For over a thousand years, Rome was the city of the world. The Romans ruled the greatest empire that had ever been seen. Even after its decline and fall it lived on for centuries by providing the western world with models of excellence in every dimension of human life from military technology to political sophistication to theory of moral character to cultural glories such as architecture and epic poetry.

Shakespeare's England was a small, vulnerable, upstart nation near the northwestern edge of the known world. When Queen Elizabeth I came to the throne, the country was in a state of near-psychotic self-division as a result of her father's break from that latter-day Roman empire, the universal Catholic church. But in the course of her reign, aristocrats, intellectuals, seamen, poets and theatre people forged an amazingly bold new vision: that one day, their tiny island-nation might become a second Rome. They laid out the building blocks for the future. Naval power saw off the might of Spain and planted the name of the Virgin Queen on distant shores. Politicians honed a system of checks and balances between the two houses of parliament and the monarchy- a system based on the Roman model of senators, tribunes and emperor, but with a more flexible legal system, based on common law 'precedent' rather than a fixed code of rules. Educators opened grammar schools for the middle classes, steeping the future administrators of nation and empire in both the Latin language and the Roman character of firm backbone and stiff upper lip (known technically as Stoicism). And Shakespeare's actors staged epic dramas in which they told the heroic history both of their own nation and of the Romans who were their ideal.

So it was that when Britannia came to rule the waves in the eighteenth and nineteenth century, Shakespeare's Julius Caesar was central to the education and character-formation of aristocrat, politician and imperial civil servant alike. True Britons were not, however, encouraged to visit Shakespeare's other Rome, the bloody world of his first tragedy, Titus Andronicus. The play was so shocking to tender sensibilities and so subversive of the Roman ideal that it was hardly ever staged and was frequently said to be by someone other than Shakespeare. You could not have the National Poet soiling himself with a barbaric feast of rape, dismemberment and cannibalism.

Yet Titus was one of the most popular plays of the Elizabethan age. A glorious mishmash of history and invention, it creates an imaginary Rome that is simultaneously a popular republic and a decadent empire. The play made Shakespeare's reputation as the authentic successor to the original angry young man of English drama, Christopher Marlowe. Aron's delight in his own villainy is shamelessly ripped off from Barabas and Ithamore's boasting in the same vein in Marlowe's Jew of Malta. Shakespeare was a contrarian. He took the commonplaces of his age and stood them on their heads-or perhaps sliced off their heads and baked them in a pasty. Rome was synonymous with civilization and the Goths with barbarism. So Shakespeare considers the possibility that Rome was just as barbarous as the Gothic forest. Roman Stoicism proposed that it was healthy to keep your emotions under tight restraint. So Shakespeare voices the need to give your feelings vent ('Sorrow concealed, like an oven stopped, / Doth burn the heart to cinders where it is'). The law prescribed that punishment should be left to the justice system, so Shakespeare dramatised the primal-though ultimately self-destructive-attraction of acting out revenge for oneself. A daughter has been raped and mutilated: the law is not there to help (even the poor Clown goes from quest for imperial justice to arbitrary execution), so Titus raises the stakes and thinks of a revenge so hideous that it outdoes the original crime. This is but an extreme version of an instinct that is still with us: the police do nothing about the burglaries, so out comes the pump-action shotgun.

Titus Andronicus plays like the work of a very clever, very naughty schoolboy. In the classroom of the Stratford-upon-Avon grammar school, young Will would have learnt that the purpose of studying the classics was to be inspired by their heroic actions and moral virtue. This was the message of books such as Plutarch's Lives of the Most Noble Grecians and Romans, out of which he would later create his Julius Caesar and Antony and Cleopatra. But what he also found in classical literature were glorious tales of blood and gore, not to mention every sex crime imaginable. The brilliance of Titus is that it is suffused with the language of the Elizabethan classroom-words like tutor, instruct, lesson-but that it uses classical literature as "pattern and precedent" not for virtue but for high crime and misdemeanour. The story of the rape of Philomel by Tereus and her sister Progne's juicy act of revenge, as told in Ovid's Metamorphoses, is explicitly invoked first by Demetrius and Chiron as the pattern for what they do to Lavinia and then by Titus as the precedent for what he will do it to them. And it is by way of reference to the actual book of Ovid that the silenced Lavinia contrives to reveal what has happened.

Again, the lesson of classical literature was that tragedy should be kept apart from comedy, high art from low. Shakespeare was perfectly capable of following this precept when he wanted: Julius Caesar probably has fewer laughs than any other play in the canon. But in Titus, he wantonly flouts the classical rules. He recognises that there is actually a very narrow borderline between tragedy and farce. Four hundred years before the enfants terribles of modern Hollywood, he sees that audiences love the shock of the rollercoaster ride from violence to humour.

Jokes are always at someone's expense and it is one of the obligations of the serious artist to push at the barrier of good taste so that we can discover when the expense is so great that we feel sick. If the play has a fault, it is that the formality of both language and action in the opening scenes create a sense of stiffness that suggests classicism at its most tedious. This is probably not Shakespeare's fault: modern scholarship has persuasively demonstrated by means of close stylistic analysis that Titus Andronicus was begun by another dramatist, George Peele, who had a high-level classical education and a taste for large-scale symmetrical stage encounters spoken in high-flown rhetoric. We don't know whether the play was written as a purposeful collaboration or whether Shakespeare came in to do a re-write or to complete an unfinished work. Nor do we know at precisely what point the writing became his alone-though there is no doubt that he is the author of all the most dramatic scenes, from the rape through the hand-chopping to the fly-killing banquet (which was his later addition, not in the earliest printed text) to the feast at the climax.

Perhaps the most profoundly Shakespearean moment-a dramatic move far beyond the capacity of Peele-comes when Titus is confronted with the dismembered ruins of his family and his brother Marcus tells him that it is time to "storm", to rend his hair and explode into a great tirade of words. But Titus doesn't. All he can do is laugh. In times of extremity, you have to throw away the rulebook. In real life, tragedy and comedy don't live in different boxes. William Wordsworth once wrote of thoughts that lie too deep for tears. Only William Shakespeare could have dramatised the astonishing but profoundly human idea that the place you get to when you go beyond tears is not silence but laughter.

Jonathan Bate is Professor of Shakespeare and Renaissance Literature at the University of Warwick, and editor of the Arden edition of Titus Andronicus.