Scene for scene, shot for shot, Paul Thomas Anderson may be the most exciting American writer-director of his generation. He’s a kind of cinematic chemist who works with unstable, dangerously flammable human particles. At any moment his characters—and his movies—are capable of exploding, and there’s no telling which way the shards will fly, or, as in Magnolia, the frogs will drop. Think of the seething ambition of Daniel Day-Lewis’s power-hungry oil magnate in There Will Be Blood; the powder keg of anger underneath the shy Adam Sandler in Punch Drunk Love; the cold, narcissistic fury behind the cocky surface of Tom Cruise’s sex-guru in Magnolia; the coke-fueled desperation of the porn-world denizens in his exhilarating Boogie Nights. There are rarely conventional heroes and villains in Anderson’s emotionally charged sagas, and that’s one of the reasons his movies feel so alive; he keeps us out of the comfort zone of predictable Hollywood formulas.

The protagonist of the magnificently unsettling The Master, Freddie Quell, may be the most volatile compound yet in the Anderson canon. Played by Joaquin Phoenix, he’s a wild, damaged World War II vet who, at war’s end, returns to California after his stint in the Pacific. An alcoholic who concocts his own bootleg hooch, a puss-hound with sex on the brain, Freddie has a violent streak that can be set off by the slightest provocation.

He’s a man who’s spent his life running away, even from the girl he professes to be the love of his life. And then Freddie meets and falls under the sway of “the Master,” Lancaster Dodd (Philip Seymour Hoffman), the founder and leader of a spiritual movement called the Cause. Anderson freely acknowledges that this flamboyant character—a self-described author, sea captain, physicist, and philosopher—was inspired by L. Ron Hubbard. Once word of this leaked out, The Master immediately got tagged as Anderson’s “Scientology movie.” “I was naive,” the director says, somewhat ruefully. “I should have known that’s what people would latch onto.” But if you’re expecting to see an exposé of that controversial “religion,” you’ve come to the wrong movie. This is not to say Scientologists are going to like what they see. But Anderson, who gets a bit stressed when the subject comes up, finds himself “much more defensive and protective of [Scientology] than I would have thought.”

When the Master first meets Freddie aboard a private luxury ship in San Francisco Bay—one of his wealthy followers has donated the vessel to the Cause, and Freddie has snuck on board, hoping to find a job—Dodd’s eyes light up at the challenge. Dodd claims that mankind can overcome its animal nature and reach its innate perfection through his methods, which involve the exploration of one’s past lives, in order to expunge one’s ancient demons. And here before him stands a beast desperately in need of taming. But there’s more to it: Freddie’s wildness titillates him, and so does his homemade booze. He’s found someone to play savior to, but he’s also found a naughty playmate, a lower companion who allows him to take a breather from his public role as the all-knowing guru.

Freddie is taken into the inner circle of the big Dodd family. There’s Dodd’s quiet but powerful wife (Amy Adams), his grown son, and his pretty daughter, whose shipboard marriage takes place as they set off for New York. For Freddie, it’s the chance to have at once a father figure, a drinking companion, and a family he never had—if he can submit to the rigorous rituals of the Cause. A question looms over the story, the same one that hung over the anarchic anti-hero of A Clockwork Orange: can this tortured, violent animal be civilized?

The Master, the rare movie shot these days on 70mm, feels epic—it ranges from the beaches of Hawaii to the English countryside—but its focus remains fixed on the passionate and mysterious bond between these two men. It becomes clear by the end that the movie is a strange kind of love story. The mesmerizing scene in the Master’s cabin when Freddie first submits to Dodd’s interrogation techniques is both therapy and foreplay. Dodd is a master of seduction. He berates Freddie for being an animal, then rewards him with the candy of praise: “You are the bravest boy I’ve ever met.”

Phoenix, with his spooky laugh that’s both defensive and taunting, is phenomenal, and scary as hell. It may be the highest compliment that a lot of people are going to think Phoenix isn’t acting at all—that they’re watching a genuine nutcase. His explosions are a force of nature: Phoenix has a scene where he goes berserk in a Philadelphia jail cell that makes De Niro’s raging bull look genteel. This is the role he’ll be remembered for.

Hoffman, a brilliant shape-shifter who’s been in every Anderson movie but one, is working in an entirely different style, and it’s thrilling to watch them play off each other. If Freddie is all inarticulate instinct, Dodd, who speaks with a formal, literary flourish, is almost always in performance mode, the self-appointed master of ceremonies. Hoffman can turn on a dime between self-deprecating charm and attack mode: when he snaps it’s a different kind of scary. The Master may be a fraud and a fabricator, but he’s no villain. He genuinely wants to heal his flock, and his belief in his own benevolence gives him power. Adams, as Mrs. Dodd, may not have a lot of screen time, but she makes the most of every moment. She’s the true believer, the power behind the throne, ever vigilant of her husband’s reputation. Her public face of calm subservience masks a steel-willed woman always on emotional high alert.

