Ferrante did read over the script, but gave only limited feedback. She gave her blessing for Gyllenhaal to change the story’s ending, though – albeit in ways which still chime with the novel’s intent. Did she glean any sense of the real Ferrante from her dealings with this literary enigma?

“Honestly, I have no more information than you do,” she insists. “But in my imagination she’s this very wise 70-year-old woman. The good thing about her anonymity is that she could be whatever I needed her to be.”

Born in New York in 1977, Gyllenhaal grew up in Los Angeles in a family of creative types: both of her parents were filmmakers, and her younger brother Jake went into acting before she did. How long had she harboured ambitions of directing?

That’s a tricky question, she says, “because I don’t think I felt entitled to want it. If you were a woman who loved movies, the much clearer path was just to become an actress with ideas.” Over the next three decades, she worked out ways to get those ideas on screen: sometimes by subterfuge – “I’d just privately take a scene in a certain direction and hope that 30 per cent of what I was doing would end up in the film” – and sometimes by talking her directors round.

On The Deuce, a recent HBO drama, set in the New York pornography business in the 1970s and 1980s, Gyllenhaal had been cast as Candy, a prostitute whose business acumen sees her ascend in the business to fully-fledged adult movie mogul. “But I thought, ‘Wouldn’t it be a more interesting story if she was a director, rather than a producer? So I kept talking to [series creators] David Simon and George Pelecanos, dropping the idea in ever so delicately, with a bit of sugar – you know, however you manage as an actress to get what you need.

“And then,” she adds with satisfaction, “Candy became a director.” Only while playing her character’s own move behind the camera did Gyllenhaal begin to realise it struck a chord with her own desires.

“It wasn’t so much that it gave me the idea, but that it allowed me to have the fancy of doing it myself,” she says. “I’m far braver on screen than in reality. I often learn things in my work before I learn them in life.”