"Humourlessness is the really scary thing right now," she offers. "I really feel that it's a time where comedy is the civilising thing. You know, intelligent, thoughtful comedy, just so we can laugh at ourselves and think about ourselves, our foibles."
In the film, Maggie (Greta Gerwig) sets out to have a baby, which she intends to raise on her own, using sperm donated by an erstwhile college friend, but her scheme is interrupted when she falls for an older married writer, John (Ethan Hawke). They seem made for each other, but when their marriage brings out the worst in John, Maggie plots to return him to his first wife (Julianne Moore).
There's a whiff of Woody Allen, a comparison not lost on Miller. Here, though, it is the older woman who ultimately gets the (slightly) younger man, gender-reversing the sometimes queasy age-gap relationships in Allen's films. "It is an inversion and it is playing Woody's game, a little bit," she agrees. "I was aware of it, for sure. It's there to be played with, and all artists play in a way."
Miller knew she was going to be an artist before hitting her teens. "By the age of 11 or 12, it seemed inescapable to me," she says, explaining that it had become clear to everyone that her creativity was her strength. "Without forcing it on me, I do think I was raised to be an artist. Like, almost cultivated. Somebody once described me as being like a racehorse that's been bred in a certain way, and I think there was a little bit of that."
She says her childhood in Roxbury, Connecticut, was "uncommonly quiet" by today's standards. "I remember we had a rowboat and a pond, and I used to go down there alone and just row around for hours, looking for frogs. I was almost in a trance." The solitude "built in me a big reserve of some sort," recalls Miller, "like a bubble that I could go inside. And I can still find that. Even in a crowded space, I can still enter that silence." Her childhood sounds lonely, I suggest. "It could be lonely at times," she admits. "But, for the most part, I wasn't lonely, I was just alone, which is different."
Her situation helped her imagination to bloom, but the directions it took her in weren't always healthy. The earliest thoughts she can remember having were about "religious things", she says -"Was there a Devil? What happened when you died?" Her mother owned a Mexican clay figurine of a chapel with people praying inside. On the roof above them sat the Devil, laughing.
"The irony that he was laughing on top of the church freaked me out so much, and really started this whole thing," Miller says. She became obsessed with the idea that the Devil lived in her house, and she got herself baptised because she feared going to Hell. Meanwhile, her parents were unaware of the darkness gripping their daughter.
"I was all by myself with that, which wasn't their fault. They were not cold people but they weren't the kind of people that were constantly asking you how you were feeling. Also, I was such a cheerful child. There was no part of me that showed what was going on. This kind of terror that was happening inside of me."
That terror fuelled her award-winning first feature, Angela, in 1995. The movie, about a highly imaginative 10-year-old girl hovering dangerously between religious fantasies and reality, was an exorcism, of sorts. But, Miller says: "I do think that my being infected by Christianity, like a kind of virus, [means] a lot of it has stayed with me, and I see the beauties of that religion, but also that there are some dangerous parts to it. And I think I was very vulnerable to those things because of guilt, and all the elements of guilt."
She wasn't drawn towards Judaism in the same way because it seemed to her like "a great male force. . . I couldn't hook on. Christianity - there always seemed to be more footholds, because it was more primitive. And there were saints and the Virgin Mary. And there were graven images, which I needed."
However, she realised while researching Jacob's Folly that there were dimensions to Judaism she'd been unaware of, and which resonated with her own interests and characteristics. When she dived into Jewish folklore, and the work of Bashevis Singer, for example, Miller realised it chimed with her own "storytelling and fascination with myth. Jewish folklore is just a goldmine of this stuff," she enthuses, "and really surreal and dreamlike."
Later, when she discovered gilgul (a Kabbalistic concept of reincarnation) and the idea of the return of the souls, and then saw how familiar it was to the family of ultra Orthodox Jews she occasionally stayed with, it made her think, "My God, this is so mind-blowing and so far away from what I thought of as Judaism."
Watching episodes of The Goldbergs, an American comedy-drama series from the '50s about a rowdy family of New York Jews, she started to recognise parts of herself in the character of the feisty matriarch, Molly. "She's like this big Jewish mother, sort of bossy and guilt-provoking, and a little bit of a caricature," Miller says. "But I was thinking, 'I'm a little like her,' and I started seeing that I have a lot of my character that's quite Jewish." She laughs loudly. "My mothering, I'm a very big mother. There's a lot of mother to my mothering. I run hot in that department."
She has three children: two sons by her husband, the actor Daniel Day-Lewis, and a step-son from his previous relationship with Isabelle Adjani. Not long after marrying Day-Lewis, Miller experienced severe writer's block and, in need of something to make herself feel useful, volunteered at a women's shelter. The experience gave her material for her first book, a collection of short stories about women at turning points in their lives called Personal Velocity.
This sudden inability to write was unusual - her mind is generally restless. Even when she isn't physically writing, she has "a story and it's like my invisibility cloak, and it's over me and kind of like protects me."
She adds: "I think that that's an extension of my childhood. Because when I was a child, I was always playing in my head. There was always some other game going on, and I don't know if it's a good thing or not. Sometimes I think it would be nice to just be able to live life, like really just live life, and have nothing else going on in my head. But whether it's a gift or a curse, that's who I am."
Given the vibrancy and vividness of her inner life, you have to wonder whether she finds it difficult balancing mundane reality and the world of her imagination.
She admits that "sometimes it can be very, very hard. But, overall, I am pretty good at focusing on my family when it's my family."
However, at "times of extreme intensity", this can still be difficult. "When I was finishing Jacob's Folly, it was really hard for me to do anything else," she says. "And when I was in pre-production on Maggie's Plan, I literally kept setting fire to the stove, to the point where my husband said:'Please, just stop cooking!'"
He may want to check that all the fire alarms are working in their New York home, because with promotional duties for the new film almost over, Miller is looking forward to her next screenplay, which she says will be more "operatic". She has also been thinking about adapting Jacob's Folly for the screen, but sees it more as a multi-part project than a movie, because of the book's scope and complexity.
"People have said, 'what a great idea.' But I have to figure out how I would do the fly. You know, what would you do with that?"
