Why wait 16 years to revive Arcadia, they’re asking the playwright, Tom Stoppard? To which the answer, begging his pardon for the presumption, must be: “Why screw with perfection?” For perfection it certainly was, even for those of us who saw the West End transfer cast, not the National Theatre originals in 1993 with Rufus Sewell, Emma Fielding, Bill Nighy, Felicity Kendal, Harriet Walter et al.

There are moments in the life of theatre that print themselves as an afterburn in the memory, punctuation marks in the history of our personal elation. Mine were Richard Burton, that fruitcake voice not yet heavily brandied, as Henry V at the Old Vic in the late 1950s; John Kane’s Puck sitting spotlit on the swing in Brook’s life-altering A Midsummer Night’s Dream; Alan Howard heavily oiled as Achilles in the RSC’s Troilus, surrounded by Kenneth Anger myrmidons in black leather; Laurence Olivier as a Rothschild-Shylock in Jonathan Miller’s National Theatre production, voice strained with humiliation. And then there was that moment at the end of Arcadia, which drew the audience to the cliff-edge of heartbreak before pulling the curtain down in our faces.

Arcadia is a play about the mischief of time. In that last scene, as if through a wormhole, one set of characters from 1993 who have been attempting to track what happened in the same house – Sidwell Park, Derbyshire – nearly 200 years before, share the Regency room in which the play is set with another group of characters, those who lived it. Each group acts as if oblivious of each other, yet they are threaded together by the ribbon of their story. Time folds in on itself; Einstein’s whiskers bristle in the wings.

The precocious teenage genius Thomasina who has intuitively discovered chaos theory, somehow aware that the heat exchange of bodies disrupts a logically ordered Newtonian universe, aches to experience Romantic uncertainty by demanding a waltz with her young Newtonian tutor, Septimus Hodge. The contemporary pair – the graduate scientist graphing the algorithm of grouse through his family game book and the literary historian Hannah – move more awkwardly to the beat of music coming from the country house marquee where a costume party is under way. As in all strong classical drama, the characters’ obliviousness to a fate known by the audience registers in stabs of ironised pain.

None of which, of course, prevented some critics in 1993 from sounding off, as they had got into the habit of doing about Stoppard, that he was all head and no heart. Re-reading the play, you wonder whether they had misplaced their cardiac machinery, so deaf were they to the tenderness washing through the wordplay. Never had the self-indulgent cleverdick charge seemed so wide of the mark.

There was of course, serious prep. Harriet Walter, who played Lady Croom in the original production, told me that the cast had to do its homework in, among other fields, fractal geometry and landscape history. James Gleick, author of Chaos : Making a New Science, was flown in to give a lecture. One imagines the kindly but exacting Prof Stoppard returning papers at the end of the fortnight’s study: “West, S, you’ve sort of got the hang of it; Kendal, F, jolly good; Sewell, R, see me after class would you? There’s a good boy.”

But, Harriet Walter says, the intensity of the engagement in the play of ideas, and Trevor Nunn’s willingness to let the actors find their way to character-clarity, paid off: each of the protagonists could realise their role in binding together the elements of pure story. For Arcadia is emphatically not a dramatised seminar, but a tightly executed plot; the way to truth as snaky as a winding path about a picturesque lake. That hapless investigator, the literary historian Bernard, is set up (as media dons generally are in National Theatre plays, can’t imagine why) for a satisfying pratfall. Running parallel to the tease of family history is the tease of the way the universe might be ordered, or fail to be ordered. But no one needs a higher degree in quantum physics to have a good time. Not least because Stoppard makes the inquiry so user-friendly: instead of equations, Thomasina wonders why jam stirred into rice pudding cannot be unstirred.

The play – even when read on the page – has some of Stoppard’s funniest exchanges, which is saying something. The ghosts of Congreve, Sheridan and Shaw romp through its nimble lines. But the great figure inhabiting this Stoppard comedy is Wilde. Told by her landscapist Noakes, busy tearing up Lady Croom’s park to create a shaggy wilderness, that it would feature a hermitage complete with hermit, she inquires where a suitable hermit might be found. “One could advertise,” suggests Noakes. “But surely,” she replies, “a hermit who takes a newspaper is not a hermit in whom one could have complete confidence.”

The jokes come hurtling from the stage like debris from outer space. But as with the best comic writing in the English tradition, they also come loaded with predictive power. “Septimus, what is carnal embrace?” is the opening line of the play, from the 13-year-old Thomasina. “Carnal embrace is the practice of throwing one’s arms around a side of beef,” he replies. The audience erupts in laughter. But that first wide-eyed question lingers like a misleadingly cute Mozartian motif that builds into something ominous; the heat exchange that ignites catastrophe while the universe grins. It’s like “Who’s there?”, the two-word opening of Hamlet that is also the entirety of the play.

Arcadia unfolds in that wonderland of mirth. But just utter the name of a minor character – Plautus the tortoise – and the Roman playwright sidles in dressed as Lewis Carroll, carrying a bundle of wistful grief beneath the chuckling. Like no one else writing today, Stoppard knows how to make us smile and how to wipe it off our chops. Among the gallery of intellects summoned is Erwin Panofsky, the art historian who first saw that Poussin’s “Et In Arcadia Ego”, the scene of shepherds coming upon a tomb bearing that inscription, had been misread as a nostalgic allusion to the deceased having once been happy in the enchanted land, whereas the “ego” in question was in fact Death himself. Stoppard’s guffaws come from a place of hard hilarity, throwing us on our back so that we have nothing else to look at but the whirling stars. From that dizzy spectacle and the place of scuttling humanity beneath it that Stoppard limns so beautifully, we draw both sadness and consolatory wisdom.

‘Arcadia’ is at the Duke of Yorks Theatre, London, May 27-September 12, www.dukeofyorkstheatre.co.uk

Peter Aspden is away