Miller has done the same in the theatre. An early production of The School for Scandal (1968) stripped away all the Georgian clichés and lace cuffs, and set Sheridan's play in a much more squalid 18th-century world. In the same year, he directed The Seagull, scrapping  the gentility and pathos of traditional English productions, all white linen suits and parasols, exploring the humour and shabbiness of Chekhov's world. And in his production of The Taming of the Shrew, for the BBC Shakespeare series in the early 1980s, Miller drew on Michael Walzer's The Revolution of the Saints to rethink Petruchio (played by John Cleese) as a 17th-century Puritan squire.

Putting classic plays in new settings is just the most obvious aspect of Miller's revisionism. Perhaps his more distinctive achievement as a director is what has been called his "theatrical naturalism", what one may also call a kind of behavioural or psychological realism. In his book of essays, Subsequent Performances (1986), Miller wrote that "the function of a director is to remind people of things they know but have forgotten. At any given moment in a rehearsal the director, like a good analyst, might say, ‘Have you ever noticed that under these circumstances people do this or do that?'"

A key influence here was the American sociologist, Erving Goffman. "Goffman," says Miller, "drew particular attention to apologies and remedial behaviour in public places: someone tripping on the street and going back to inspect the pavement in order to deflect the accusation that he is a fool."

We don't normally pay attention to these "seemingly negligible actions", Miller went on, all those little behavioural or verbal tics that fill our conversations. "It's like an orchestral score: you may not notice the woodwinds under the strings' melody but it enriches the harmonic structure."  

Critics often accuse Miller of imposing interpretations on a play from the top down, choosing a big idea (a fascist Tosca or a Fidelio set in Pinochet's time). But more often he works from the bottom up, taking a telling detail to make sense of characters and their relationships. "My approach," he wrote in Subsequent Performances, "is very similar to that of the palaeontologist Cuvier, who believed that you could reconstruct the entire body of a fossilised mammal by a careful and intelligent series of deductions made from a very small, and apparently unrepresentative, fragment. By looking at the toe, or the shape of a tooth, he might discover what sort of terrain it walked on, or the kind of diet the creature had."  

The enemy is the cliché or the over-familiar: Hamlet as the gloomy young Dane, the blowsy Gertrude, the bullying Petruchio. Instead, Miller constantly seeks a new way of seeing classics, asking questions and following them to see where they might lead. Why does Ophelia go mad? "People do not go mad as a result of grief," he writes, so what's wrong with Ophelia? Did Lear's daughters drive him mad or does he drive them mad? In Shakespeare, why are fathers so often betrayed by their daughters? Why are there so many references to time in Three Sisters? What would happen with Long Day's Journey Into Night if instead of running it, reverently, at four hours, you had the Tyrones talking over each other all the time, like any other family?

Miller's creativity as a director does not clash with his scientific and psychological interests, it draws on them. His critics have often said this has made him too gimmicky, over-cerebral, a show-off, a cleverclogs. The better question, rather, is: what have his reading and thinking allowed him to do? What kind of ideas have interested him?