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Jacquelyn Reingold’s String Fever is a romantic comedy about a woman who falls for a no-account physicist.

Tom Stoppard’s Hapgood is a whodunit about a spy agency that nearly falls when it can’t account for a physicist.

Reviewing them unaccountably falls to a guy who never sat through a physics class.

Anyone got a theory to handle that? Wave?…Particle?…String? Actually, Reingold’s play posits a theory—that strings combine into webs—that sounds promising, at least to me, as I feel myself getting ensnared in a linguistic web of my own devising. Happily, while both shows talk a good physics game, appreciating them requires no pre-show studying. They’re designed first and foremost as entertainments, with Hapgood—having been designed, intelligently, as it were, by the world’s cleverest dramatist—managing to be a bit more than that. Whereas Reingold’s romance leaves you smiling, the Cold War intrigue Stoppard whips up will leave you feeling smiley in both the Tinker, Tailor, Soldier, Spy sense and in the pure joy sense.

Well, not quite pure, if you require the engagement of both intellect and emotion. As mounted by the Washington Shakespeare Company, Hapgood is pretty much entirely an intellectual exercise: a brisk, witty riff on le Carré. It begins with the title character (Kathleen Akerley), a British intelligence supervisor overseeing a Keystone Kops–ish ballet involving mix ’n’ match briefcases, rolled-up towels, curtained stalls, and secret agents at a swimming pool. A drop, a sting, and a switch all go complicatedly wrong in just a few moments, and then, as the characters start puzzling out what happened—in a nifty illustration of the physics principle that reality is altered by the act of observing it—the play turns into a dazzling display of plot twists, purposeful double crosses, and doubles working at cross purposes.

“Somehow light is particle and wave,” says antimatter researcher Kerner (Bruce Alan Rauscher) to Hapgood’s boss (Ian Armstrong), who’s beginning to suspect he’s being triple-crossed by a double agent. “The experimenter makes the choice. You get what you interrogate for. And you want to know if I’m a wave or a particle.”

True enough, but either way, he’s no longer regarded as trustworthy, and therein hangs a tale that can be further explained only by giving away its surprises. So let’s talk of performance rather than plot. As befits a play that traffics in twins and double dealing, WSC’s production has been mounted by not one but two directors, Christopher Henley and Alexandra Hoge, who have choreographed its elaborate subterfuges with an eye to keeping sight lines as clear as lines of inquiry. Elizabeth Jenkins McFadden’s deco-ish setting features wave forms, both on walls and in the curved furniture that is constantly reconfigured—into offices, spas, apartments, even a rugby pitch. Bold shades and deep shadows predominate in Jason Arnold’s lighting scheme, while Erik Trester’s sound design pushes ditties by Billy Idol, David Bowie, and the Cure—’80s reference points for a Cold War tale that Stoppard penned in 1988 but that wasn’t produced in this country until after the fall of the Berlin Wall had made it feel slightly dated.

In the title role, Akerley is a calculating, self-contained commander with a wild streak that surfaces late in the game. She’s a spy’s spy, known as Mother to her men and as Mum to her rugby-playing son (a nicely understated Brandon Thane Wilson), whose kidnapping figures prominently in the second act. The male cast around her is dominated by folks who bluster as they conceal, but a bit of emotional resonance is supplied by Rauscher’s sad, conflicted scientist, and by Hugh T. Owen, who has the look and manner of a 007 wannabe, as he plays an agent whose self-assurance masks a tendency to let his feelings run away with him.

While the evening qualifies as a tricky intellectual puzzle and is filled with ear-catching notions (“Every atom is a cathedral”), Stoppard hasn’t made his script as satisfyingly three-dimensional as that of Arcadia, his other science- and history-inflected mousetrap. The world theoretically hangs in the balance in Hapgood, but perhaps because the Cold War feels distant and just a bit quaint in these days of color-coded terror alerts, there’s never a sense that anything terribly real is at stake. Hapgood is just an arch take on counterespionage—a chesslike game of cerebral positioning and verbal feints—forgettable by the time you reach the parking lot, but fun while it’s in progress.

Even at that, it’s more substantial than String Fever, the frothy comedy now at Theater J, in which 40-year-old Lily (Melinda Wade), a divorced music teacher and failed concert violinist, belatedly awakens to the dissonance of a universe composed of subatomic, multidimensional vibrating filaments.

It’s her physicist boyfriend, Frank (Gary Sloan), who explains those filaments to her in a first-date discussion of string theory, taking pains to explain that it is one of two contradictory but equally valid ways of explaining the universe (the other being particle physics, I think, though waves and relativity figured in there somewhere). Lily finds Frank’s ability to consider macro and micro concepts at the same time intriguing, and the fact that he’s able to deal with her dad (Conrad Feininger), who is both cantankerous and dying, is a definite plus. But those extra dimensions required by string theory start to confuse Lily at about the same moment that Frank’s mixed messages about his intentions do.

Perhaps understandably, she reacts with spunk, raised eyebrows, and the sort of exasperated wisecracks generally trafficked in by Wendy Wasserstein heroines, while supported by a pair of equally Wassersteinian buddies—an Icelandic comedian in rehab (the amusingly pixillated Steve Brady) and a down-to-earth cancer survivor (graceful Lynn Chavis). Also on hand, to provide a midlife crisis or two, is Lily’s barely functional ex (Field Blauvelt, sounding persuasively scattered). Lily is, let’s note, excellent company for all these folks and for the audience, gamely dealing with the string of dysfunction, dyspepsia, and even death that the author throws her way.

Still, crises and quite a few laughs notwithstanding, there’s not much to the play, which was commissioned by a foundation that has a goal of bridging the gap between science and the arts. It does a better job of that than Peg Denithorne’s attractive staging does of bridging the gap between the actions on stage and life as most of us live it, however. On a lovely, planetarium-evoking set that Anne Gibson might have crafted for an exhibition at the National Air and Space Museum, the evening plays with an urban sophistication and polish that makes it feel at once safe and slightly distant—those vibrating filaments merging into a music of the spheres that sounds a tad more soothing than is probably intended.CP