CHICAGO — Rebecca Miller did me a big favor 14 years ago, when I was doing a Chicago Tribune Magazine profile of her formidably famous father, playwright Arthur Miller.

The piece needed something – I wasn’t sure what – and, just before deadline, she returned a weeks-old call, from her then-home in County Wicklow, Ireland, where she lived with her husband, actor Daniel Day-Lewis, and their sons. (They’ve since moved back to New York City.) Free-associating through memories of time spent with her father, Miller, who is a screenwriter, director, novelist, artist and actress – recalled a particular moment on a Manhattan sidewalk.

On their walk her father stopped beside a platform-loading garbage truck, its various interlocking mechanical parts doing their thing in noisy harmony. “I was trying to figure out why he was watching with such interest,” the younger Miller told me. “He said: ‘It’s beautiful.’ I said: ‘Why?’ And he said: ‘Because everything has a function.’ I think that was his best advice to me. He believed everything had its function, including a garbage truck. And he believes everything you write has to have a function.”

That same year, 2002, was the year of Miller’s second feature film as writer-director, “Personal Velocity.” The droll seriocomedy “Maggie’s Plan” starring Greta Gerwig, Ethan Hawke and Julianne Moore, and now playing is Miller’s fifth.

The story’s based on unpublished material by a friend of Miller’s, Karen Rinaldi. Over coffee recently, Miller clearly relished having made a movie that lent itself to a “hook.” The hook: “What happens when you realize your husband is perfect for his ex-wife? It was the first time I started a story with a hook. For me, generally, the hook comes out of many drafts and a long time, when I’m trying to find (the shape of the narrative). But in this case I already had it, so in a weird way, I worked backwards, and created the characters to fill up the idea.”

The Gerwig character, Maggie, works in Manhattan as a New School career counselor. Just as she decides to become a single parent via sperm donation, she meets a “ficto-critical anthropologist,” struggling novelist and amiable narcissist (Hawke) who’s married, unhappily, to a fearsome Danish academic (Moore). Sparks, divorce, remarriage. But as time goes and children come into the picture, Maggie suspects her medium-unhelpful husband and co-parent was better off before, as was she. In blithe, easygoing fashion, “Maggie’s Plan” puts a plan into motion.

The film belongs to the old romantic comedy subgenre of remarriage stories. The emotions, Miller says, are meant to be real. Her film, she hopes, “is light, but heavy. Like life.” Certain side details, she says, spring from the 53-year-old Miller’s earlier years in New York. At one point Maggie sublets a book-crammed apartment from an unnamed poet; Miller re-created the physical space based on a similar apartment (sublet by the poet W.S. Merwin) she had for a while.

Miller shot the movie in February, “the most dire time,” as she says, laughing. “But it’s a wonderful time to capture. We benefited from the light. It’s not harsh, it’s almost like a dawn quality all day. That clean winter light.”

As for Gerwig, Miller can’t say enough about the actress with the uniquely off-kilter timing. “That wonderful combination of willfulness and innocence! She’s the girl next door, but she can do stuff you wouldn’t dream of doing, and you just sort of go with her.” Maggie, as written, is meant to be a paradox, modest but not a prude, old-fashioned in some ways, modern in others. “I mean,” says Miller, “human beings are full of contradictions. I am, anyway.”

It took her a while to find her artistic homes. Growing up with a legendary father and an accomplished photographer mother (Magnum’s Inge Morath), the imaginative Miller explored various pursuits. She enjoyed some success as a visual artist and as an actress; in one of her larger roles, in director Alan Pakula’s “Vertigo”-inspired thriller “Consenting Adults,” she co-starred with Kevin Spacey and the headliners, Kevin Kline and Mary Elizabeth Mastrantonio. Next year she’s back in front of the camera, for a supporting role in a new Noah Baumbach picture with Adam Sandler, Emma Thompson, Ben Stiller and Dustin Hoffman.

Miller has described herself as a third-generation New Yorker. “I loved living in Ireland, too,” she notes, adding that she and Day-Lewis maintained a New York apartment for the summers. “Rural Ireland and New York City, because they’re the opposite of each other. I love writing books and I love making movies, because they’re the opposite of each other. I’m not a big fan of the middle of anything. I don’t love suburbs. I don’t like tepid feelings. If I love someone, I’m really loyal until they’re disloyal, which generally means we’re done.” She laughs. “I’m a little Cosa Nostra that way.”

At the keyboard, especially, Miller says she has learned the artist’s paradox: “You have to be vulnerable or you can’t do the work, but you have to toughen up, or you’ll die, basically.” A few years ago, she says, she was “walking down the street. I’d just eaten at a restaurant. One of the waiters came running after me, wearing one of those long aprons. I thought I must’ve left my credit card or something. And he said: ‘Just wanted to let you know: I think you’re incredibly underrated.'” Miller cracks up at the memory of that sort-of compliment. “And I said: ‘Thank you!’ Then I went home and told my husband about it, and he said, ‘Well … better underrated than overrated.’ It was one of life’s little pleasure/pain moments.”

I thank her for adding to my piece on her father years earlier. “I remember that,” she says of the garbage truck lesson in functionality. “That was a good moment for him. I learned a lot from that moment.”