The Master (in theaters Sept. 14) feels of a piece with There Will Be Blood, the first film in which Anderson traded in his hyperkinetic style for a simpler, more concentrated focus. At 42, he’s no longer the hotshot wunderkind, intent on dazzling us with every bravura Steadicam shot. In his personal life, he has put his past excesses behind him—he’s married, to actress Maya Rudolph, and the happy father of three young kids. He can look back with humor at the brash young filmmaker who fought with his producers over every frame of his first film, Hard 8. “No one could possibly tell me anything, because I’d painted them as the enemy,” he says. “By Punch Drunk Love I’d mellowed, I felt more confident in myself. I didn’t have to defend every B+ idea I had.”

But in another sense his movies have become fiercer, and more formally and emotionally challenging. The Master is a slap in the face of the screenwriting rulebook that insists on a clear three-act structure, tidy resolutions, and characters whose “arcs” make a neat trajectory from A to C. He likes, he says more than once, to keep things “liquidy,” and there are scenes, like one in the balcony of a movie theater, that blur the line between reality and dream. Like Jonny Greenwood’s gorgeously dissonant score, the movie keeps you off balance and on edge. The spell it casts is both passionate and cool, like a fever dream from which any trace of sentimentality has been expunged.

When he first started writing The Master, Anderson had no idea what it was, where it was going, or where it would end up. “I was first writing scenes that didn’t have a home. I do that a lot, and then finally they come together. I like to write every day and keep working and not wait around for something to happen,” he says. “Richard LaGravenese [the screenwriter] once said that writing should be like ironing a shirt: you keep going over the same spot, and you go a little deeper and a little deeper. I don’t want to sound all mumbo jumbo, but it gets to a certain point, if things are going well, where you’re not writing it; the character is going where he’s going.”

Kind of like the mixologist Freddie, who makes booze from whatever is at hand, be it guavas or paint thinner, Anderson gathered pieces for his movie from disparate sources. There were scenes he’d written early on for There Will Be Blood he’d never used. There were stories Jason Robards had told him on the set of Magnolia about his drinking days in the Navy during the war. Chunks of Freddie’s experiences as a migrant field worker and wanderer were lifted from John Steinbeck’s life story. There was his fascination with the larger-than-life Hubbard. “But I didn’t want it to be a biography. It’s not the L. Ron Hubbard story,” Anderson says. He was inspired by a quote he read that the period after wars was a particularly fertile time for spiritual movements to start. “That was a hook you could hang your hat on.”

He knew from the start he wanted Hoffman to play the Master, and his actor-friend was an integral part of the writing process. “He was my first audience. I’d hand him chunks and hear what he responded to.” For the longest time Anderson wasn’t even sure whose story it was. It was Hoffman who clarified it for him: “This is Freddie’s story.” He also had Phoenix in mind as he was writing, and he knew the actor would keep his writing from sounding too literary. “At a certain point, Joaquin is just incapable of faking it.” Anderson was amazed by Phoenix’s discipline on set. “He’s like Daniel [Day-Lewis], his level of concentration. He just got in character and stayed there—for three months he didn’t stop. Joaquin is very unpredictable. A lot of the time I didn’t know what he was going to do.” In one scene Freddie has to be restrained by a cluster of policemen. He laughs remembering the head of the stunt crew advising his men to take it easy on the star. “Six of these stunt guys couldn’t hold him down!”

When I mention that The Master, like so many of his movies, is about the creation of a makeshift family, and that there are similarities between the monomaniacal, alcoholic antiheroes of his last two movies, he seems slightly embarrassed. “I know, it’s the same thing again. No matter how hard I try to set out to do something different,” he says. “I wish I would have more diversity as a filmmaker.” It’s a complaint no one else has made.

Because his über-stylish movies are so immaculately shot and edited, and because there have only been six in the past 16 years, and because he’s a bit of a control freak, Anderson has often been called a perfectionist. Terrence Malick, whom he reveres, gets the same label. But in fact they’d both be better labeled imperfectionists, for they are instinctual artists, who often don’t know what they’re after until they see it in front of them. The last shot of The Master, for example, was something he discovered in the editing process. “It just felt right. I can’t tell you why. If I have a strong instinct, I go with it, and try to get the intellectual chatter out of my head,” he says. He’s absorbed the lessons of his idols, the formalist Scorsese and the improvisational Altman, and merged them into a passionate style all his own. It’s there in every haunting scene of The Master, the impeccable, classical craftsmanship in search of the live-wire moment of emotional truth.