Norris Shapiro

Director Anna D. Shapiro and playwright Bruce Norris on the set of the play "A Parallelogram" at the Mark Taper Forum in Los Angeles. (Allen J. Schaben / Los Angeles Times / July 13, 2013)

A refresher course in high school geometry isn't a prerequisite for "A Parallelogram," the play by Pulitzer Prize-winner Bruce Norris running at the Mark Taper Forum. But it certainly wouldn't hurt.

The four actors in Norris' strange, ambiguous domestic drama serve as the corners of a narrative quadrilateral that keeps shifting and changing shape, at times threatening to break apart and enter another dimension.

The more relevant course work might be advanced geometry of the non-Euclidean variety. In one scene, a character describes the counterintuitive notion that two parallel lines can in fact intersect.

"Imagine that each line also extends indefinitely in all directions and since space is infinitely curved, that means that any two parallel lines eventually cross at some point. You follow me?" she says.

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It's understandable if theater audiences can't. "A Parallelogram" isn't a play about geometric theorems but rather a psychological study of a woman whose mind disintegrates when she is inexplicably visited by an apparition of her older self.

Norris declined to explain the play's meaning. "You don't set out with a thesis statement. My intention is to create an experience, a sensation," he said

In person, Norris, 53, can be prickly and peevish but in a knowing, sometimes humorous way that actually comes off as endearing. He was seated next to director Anna B. Shapiro in a small, barely furnished dressing room backstage at the Taper.

Shapiro, the Tony-winning director of Tracy Letts' "August: Osage County," is as outgoing and personable and Norris is reserved, and together they make an intriguing creative duo. This fall, they will team again in New York for Norris' latest play, "Domesticated," a politically themed drama starring Jeff Goldblum, that will open at Lincoln Center on Nov. 4.

"A Parallelogram" was first presented in 2010 at the Steppenwolf Theatre in Chicago. Since then, it has undergone light revisions because of what the playwright said were befuddled reactions from audiences.

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The playwright said "Parallelogram" was partly inspired by a recent revival of "Our Town" by Chicago's Lookingglass Theatre that was co-directed by Shapiro. In particular, the role of Thornton Wilder's Stage Manager, who narrates the classic play, proved especially intriguing.

"We wanted to mess with the concept of the narrator as the audience's surrogate," he said.

In the play, thirtysomething Bee (Marin Ireland) is visited by the specter of her older self (Marylouise Burke), who sits in an armchair and dispenses jaded wisdom. Young Bee is amid a relationship crisis with her significantly older boyfriend (Tom Irwin); she also develops a growing affection for the young man who tends to her yard (Carlo Alban).

Shapiro has described "Parallelogram" as being in part about the "belief in the power of the do-over." In certain scenes, the older Bee uses a supernatural remote control to rewind a conversation. Time is flexible, and so is one of the characters' identities.

This is especially true in the play's second half, which offers a twist that suggests the David Lynch movie "Mulholland Dr." crossed with ABC's "Grey's Anatomy." (Norris didn't agree with the Lynch comparison. "David Lynch is a mystic. I'm not a mystic," he said.)

The second act has been reworked since the Chicago run, where Norris said he became "concerned that audiences misinterpreted facts in the play." During audience "talk backs" after a play — which, no surprise, Norris dislikes — he and Shapiro found that viewers were interpreting the story rather freely.

"Neither of us likes to point out things directly," the playwright said. "But that made me very uncomfortable."

On a roll

Since winning the Pulitzer and Tony Award for his play "Clybourne Park," which ran at the Taper last year en route to Broadway, Norris has vaulted to the top echelon of American playwrights.