Richard Greenberg grew up on Long Island, not in Levittown, where his new play, The Babylon Line, takes place, but close enough to have imbibed that community’s atmosphere. “We were all about 45 minutes from the city,” he told me before rehearsal the other day, “and though there were distinctions between towns” – for example, East Meadow, where Greenberg was raised, was known for a fine public library – “there were also similarities.”

The play’s three middle-aged stay-at-home mothers are a mixture of like and unlike. “They are like many of the women I knew,” Greenberg said, “but they are not based on any people in particular.” They have grown up in the city, during the Depression, in luxury-deprived circumstances, with plenty of people around them night and day. “They came to Long Island as an escape, and for something better, but their sociability was probably too ingrained to be shed. They were neighborly.”

“When I was a child,” Greenberg said, “I always thought it was a little odd that people were friends because of proximity.” He added: “But to these people knowing their neighbors was comforting. They would sit outside together on lawn chairs, and the mothers would visit each other for coffee.”

More intractable city folk might find the behavior of such women – in the play the characters are called Frieda, Anna, and Midge – prying. “I don’t think they thought of themselves that way,” Greenberg said. “They thought they were concerned about each other.”

Privacy and prying collide when a 38-year-old writer named Aaron comes to Levittown to teach an adult class in writing. The women want to know more about him, and about his relationship with Joan, another student in the class. “They live in a world where people know about each other,” Greenberg said. “They think they are exercising natural curiosity.”

Greenberg’s own curiosity about the world has been reflected in a couple dozen plays he has written since he graduated from Princeton and the Yale School of Drama in the 1980s. Lincoln Center Theater has presented Everett Beekin and The House in Town. His 2002 work about baseball, Take Me Out, won the Tony Award for Best Play. The Assembled Parties and Our Mother’s Brief Affair, his most recent plays produced in New York, have, like The Babylon Line, featured especially rich roles for women over 40.

I wouldn’t dare to pigeonhole Greenberg as “a women’s writer” or “a men’s writer” or anything else so reductive. But it’s undeniable that he has recently created complex portraits of women reacting to the pressures of memory and of change.

One of Greenberg’s own relevant memories: “When I was 19, I was a counselor at an arts camp for a month. Some of the kids were as young as two-and-a-half. But by 3 and 4 the girls were already more complicated in their responses to their environment than the boys were.” Attending closely to the responses of girls and women has paid off in Greenberg’s work.

Which brings us to Greenberg’s highly enjoyable new book of short essays, Rules for Others to Live By: Comments and Self-Contradictions. “The title is related to the fact that for a long time people would come to me with their problems,” Greenberg said. “They thought I was a good listener. I dispensed advice – rules of a sort – and my advice was listened to.” But, Greenberg continued, “I think everybody else is more competent than I am and as a result capable of taking advice that I’m helpless to follow myself.”

The brevity of Rules is part of its beauty. “I’m attracted to short forms,” Greenberg said. “A few years ago, I saw Adam Bock’s play, The Receptionist. It was 66 minutes long and completely satisfying. Ever since then, I’ve wanted to write a play that’s 66 minutes long and completely satisfying. But I haven’t even been able to write a play that’s 66 minutes long and sucks.”

Brendan Lemon is the editor of