Adam Driver has a reputation for being a serious young man, which is partly a matter of attitude and partly, I suspect, to do with some aspect of his physiognomy: he has a large head and outsize features that somehow combine to give an impression of gravity. Before the photoshoot, he let it be known that he finds it uncomfortable to have a journalist (me) in his sightline on set, the kind of specification one might expect of a particularly precious Hollywood star. But this turns out to be misleading. Driver’s discomfort is with the entire celebrity aspect of his job, which makes talking about his role in the latest Star Wars trilogy somewhat tricky. I don’t even know where to start with The Last Jedi, I say, as we settle down after the shoot, and Driver grins, then looks gloomy. “Me, neither,” he says.

We are in downtown Manhattan, a few miles from Driver’s Brooklyn Heights neighbourhood (Lena Dunham lives there, too) and a more upscale part of Brooklyn than the grungy Greenpoint location of Girls. That show, the sixth and final season of which ran on HBO earlier this year, was watched by relatively modest numbers, but has had an outsized influence on the culture. Barely a day goes by without Dunham being mentioned in a blogpost somewhere, and it gave Driver, who played her on-off boyfriend, the kind of career launch twentysomething actors can only dream of. At 34, not only does he have his second go as Kylo Ren in the latest Star Wars movie, but he has just shot The Man Who Killed Don Quixote, directed by Terry Gilliam, was in the Steven Soderbergh film Logan Lucky and played the title role in the Jim Jarmusch movie Paterson. Pretty good, I’d say, although I assume the two Star Wars films – The Force Awakens and The Last Jedi – are the real life-changer.

“No,” Driver says, looking genuinely baffled.

But to be part of a juggernaut that size – wasn’t he warned it would change his life? “I don’t think anyone said that, and I wouldn’t have listened to them, anyway. As a person, I’m the same. The problems I had before Force Awakens, it didn’t solve any of them.” He laughs. “For me, the only noticeable difference is your visibility as a person. Loss of anonymity is a big thing. I didn’t realise how I would see that in a billion little ways.”

The fame he had before Star Wars was somewhat localised. As Driver says drily, “In my neighbourhood, a lot of people watch HBO.” Star Wars is different: “Seven-year-olds to 70-year-olds.” It is global and almost impossible to escape. Driver is 6ft 3in and distinctive-looking, like a child’s drawing of a man brought to life. He’s even recognisable when travelling at speed. “I thought, I’ll ride my bike around the city,” he says, “and within two seconds I got pulled over by the cops, who said, ‘Hey, can we take a picture?’”

Really? “Yeah. I mean, I also ran a red light, so it was fair.”

Driver has been in New York since his early 20s, and part of his appeal as an actor has to do with his background. Before attending drama school at Juilliard, he was in the Marines. He was discharged after two years of training, and before his unit got shipped to Iraq, following an injury brought on while he was out mountain biking, a terrible blow at the time.

It is this – the combination of the classical theatre training and the military experience – that gives Driver an unusual ruggedness. As with most things that come up during our conversation, he is mildly amused and emphatically deflating about the role of the military in his appeal as an actor. He already knew he wanted to perform when he joined the Marines in his late teens, a move partly inspired by 9/11 and partly by youthful lack of direction. Driver’s application to Juilliard had been rejected; he had no other plans and was listlessly living in his mother and stepfather’s house in Indiana when 9/11 happened, filling him with what he described in a recent TED talk as “an overwhelming sense of duty”. He was also feeling “generally pissed off” and underconfident, and for some reason – he agrees, looking back, that it was in many ways an odd move – signing up seemed to be the answer.

At high school, Driver wasn’t particularly macho. “I didn’t do organised sports, not because I didn’t like them, but because I wasn’t very good at them. Except basketball. But I was never, like: let’s play football.”

He mainly hung out with the high school drama nerds. “I wasn’t someone who was into groups of guys – we’re men! We’re going to eat meat!” He looks momentarily wry. “I don’t know what guys do. Anyway, I would never have talked to those people before the military. Now you’re stuck in the epitome of alpha-male territory.”

To everyone’s surprise, he loved it. One can almost see why: there is an earnestness to Driver that relished the purity of military life and the more he talks about it, the more he makes it sound like a combat version of Buddhism. “There’s something about going into the military and having all of your identity and possessions stripped away: that whole clarity of purpose thing. It becomes very clear to you, when you get your freedom back, that there’s stuff you want to do.”

