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The hype on Tom Stoppard’s sparkling intellectual comedy, Arcadia—which began emanating from London in early 1993 and survived what nearly everyone agreed was a flawed New York mounting last year—turns out to have been entirely justified. A flat-out joy from its opening line (a 13-year-old’s query to her unflappable tutor, “Septimus, what is carnal embrace?”) to a final directorial fillip that sends not just the actors but the universe spinning, Arena Stage’s passionately elegant production is a luminous triumph.

Zelda Fichandler was in the opening-night audience, and it’s hard to imagine that she wasn’t immensely pleased to see the troupe she founded producing work this exhilarating in its 46th year. Arcadia is the sort of emotionally resonant play of ideas that the regional theater has championed since its inception. And the company clearly relishes the play’s heady language as much as director Douglas C. Wager enjoys its stripped-down theatricality. For while Wager is a master at maintaining focus in densely populated Marx Brothers musicals and set-heavy dramatic spectacles, he’s always most evocative when working as he does here, in the spare mode he brought to last year’s gorgeously austere Long Day’s Journey Into Night. Playwrights with as much going on as O’Neill and Stoppard needn’t be constantly goosed into life.

Arcadia leaps around temporally from the early 19th century to the present, and philosophically from arguments about landscape design and Byron to discussions of chaos theory and fractals, but isn’t remotely hard to follow. You do need to keep your wits about you as the playwright bounces ideas off every available surface, but no more so than during an evening by Shaw or Wilde.

Stoppard begins in 1809, in a sitting room overlooking the elegantly designed “natural” gardens of the Coverly estate, which Lady Croom (an imperious but pragmatic Tana Hicken) is trying to protect from a designer of steam-powered waterfalls and faux-Gothic ruins. She’s also trying to protect her precocious daughter Thomasina (Wendy Hoopes) from too much education, but the child has an agile mind. So agile that she’s curious not only about carnal embraces but about the possibility that God might be a Newtonian.

“If you could stop every atom in its position and direction,” Thomasina posits, “and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra, you could write the formula for all the future.”

Her tutor Septimus Hodge (seductively played by J. Paul Boehmer) is momentarily thrown by this, partly because for all his erudition he’s a bit out of his depth, and partly because he’s just discovered that his dalliance with the wife of third-rate poet Ezra Chater (an uproariously foppish David Marks) is an open secret in the household. Duels are proposed, as are mathematical proofs, and a hermit is scrawled as a literary joke in a landscape illustration, all with trademark Stoppardian wit.

Then, at about the moment patrons will be congratulating themselves on keeping up, the action shifts to the present day, and we meet a trio of academics who are trying to piece together what happened all those years ago. Coverly scion Valentine (Alex Draper) has inherited the family passion for math and is poring over the estate’s game books trying to find a formula to predict grouse populations. Best-selling scholar Hannah Jarvis (Christina Haag) is researching a book on the mysterious hermit who apparently lived in the estate’s garden. And arrogant literary critic Bernard Nightingale (Terrence Caza) is trying to establish that it was Lord Byron’s involvement in the murder of a third-rate poet named Chater that caused the famous writer to flee England in the summer of 1809.

That’s as far as I’ll take the plot, though we’re only at Scene 2. Suffice it to say that the research of the contemporary characters dovetails in unexpected ways, while love (“the attraction which Newton left out”) proves a decidedly unpredictable free radical in the evening’s equations. The logic of fractal geometry actually starts to inflect the structure of the play as characters concentrate single-mindedly on the points of insight that interest them, at the expense of the big picture. You don’t need to follow this, but for those who enjoy puzzles, there are some genuinely engaging ones here.

At one point fairly early on, a character suggests reversing x and y factors in an equation, and at intermission, you may find yourself having a spirited conversation about how the author has done the same thing with x and y chromosomes, reversing the sexes of characters with near-identical concerns and personalities as he leaps forward in time.

Or you may just be chattering about the ensemble, which has clearly been having a ball. In the contemporary scenes, Caza and Haag are nicely matched predators as the determined (and often dead wrong) literary scavengers who try to divine the past from margin scribblings and letter fragments. And Draper, who has long been one of the most reliable pleasures of Potomac Theatre Project’s forays into the work of Howard Barker, is as movingly hilarious here in his anguish over mathematics as he was in his anguish over censorship as the Doge in PTP’s Scenes From an Execution last year. Also amusingly conflicted is Holly Twyford as Valentine’s decorous but hot-to-trot sister.

Holding down the 19th-century fort (or hermitage, perhaps), Boehmer’s dashing, tart-tongued tutor is neatly partnered by Hoopes, who may be a bit old to be playing 13 but who makes her inquisitive math prodigy’s leaps of logic remarkably easy to follow. There’s a lovely, simultaneously funny and harrowing moment in the second act when Boehmer’s 19th-century world is knocked off its axis by a blithe remark she makes about an equation. Hicken’s grande dame is graceful, aristocratic, and very funny when she’s on the receiving end of a seductive pass, while Marks’ self-impressed poet lacks grace and aristocracy almost completely, and is very funny when on the receiving end of a literary compliment.

Bridging the play’s two eras as a pair of diametrically opposed juvenile Coverlys (one an imperious terror, the other a silent waif), ninth-grader Michael Barry caps an impressive year that began with a fine professional debut in Source Theatre’s Loman Family Picnic and continued royally with young-monarch roles in Shakespeare Theatre’s Henry VI. In smaller parts, Arena regulars Wendell Wright, Ralph Cosham, and Richard Bauer are restrained and briskly effective in the service of Wager’s admirably uncluttered production.

It’s the sort of evening in which the curlicues in Zack Brown’s inlaid floor, the decorative fringe in Paul Tazewell’s gorgeous costumes, and the quasi-classical noodlings of composer Jeffrey (Wings) Lunden all seem to offer counterpoints to Stoppard’s verbal rhythms and the shape of his arguments. At one point I scribbled in my notes, “even the lighting is thrilling”—perhaps when a spotlit apple allows the play to leap back two centuries in a matter of seconds. In fact, by intermission, things are perking along so splendidly that Wager could bring on the second act of Whistle Down the Wind and still end up with one of the year’s most scintillating evenings.

The production is not flawless. The director needn’t have gilded his lovely final image with falling leaves for us to get the point that change is in the air; our world is already spinning by that time. And in an 800-seat, in-the-round auditorium, illustrating fractals on a laptop computer screen, or landscape design with a medium-size sketchbook, doesn’t really work, no matter how naturally the actors can be made to turn those objects N-S-E-W so that everyone can view them.

But these are quibbles beside such unexpected pleasures as an Antony and Cleopatra joke that seems to have ricocheted over from the Shakespeare Theatre. And a second act that is as poignant as the first is bright, with no diminution whatever in hilarity. And a breathtaking display of erudition and wit concerning every subject that comes up, from the perils of academic publishing to the sexual appetites.

Whether you’re struck by Stoppard’s deliciously convoluted observations on the Second Law of Thermodynamics (which concerns the inevitable cooling of the universe), or by Thomasina’s down-to-earth observations on the world around her (“You cannot stir things apart”), or by the play’s tug of war between intellect and feeling, you will be struck—and struck hard—by the ideas and emotions being batted around in Arcadia.

Not to put too fine a point on it, but this is what you go to the theater for. Don’t even consider letting Arcadia slip away.