He lived and wrote in听, when听听were transforming perceptions of the world. Part of the role of the theatre was to process the cultural implications of all these changes.
People in Shakespeare鈥檚 time were used to the idea of the听: the planets, the heavens, the weather. But they were much less used to the inverse idea that the very small (and even nothingness) could be expressed by mathematical axioms. In fact, the first recorded English use of the word 鈥渮ero鈥 wasn鈥檛听.
Thinkers like Italian mathematician听, who lived in the 13th century, helped to introduce the concept of zero 鈥 known then as a 鈥渃ipher鈥 鈥 into the mainstream. But it wasn鈥檛 until philosopher听听and mathematicians听听补苍诲听听诲别惫别濒辞辫别诲听听in the late 16th and early 17th centuries that 鈥渮ero鈥 started to figure prominently in society.
Moreover, scientist听听didn鈥檛 discover microorganisms until 1665, meaning the idea that life could exist on a micro level remained something of fantasy.
With the听听in England, small, insignificant figures had begun to be used to represent very large concepts.
This was happening both in modes of calculation (which used proportion) and in the practice of writing mathematical symbols.
For example, during the 16th and early 17th centuries, the equals, multiplication, division, root, decimal, and inequality symbols were gradually introduced and standardised.
Alongside this came the work of听听鈥 a German Jesuit astronomer who helped Pope Gregory XIII to introduce the Gregorian calendar 鈥 and other mathematicians on fractions. Then referred to as听, they听听among those who clung to classical models of number theory.
The struggle to come to terms with the entanglement of the very large and the very small is splendidly displayed in many of Shakespeare鈥檚 works. This includes his history play Henry V and tragedy Troilus and Cressida.
The opening chorus of Henry V displays Shakespeare鈥檚 interest in proportion and the听听through its repeated 鈥淥鈥 and references to contemporary mathematical thought:
O for a muse of fire, that would ascend / The brightest heaven of invention: / A kingdom for a stage, princes to act, / And monarchs to behold the swelling scene [鈥 / may we cram / Within this wooden O the very casques / That did affright the air at Agincourt? / O pardon: since a crook猫d figure may / Attest in little place a million, / And let us, ciphers to this great account, / On your imaginary forces work.
听largely agree that Shakespeare鈥檚 鈥渃rook猫d figure鈥 is actually zero. This is despite, of course, the rather obvious objection that zero is the least crooked of all numbers.
In the line 鈥渁 crook猫d figure may / Attest in little place a million鈥, Shakespeare references 16th century听听surrounding the idea that the very small is capable of both representing and influencing the very big. In this case, the zero is capable of transforming 100,000 into 1,000,000.
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In this mathematical analogy, 鈥渃rook猫d figure[s]鈥 can 鈥渁ttest鈥 much greater things. The chorus suggests that by using one鈥檚 鈥渋maginary forces鈥, much greater things may come from the forthcoming stage performances.
This extended metaphor reappears in Shakespeare鈥檚 tragicomedy,听听when the 鈥溾 (numbers) transform into many thousands of thank yous:
Like a cipher, / Yet standing in rich place, I multiply / With one 鈥淲e thank you鈥 many thousands more / That go before it.
There is a further, visual metaphor in Henry V鈥檚 opening prologue where the chorus asks pardon of an 鈥淥鈥 to help them represent many things in the 鈥渨ooden O鈥 鈥 the听. This is perhaps evidence of Shakespeare鈥檚 ongoing interest in insignificant figures 鈥渁ttest[ing]鈥 much greater things.
Elsewhere in his work, mathematical metaphors encircle themselves in moments of crisis. In Troilus and Cressida, Shakespeare uses mathematical language to chart the slow motion collapse of听听after witnessing his lover Cressida鈥檚 flirtation with another man.
For Troilus, Cressida disintegrates into 鈥渇ractions鈥, 鈥渇ragments鈥 and 鈥渂its and greasy relics鈥. To mirror this, Shakespeare鈥檚 verse descends into jagged pieces, like the early modern name for fractions: 鈥渂roken numbers鈥.
With 2023 marking 400 years since the publication of Shakespeare鈥檚 First Folio, it is exciting to see how the Bard鈥檚 plays spoke to significant developments in the 16th-century mathematical world.
Shakespeare鈥檚 plays registered the 16th-century crisis of classical mathematics in the face of newer ideas. But they also offered space for audiences to come to terms with these new ideas and think differently about the world through the lens of mathematics.
This article by听Madeleine S. Killacky, PhD Candidate in听 Medieval Literature, at 香港六合彩挂牌资料听 is published under a creative commons licence by The Conversation. .
