In fact if you wanted to witness thousands of people up close, the place to be was none other than Shakespeare’s Globe theatre itself. It’s been estimated that the theatre could hold about 3000 people, roughly double the capacity of its modern replica. Health and safety were not a big concern in Tudor times, and little thought was given to putting comfortable legroom between seats or aisles between rows. A Globe audience must have felt like a vast intimidating mob. That was what three thousand looked like.

What this all means is that anything above a few thousand was a massive, almost unthinkable number to your average Tudor, and so when Shakespeare referred to numbers this big, they’d have had quite an impact on his audience.

In Shakespeare’s plays, the biggest numbers tend to crop up in three places: time, armies and money.

For example, it was common knowledge in Christian Europe that the world had been around for a very large number of years. According to Rosalind in As You Like It,

The poor world is almost six thousand years old.2

Perhaps Shakespeare believed this too. If so, it is probably the only number that he ever under-states (unless you are a Young Earth creationist).

Meanwhile there are plenty of references to wealth and debts running into the thousands: ‘three thousand crowns’, ‘ten thousand ducats’ and so on (we’ll find out more about the maths of money in Chapter 4).

The biggest ‘real’ number of all to be found in Shakespeare is the fortune of one hundred thousand crowns that Ferdinand allegedly owes to the King of France in Love’s Labour’s Lost. That same fortune of one hundred thousand crowns is also to be found in Richard II. It’s the equivalent of several million pounds today.

But Shakespeare’s big numbers weren’t limited to tallies of actual things. Numbers came into their own when they could be exaggerated to make a point. Occasionally Shakespeare left big numbers to the imagination, for example in the play Pericles the character Boult says he’s described a woman down to ‘the number of her hairs’. That’s clearly a big number (the typical full head of hair has tens of thousands of follicles), but nobody’s counting here.

Usually, however, Shakespeare does like to put a figure on it. When Henry VI is mourning the death of his uncle, Duke Humphrey, he wants to show the depth of his grief:

Fain would I go to chafe his paly lips

With twenty thousand kisses, and to drain

Upon his face an ocean of salt tears.

Can we beat 20,000? Yes! Hamlet claims that his love for Ophelia is greater than that of ‘forty thousand brothers’.

In A Midsummer Night’s Dream, Oberon claims that Cupid’s arrow should pierce ‘one hundred thousand hearts’, and in other plays we encounter one hundred thousand welcomes (Coriolanus), deaths (Henry IV) and flaws (King Lear).

Yet even one hundred thousand is not enough hyperbole for Shakespeare. He goes bigger still: Cranmer offers Henry VIII ‘a thousand thousand’ blessings (that’s a million); Ferdinand offers Miranda a thousand thousand goodbyes; and Othello reckons that Bianca’s singing makes her a thousand thousand times more contemptible than she would otherwise be, which means she must be very, very awful.

There are more than ten references to ‘million’ too.

But the biggest number of all to be found in Shakespeare’s work is a little more disguised. It features in Romeo and Juliet, the play where melodramatic love and grief are at their most extreme.

The friar tells Romeo to escape to Mantua until his marriage can be announced in public. He reassures Romeo that, when he returns, Romeo will be greeted with vastly more joy than he’ll feel when he leaves. But by how much more joy will that be, exactly? The answer is:

Twenty hundred thousand times more joy

That’s an increase in the level of joy by a factor of two million, which to a Tudor audience was an astronomically large number.

MUCH ADO ABOUT NOTHING

Nothing can come of nothing.

KING LEAR

We’ve seen how Shakespeare enjoyed using huge numbers for dramatic effect. But there was another aspect of numbers that seems to have intrigued him even more.

It turns out that William Shakespeare lived through what was arguably one of the most important revolutions in mathematics of all time, in terms of its impact on the economy, education and society as a whole. Not only did Shakespeare know about this revolution, but he weaved its fundamental idea into his plays. It was a revolution that would make possible huge and rapid advances in knowledge across all of the sciences. And it would ultimately lead to the modern data-driven society that we live in today.

What was this revolution?

It was nothing. Or, to put it another way, it was the introduction of the digit ‘0’ which, along with the digits 1 to 9, had made its way from India to the Middle East and then to Europe via the trading ports of Italy (including the merchants of Venice) and had arrived in England just a couple of decades before Shakespeare was born.