The bonds Driver made with his fellow Marines were startling to him, given how different many of them were in terms of background. (In his own family, his mother is a paralegal, his stepfather a Baptist preacher and his father works “at the copy counter at Office Depot”.) In the military, Driver says, none of that mattered. “You’re in this high-stakes environment where who you are as a person is constantly tested. And, in my experience, a lot of the people I was closest to in the military were very self-sacrificing. For me, it speaks volumes, more than how well they were able to articulate, or whatever front they were putting on. You get to see them at their most vulnerable and they’re literally going to back you up. All pretences dissolve.”

Being discharged on medical grounds before deployment was devastating for Driver; but the experience of having been in the military also made rehabilitation easier. Nothing, he believed at the time, could be as hard again, and after a period of working in a warehouse back in Indiana, he found that he still wanted to act and reapplied to Juilliard. It was different this time. “Whereas at 17 I just wanted to be liked, and to be funny, and accepted, later I had a bit more life experience.” He was accepted and moved to New York.

He has worked almost constantly since then, to the extent that he took four months off recently just to hang out at home with his wife Joanne Tucker. (They met at Juilliard and she is also an actor.) Most of his early roles – he was in Frances Ha, the excellent Noah Baumbach movie, and in the Coen brothers’ Inside Llewyn Davis – were very good, but relatively small scale and indie. Even Girls, his breakthrough role, didn’t look like much when it first came on screen. The Force Awakens, on the other hand, became the fastest film to take $1bn (£740m) at the global box office. I try again: surely this does something to Driver’s basic levels of self-confidence?

“No, because that’s not what I was after when I started to be an actor,” he insists. “It would if that was my goal. I know people think that if you’re an actor, it’s your goal to be famous and wealthy. Surely you want to be famous and wealthy! And there are great things about that part of it – it frees you up to do other things. But part of my job is being anonymous and I think being able to live, to observe more than to be observed, is important. [Being famous] seems counterintuitive to my job. It’s a weird dynamic when you walk into a room and there’s an image people project on to you.” He interrupts himself to say, conscientiously, “My problems compared with global issues, or anybody else’s, are very small. Even that I have time in my day to think about the existential.”

This is how it goes with Driver: he is assiduously mindful of broader sensitivities and somewhat embarrassed to air his own. “What it means to lose anonymity is a bougie problem in and of itself. And I won’t garner sympathy, nor am I asking for it. The image of us on our red carpet wearing expensive suits, where people naturally assume your life is, is not what I was after when I started this job. Believe it or not.”

I do believe it, I say. One has only to look at him, twisting this way and that in his chair. (“I’m not doing it on purpose to get away from you,” he says.)

So he doesn’t take any credit for, or validation from, the success of Star Wars? “You mean, am I, like, yes!” He gives a little satirical air punch. “I’m excited that people liked it, but do I think that I got it right? No. If I had directed it, maybe. But I didn’t write it, direct it, pick out the costumes. All these decisions – about the lightsaber, that it’s unfinished and unpolished – none of those were mine. I know enough about this job not to take credit.” He looks pained. “That would be an illusion.”

***

Driver’s family have no roots in acting, although his stepfather’s job as a minister might be said to have some performance aspect to it. Driver sang in the church choir well into his teens, which, he says, gives you an idea of how left-field his decision to enlist was. When he joined the school theatre, it was because his friends were doing it and it looked fun. “They auditioned for Oklahoma!, so I did. And I got a part in the chorus. I remember being backstage and it seemed like a community that was a bunch of weirdos, and I liked that part of it. I also felt that I was kind of OK at it. I tend to get frustrated with things that I don’t pick up right away.”

When people in the US think of Indiana, he says, they think of somewhere “boring and flat”. It is also deep into Trump country, such that Driver and his family are careful to avoid talking about politics when he goes home for the holidays.

Occasionally, his worlds collide. A few years after being demobbed, Driver set up a nonprofit organisation called Arts In The Armed Forces, which puts on theatre performances for personnel at military bases. His burgeoning celebrity has made it easier to recruit other well-known actors to the cause, but it is testament to his management skills that from the outset, the company has been smartly and seriously run. His aim, he says, was to broaden the range of entertainment put on for the troops. When Driver was stationed at Camp Pendleton, in California, the troop entertainment was, “‘The Dallas Cowboys cheerleaders are going to come and dance for you.’ Which is great, but there wasn’t anything like theatre or performance art brought to us.”

