Much Ado About Numbers

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?

Bianca is demonstrating some nifty mental arithmetic. She's letting the audience know that there are 7 × 24 = 168 hours in a week (or, as she puts it, 8 × 20 (a score), plus 8, which comes to the same thing).

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...