These ‘Indo-Arabic’ numerals (shortened to ‘Arabic’ from here on) were taking over from Roman numerals I, II, III, . . . and in the process were revolutionizing the way that numbers could be presented and manipulated. They had already had a huge impact on the way that business was conducted across continental Europe, because they enabled calculations to be done far more quickly, making trading much more efficient. Now England was joining the party.

Today we call the symbol for nothing ‘zero’, but that word wasn’t in use in Shakespeare’s time. Zéro first appeared in France around the year 1600 but didn’t fully establish itself in the English vocabulary for another hundred years.

Instead, the word that Shakespeare’s generation used for the zero digit was cipher, which (like zero) derives from the Arabic word sifr meaning nothing or emptiness. Today, a cipher is a code, a mystery that has to be solved, but that meaning evolved from the digit zero which to many people resembled something of a mysterious new code that had to be deciphered.

The ‘new’ digits from 9 down to 0 were introduced to the British public in Robert Recorde’s 1542 book The Ground of Arts. This image comes from the 1618 edition, and shows that, even two years after Shakespeare’s death, the French word ‘zero’ was not in popular use in England.

Cumbersome Calculations

You might be wondering why zeroes had such a profound impact on the way we handle numbers. Until the sixteenth century, numbers in England were written using Roman numerals. Seven letters, I, V, X, L, C, D and M, were used to express numbers up to the thousands. The year 1066, for example, would have been written as MLXVI. But Roman numbers could be cumbersome, especially when it came to doing arithmetic.

When Shakespeare’s father John was a child in the late 1530s, if he wrote numbers at all it’s likely that he would have exclusively used Roman numerals – his was the last generation to do so. If he wanted to use a written method to add numbers such as 12 + 25 he might have scrawled XII and XXV, and the letters could just be lumped together to get the answer XXXVII. (In practice, when he was doing calculations, he is more likely to have used his fingers, or counters on a table, and he’d then simply write the answer in numerals.)

Division and multiplication using Roman numerals could be harder. What’s half of XLVI (46)? Without the aid of modern numerals and mathematical symbols, it’s quite messy to work out. (The answer is XXIII.)

Multiplying would be equally cumbersome: twice 39 is 78, but with Roman numerals XXXIX doubles to LXXVIII. Expressing large numbers could require an ungainly number of characters. If you wanted to write 3874 you’d need twelve characters MMMDCCCLXXIV.

This is why the Arabic decimal system popularized in England by Robert Recorde was so powerful. It introduced the idea of place value, so that a single symbol such as ‘5’ could do much more work: it could be worth 5, 50, 500 or higher depending on which column it was placed in, with ciphers being used to indicate its value.

Perhaps the most famous example of Shakespeare using the word ‘cipher’ is in the Prologue for Henry V, when the Chorus (effectively a narrator), enters to announce that this small troupe of actors is about to recreate the glorious history of the battle of Agincourt. Just six or seven men will try to represent a huge army. He asks the audience to use its imagination: think of each actor as a zero. This little ‘1’ (a ‘crooked figure’3) can be turned into something vast, a million, when followed by six zeroes. The Chorus puts it this way:

O pardon, since a crooked figure may

attest in little place a million,

And let us, ciphers to this great account

On your imaginary forces work

Shakespeare makes references to nothing-ness throughout his work. The word ‘cipher’ itself (in its zero sense) appears only five times, but he uses ‘nought’ or ‘naught’ (he seems to have been fairly flexible on spelling) 84 times, and the word ‘nothing’ itself crops up a staggering 590 times, not least in the title of one of his most popular comedies, Much Ado About Nothing.

The word ‘Nothing’ in that play’s title is actually a four-way pun. Its most obvious meaning is its ‘numerical’ one, that this play is about making a big issue out of something trivial. But, in Shakespeare’s time, ‘nothing’ was pronounced in a way that made it sound like ‘noting’, which was a word for gossip (a feature of the play). Noting also referred to music, in the sense of making notes, and this musical meaning of noting is used in an exchange between two characters, Balthasar and Don Pedro:

Balthasar: