Had William Shakespeare ever browsed the textbooks in a medical library, he would have been confronted with a variety of opinions about the apparent differences between the sexes.

Turning first to On The Usefulness of the Parts of the Body by the 2nd-century Greek physician Galen, still in active use in the 1600s, Shakespeare would have read that women and men were inverted copies of one another. A woman’s sexual organs were precisely the same as a man’s, wrote Galen, ‘the difference between them lying in only one thing… namely, that in women the parts are within the body, whereas in men they are outside.’ According to Galenic theory, it was male ‘heat’ that pushed out the genitalia during a foetus’s gestation, creating the only significant distinction between male and female forms.

But then Shakespeare might have picked up John Banister’s The History of Man (1578), which suggested something quite different about the nature of men and women: Banister advised doctors to ‘wholly abstain’ from considering female anatomy at all, as the alien mysteries of femininity were likely to confound (and probably dangerously arouse) the wisest surgeon. Another influential medical work, a compilation published in 1597 as The Problems of Aristotle, identified women as alarming deviations from the male norm, ‘monster[s] in nature’ whose toxic bodily emissions posed a threat to masculine virility. Human physiology was – it’s fair to say – a matter of debate in Shakespeare’s England.

But although Renaissance surgeons had a somewhat foggy notion of anatomical sexual difference, early modern culture had very set ideas about gendered behaviour: men were distinguished from women through employment, social status, dress, comportment and speech, and it was a matter of supreme importance that these distinctions were preserved. Doctors might have scratched their heads about what, precisely, made a person biologically male or female, but cultural commentators had no doubt about what made someone a man or a woman. Men were active, vocal and born to control a household. Women were passive, meek and designed to obey. It was through the performance of these social behaviours that an individual manifested their gender.

Shakespeare’s contemporaries were taught that rigorous self-policing was required to maintain maleness and femaleness as meaningful categories: mannish women and effeminate men ran the risk of doing permanent damage to their bodies and souls. As the Puritan polemicist William Prynne put it in a diatribe against transvestite boy actors, cross-dressing teenagers strive ‘thus purposely, yea affectedly, to unman, unchristian, uncreate themselves, if I may so speake, and to make themselves, as it were, neither men nor woman, but monsters.’

All of which makes William Shakespeare’s achievement in Twelfth Night truly remarkable. His cross-dressed heroine Viola – who calls herself a ‘monster’ in Act II, scene 2 – is no social pariah, but a glorious demonstration of the range of gender possibilities available to early modern people. Viola disguises herself as a boy and wins the love of a man and a woman (Orsino and Olivia); her epicene twin brother Sebastian is beloved of both Olivia and the lovelorn Antonio. On the seventeenth century stage, with female roles taken by boys, the play was even more giddily fluid in its gender dynamics: Viola is in fact a boy playing a girl playing a boy for most of the play, indistinguishable from a boy playing a boy (Sebastian) and surrounded by boys playing women (Olivia and Maria) as well as men playing men. In Twelfth Night gender really is what a person makes of it, no matter the story beneath the petticoat or hose.

In Shakespeare’s Illyria, sexual dimorphism isn’t all it’s cracked up to be. Dressed as the boy Cesario, Viola is regarded by Orsino as an apt wooer for Olivia precisely because of the youth’s alluring androgyny: ‘Diana’s lip / Is not more smooth and rubious,’ observes Orsino. ‘Thy small pipe / Is as the maiden’s organ, shrill and sound, / And all is semblative a woman’s part.’ If Malvolio sniffs that ‘one would think his mother’s milk were scarce out of him’ when he meets the young Cesario, we realise that this is not just an indication of Viola’s disguised femininity when her twin brother Sebastian – born a male but indistinguishable from his sister – admits to Antonio that ‘my bosom is full of kindness, and I am yet so near the manners of my mother that upon the least occasion more mine eyes will tell tales of me’.

It might surprise us that, in the world of Twelfth Night, Viola can effect such a successful gender switch that she convinces everyone around her of her new identity. Olivia certainly has no doubts. ‘I’ll be sworn thou art’ a gentleman’, she says of Viola. ‘Thy tongue, thy face, thy limbs, actions and spirit / Do give thee five-fold blazon’. By adopting the manners, habits and behaviours of a man, Viola has to all intents and purposes become one. Her maleness seems hard to shake off – Viola never changes out of her boy’s attire, and Orsino is still calling her Cesario in the final lines of the play, well after her identity as a woman has been revealed.

Shakespeare’s vision of a gender identity that can slip along the scale from female to male and back seems familiar. The past few decades have seen a striking increase in the visibility of the transgender community, and a more confident assertion of every individual’s right to live the gendered existence that accords most closely with their identity. But if the number of transgender people seems greater today than in the past – the American charity GLAAD reported a few years ago that more than one in ten young people identified as gender non-conforming, compared to 3% of the over-50s – it’s worth remembering that gender fluidity is no 21st-century invention: Shakespeare’s comedies, and Twelfth Night in particular, show that when it comes to gender, it’s all a matter of performance. As the philosopher Judith Butler put it in 1990, gender is ‘not something that one is, it is something one does’ – and Shakespeare’s characters do it every which way they like.