Intriguing word, ‘octoroon’. Does it mean an eight-sided almond-flavoured cakelet? No, it’s a person whose ancestry is one eighth black. New Yorker Branden Jacobs-Jenkins wants to explore this factoid in his farce An Octoroon, which opens with an angry African-American playwright delivering a comic monologue. He tells us a story about ‘my shrink’. Then he tells us that ‘my shrink’ doesn’t exist. Then he talks about ‘my shrink’ again. Right, so is ‘my shrink’ real or not? Obviously the writer doesn’t care.

A second dramatist enters, an Irishman, in Victorian costume. This is Dion Boucicault, a 19th-century writer whose comedies were enormously popular in London and on Broadway. Boucicault’s opening line is ‘Fuck you,’ which he addresses to the black playwright. ‘Fuck you,’ comes the reply. This phrase is repeated 20 times between the amusing wordsmiths and they try to make their repartee even funnier by screeching the lines at the volume of an exploding barrel bomb. After this, the play rather tails off.

The writer sets out to examine the issue of racial imposture on stage but he has nothing to say about it. He creates a 19th-century scene in which a black performer dressed as a white character says ‘Nigger Pete’ to a white performer dressed as a black character. Once delivered, the label is discarded without comment. What’s the point of giving a fresh currency to these extinct slurs? To increase racism, perhaps, although that seems a strange ambition for the National Theatre. The only other purpose is to make us feel slightly ashamed of our ancestors. Whites were overly brutal, blacks overly subservient. OK. What’s new?

Two gossiping slave girls appear and they become entangled somehow in a melodramatic pastiche that features a screaming heiress, a stolen baby, a gesticulating bandit, an axe-waving Cherokee and a rich fool fumbling with a primitive camera. I say the girls ‘become entangled somehow’ in a pastiche because the narrative is so confused, the performers so enamoured of their over-acting, and the production so choked with intrusive effects that the story’s meaning is rendered opaque. Many spectators struggled with drowsiness as the chaotic action wore on. And because the house lights were up — always a bad idea — the sleepyheads were openly visible to their neighbours and to the unfortunate performers. Another hour or two passed, and on trooped a group of labourers who spent several minutes removing some floorboards from the stage to reveal a trench into which flammable liquid was poured and ignited. This meant that a boat was alight. What boat? Why alight?

Every few years in the theatre I suffer a weird reality shift and become convinced that I’m not a reviewer but a hostage lured into an asylum by deluded exhibitionists. Part of me wants to escape but my duty to the reader holds me in place, a bemused invigilator, as my sad captors attempt unavailingly to amuse their fellow earthlings. Such was this ordeal. The Critics’ Circle last year gave Jacobs-Jenkins its ‘most promising playwright’ award. (Rather a disingenuous accolade: we never said he was good, only promising.) I would no more see a play by a ‘promising’ writer than I’d make an appointment with a ‘promising’ dentist.

The Donmar has hired Polly Findlay to direct a revival of Muriel Spark’s The Prime of Miss Jean Brodie. The character is an unorthodox teacher whose encouragement of rule-breaking among her pupils leads to tragedy. Brodie is an archetype, a disappointed rebel, like the Fonz, who creates a gang of admiring younger acolytes to compensate for her personal failings. Findlay has produced an unfussy and faithful version of the story which, by some miracle, finds the theatre’s sweetest spot. Every moment of the play is deliciously poised between sadness and laugh-out-loud hilarity.

The cast are terrific. Sylvestra Le Touzel is wonderfully grisly as the puritanical Miss Mackay. Rona Morison delivers a puckishly intelligent Sandy. Gordon, the silky old lothario (Angus Wright), comes across as a park-bench pervert in a well-cut suit. For Lia Williams the role represents a huge challenge. On paper Brodie is awful, a priggish needy sentimental snob whose worship of Italy doesn’t preclude an enthusiasm for Mussolini. But in the flesh, she’s irresistible, a born seductress, a mythical she-wizard whose incantations create magic and disaster. Williams blazes forth in the role, fully fledged, a brand-new star, in complete command of her art. Relish every detail: the humour, the charisma, the mischief, the steeliness, the pathos, the technical exactitude and the unmistakeable background murmur of eroticism.

I confess I’ve seen Williams in two celebrated shows and I barely noticed her. But the roles were duds, not her. She took the lead in Schiller’s coma-inducing Mary Stuart and she played Clytemnestra in a bore-of-the-year version of the Oresteia. But this is something else. If it doesn’t reach Broadway, what’s Broadway for?