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Diana Donnelly, left, plays Hannah Jarvis and Kate Besworth is Thomasina Coverly in the splendid Shaw Festival production of Tom Stoppard’s Arcadia.David Cooper

"Oh, phooey to Death!" exclaims Thomasina Coverly, a 13-year-old math genius, even as she forecasts the ultimate demise of the universe based on her observations of how jam reacts in her bowl of rice pudding. Before the end of Tom Stoppard's Arcadia, her childish defiance of mortality will come back to haunt you and break your heart.

This is quite possibly the British playwright's most brilliant, and certainly his most moving, play. It's no surprise that the Shaw Festival's new production was sold out before it opened Saturday – I'm sure many people consider it their favourite Stoppard work. It's mine as well and, happily, this splendidly acted revival does it justice.

How do you begin to describe a comedy that encompasses, among other things, iterated algorithms, chaos theory, ornamental hermits, botany and Lord Byron? One so intricately plotted, so full of mirror images and incidents, that it takes your breath away? It's a cerebral treat, but one that keeps you constantly on your toes. Let your brain cells rest for a second and you'll miss this allusion to Stephen Hawking, or that elaborate joke about a Latin translation of Antony and Cleopatra.

Stoppard isn't just a show-off, however. Every concept he touches on, every erudite reference informs or resonates in his story. And befitting a play set partly at the dawn of the 19th century, when the Age of Enlightenment was giving way to the Romantic era, it is also about sex, love, jealousy and other messy human emotions that can't be neatly reduced to a mathematical formula.

And speaking of concepts, Thomasina (Kate Besworth) has stumbled upon the second law of thermodynamics while pondering her pudding. It's 1809 and we're at Sidley Park, the Coverlys' country house in Derbyshire, where the girl is at her lessons with handsome young tutor Septimus Hodge (Gray Powell). He's pretty bright himself, and a school chum of Byron's to boot.

Like Byron, Septimus is also a bit of a rake and has been caught in "carnal embrace" in the park's gazebo with the wife of aspiring poet Ezra Chater (Andrew Bunker). Now Chater wants to settle the matter with pistols at dawn. Meanwhile, Thomasina's mother, Lady Croom (Nicole Underhay), is upset about another outrage – she's just learned that landscape architect Mr. Noakes (Ric Reid) plans to transform her once-classical garden into a bleak Gothic wilderness after the latest fashion.

Cut to Sidley Park in the present day, now invaded by a pair of literary historians in search of a scoop. Hannah Jarvis (Diana Donnelly) is interested in the house's Gothic garden, complete with hermitage, and the identity of its mysterious resident hermit. But cocky Bernard Nightingale (Patrick McManus) has bigger fish to fry: He's convinced Byron stayed there in the spring of 1809 and killed a forgotten poet named Chater in a duel.

Mr. Noakes has an ingenious flip book that allows his clients to the see the "before" and "after" appearance of his landscape designs. The play, set in one room of the house, essentially does the same thing. The scenes keep flipping back and forth in time until present events are superimposed over those in Thomasina's day. The action is propelled by twin plots that feed one another: We follow the happenings at Sidley Park in 1809 and the way the modern scholars interpret and misinterpret them in their search for both the truth and a juicy academic coup.

Arcadia, first produced in London in 1993, is a perfect fit at the Shaw Festival, whose audiences are accustomed to the intellectual rigors of Bernard Shaw and the rapid-fire wit of Oscar Wilde – two of Stoppard's most obvious antecedents. Indeed, many of the cast members can also be found in the visually dazzling production of Wilde's Lady Windermere's Fan on the festival mainstage. Arcadia director Eda Holmes attempts nothing so ambitious in the cozy Studio Theatre; simply using a serviceable set by Sue LePage and some apt but muted piano music by Allen Cole, she's content to leave the dazzle to Stoppard's dialogue and some expert actors.

McManus reaps the biggest laughs as florid Nightingale, the smug, snotty, sexist Byron expert, and plays the role with palpable relish. Donnelly is his perfect foil as sturdy Hannah, who holds her own against Nightingale's bullying while besting his dodgy scholarship with some real discoveries. Aiding her is Martin Happer's moody Valentine Coverly, a scientist who has inherited his ancestor's math gene and finds some startling stuff in Thomasina's old schoolbooks.

Back in 1809, Besworth's frizzy-haired Thomasina scampers about like a prepubescent female Einstein, ideas going off in her head like fireworks. As Septimus, Powell does both "dashing" and "dejected" in the best Romantic manner. Bunker's Chater is a delicious ninny, while the luminous Underhay is an imperious but wanton Lady Croom, who changes her lovers as and often as she changes her hats.

Arcadia takes its title from the Latin motto, spoken by Death, Et in Arcadia ego (Even in Arcadia, there am I). And sure enough, Death eventually shows up in Stoppard's lush garden of ideas. But ultimately the playwright says phooey to tragedy. Instead, the play ends with past and present, reason and romance, joined together in a bittersweet waltz – an exquisite conclusion to a sublime work of art.

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