Unlike Bryan Doerries’ excellent stage project Theatre Of War, in which Greek drama is performed before military audiences as a public health initiative, there is no therapeutic element to Driver’s nonprofit. Still, it can have an interesting impact. “In one of our first performances, Laura Linney did a monologue from this Scott Organ play called China, about a female employer reprimanding a female employee for not wearing a bra. It’s really funny, that’s why I picked it – not really thinking it through. It was one of a series of monologues, and the male Marines were coming out and saying, we really liked it, but we thought [that particular one] was an indirect attack on how we do things in the military.”

When Driver asked why, they replied, “Because there’s a uniformity and structure and a reason in the military, and we thought that’s what you were trying to criticise. I said, OK, that’s interesting. And then the female Marines were coming out and saying, I liked the whole thing, especially that monologue, because I know what it’s like to be a female in a very male-dominated environment. That’s the best response we could’ve asked for. Hopefully they like it and it’s entertaining. But it also confronts them, and they bring something to it that a civilian audience wouldn’t think of.”

It can take a little persuasion on Driver’s part to get officers to allow him on to the base, and if he is adept at overcoming the military’s initial scepticism towards theatre, it is thanks to the experience of having overcome similar prejudice in himself. Theatre school seemed insane after the Marines, he says. “It is a very egocentric four years, just sitting around and focusing on what does the back of my tongue sound like when I make this sound? What is a Scottish dialect?”

Failure didn’t particularly worry him; he was still in his early 20s and brimming with the confidence of youth and the machismo of two years of hard training. “In the military, you are put in hard circumstances, so I’m thinking, I’ll move to New York and be an actor, and if it doesn’t work out, I’ll just live in Central Park. You know, compared with the military, it can’t be that difficult. I’ll dumpster dive. I’ll survive. Civilian problems compared with the military are small; that was my thinking at the time. That’s not right. But at the time, that’s what I thought.”

It wasn’t just the contrast between the two worlds that gave Driver confidence. There is something almost fanatical about his belief in the right and wrong way to do things. When he was still at school and decided to be an actor, the only place he applied to was Juilliard; nowhere else, no backup. He had heard it was the best place in the US to train, so that’s where he wanted to go.

Unsurprisingly, perhaps, he isn’t on social media. Those kinds of exchanges don’t interest him. As a result, he missed out on a lot of the hype around Girls, although even he couldn’t fail to recognise that the show was a hit. (Driver won three consecutive Emmy nominations for his role as Adam Sackler.) It was a strange thing, he says, to sign up for what felt like a relatively obscure show – “Something that felt like it was made in the basement of a friend’s house” – and watch it rise, while he and his friends rose with it. (We speak before the controversy over Lena Dunham’s defence of a Girls writer against an accusation of rape.)

It did not escape Driver’s notice that his own nudity on the show was less remarked upon and criticised than that of Lena Dunham, even though Dunham wrote, produced and directed the show. “Of course there’s a double standard for men and women. I don’t think that’s a controversial thing for me to say. It’s so obvious, and one of the things that she was fighting against, which I understood right away, is that it wasn’t gratuitous. There was always a point behind it, it was always still storytelling. It just seemed very natural. We talked just as much about being naked, and what was the story and the sex scenes, as we did about scenes where there’s dialogue.”

It wasn’t uncomfortable to film? “If it’s for no purpose whatsoever, that would be very uncomfortable. But part of the storytelling is about our bodies and how they look, and if there’s something that’s not flattering about it, that was probably what we were going for. That’s my job, to tell the story.”

What did he learn from Dunham?

“Um. I mean, Lena is a great writer. She’s a good thief, also: she’s very aware of her environment and is very good about processing her experience of something immediately. I feel like I need more time to get distance on it, so I can look back and have an opinion. She is forming opinions as she does things. Which I think is a rare ability.”

Driver sometimes wonders if he’ll ever come to firm conclusions about anything. “I never figure anything out,” he says, winningly. “I do my job. That’s my goal, to be as economical as possible. Basically, the only thing I try to do is know my lines.”

His ego is contained, too. “Usually, the mood of the set is what I adapt to, as opposed to having a set way of working and imposing it on everybody else. If you need private time, usually people give you space for that. But getting set into one way of doing something seems like closing yourself off from being wrong.” On the other hand, “interesting things can come out of being wrong”. He smiles. “Sometimes.”

Can he let things go?

“No. I don’t think so. Maybe after a while. I keep replaying scenes in my mind. That’s why I don’t like to watch anything I’m in – it’s not my responsibility.” It’s a Zen attitude Driver has worked hard to perfect and he frowns with the effort of maintaining it. To be a small part of the machine is where he has always felt comfortable. “It’s not about me,” he says .

• Star Wars: The Last Jedi opens on 14 December.

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