One key scene in Paul Thomas Anderson’s brilliant new film has Lancaster Dodd (aka The Master, played by Philip Seymour Hoffman) drive his daughter Elizabeth, son-in-law, and Freddie Quell (Joaquin Phoenix) out to a wide expanse in the desert and tell them they’re going to play a game called Pick a Point. You look to the horizon, find a far-off landmark, and ride a motorcycle as fast as you can in a straight line toward that spot. Master hops on and roars off, exhilarating in the speed and direction while his daughter cheers him on from their starting point. When he returns, Freddie dutifully but unenthusiastically takes his turn on the machine. Elizabeth still cheers. At first the Master enjoys watching it too. “He’s going really fast,” he comments to no one in particular. Then his face alters, as he’s hit with waves of ambivalence.

One can read so many things into that face. After seeing it, we argued about moments like this for ninety minutes afterward, surprised to find such different opinions about the film’s central concerns. That’s what makes this film so rich: its open ends beg you to comb over its conversations and vignettes.

I wish I’d gone to see this film with a psychologist, for it most fundamentally asks whether a damaged psyche can heal (and doesn’t offer a rosy answer). Not that conventional psychology is the answer. By the latter days of World War II Freddie is already so far gone on self-destruction that he gets marched in to see a couple of army shrinks, but their clunky approach to the talking cure hits no targets. Self-medication is Freddie’s game. He self-administers cocktails made with virtually anything — paint thinner, photo processing chemicals, Listerine — which permit him to keep slurring his words, living in a haze, remaining mostly unemployed.

But the film also treats the intensity of a relationship between one as utterly lost as Freddie, and the Master who thinks he can help. Can we call it “help”? Or should we term it love? Just what Freddie and Master get out of their relationship is never clear, nor do we really understand the intensity of their bond. No matter. It’s supposed to be open-ended. It’s the most compelling male relationship I’ve ever seen onscreen.

Don’t be fooled by the notion that they are Master and acolyte. Sure, this is partly a story about an L. Ron Hubbard style charismatic leader who inspires a cult-like following based on an idiosyncratic concoction of psychology, hypnosis, past-life regression, compelling storytelling, and a good singing voice. But you’re not watching this film to learn anything new about cults or charisma or the psychology of followers.

Because Master is not really in control. Nor is he entirely successful as a charismatic leader — why, just look to members of his own family for doubt. Even his apple-faced new wife (Amy Adams) has more iron control packaged into a glowing, pregnant, schoolmarm-ism than Master could ever demonstrate. Master is not drawn to Freddie simply to control him.

Nothing could make a better contrast/ incongruity than the two men’s bodies. Years of dedication to drink have left Freddie gaunt, with weedy chicken arms and a stooped frame, as if his ravaged kidneys won’t allow him to stand up straight. You’d never guess Joaquin Phoenix is only 37 years old, for his thinness in this part is well-nigh alarming — equivalent to the horrors of Christian Bale’s skin and bones in The Machinist (2004). Meanwhile, no one looks so self-satisfied, porcine, and gleaming as the Master. Especially when stage-lit in front of Freddie’s camera, as below. When Freddie only gets more emaciated throughout the course of the film, the thought flicks across your mind that it’s as if Master were eating all the untouched servings on Freddie’s plate … and perhaps getting additional nourishment from Freddie’s oh-so-available soul, like a Dementor in Harry Potter.

What writer-director Anderson does in bringing these men together is allow them to develop a relationship beyond the bounds of the roles you might expect here. Himself a master of creating conflicting, deeply uncomfortable situations for his characters, Anderson forces these two men to face up against each other in a variety of ways that have no clear outcomes and intermittent catharsis. Most uncomfortable of all is the realization that no matter how kooky (and creepy) Master’s psychological methods, they’re far more effective than anything Freddie ever got from straight-up psychologists.

Yet The Master is not a story of redemption and healing. In fact, if anything it’s the most honest film about treatment I can think of — so much more powerful than David Cronenberg’s A Dangerous Method (2011), for example — in displaying not just the uncomfortable love and transference between the two figures, but the way that aggressive psychological treatments that demand honesty, self-revelation, and forced psychological breakdowns comprise a form of rape.

Tortured by lost opportunities and deeper demons, Freddie treads water and gulps his toxic cocktails while the Master fights the law on one side and, on the other, acolytes who question his intellectual consistency. No wonder the two men cling together in this crazy embrace, alternately lashing out at one another with the only tools they have available to them. For Freddie it’s sheer physical rage. For Master it’s blarney and a nice trick for maintaining a crowd around him to sustain the illusion of relevance.

And all around them are women. Amy Adams’ terrific turn as the Master’s wife, far more talented at the job of managing a movement than he is; Freddie’s idealized memory of the girl back in Lynn, Massachusetts who got away; Master’s lovely, unavailable daughter Elizabeth; and that big-breasted sand-castle woman his buddies made on the beach, only to have a drunken Freddie feign aggressive sex with it and ruin all the fun.

Like so many self-consciously “serious” Hollywood films, this is about men — but the difference here is that this is a film fundamentally concerned with gender and sex so much so that Freud would have had a field day. From male bonding to psychological rape to a couple of fantasy sequences and Freddie’s pathetic impotence, this film shows that Anderson has a lot more sensitivity toward women than his prior films would suggest.

I’m telling you, this is not an easy film — nor does it have the grandiose spectacle of Anderson’s earlier films, like There Will Be Blood or the occasional sweetness of Punch Drunk Love and Magnolia — rather, it’s a brilliant work about a male relationship conditioned by sex and love and women and trauma and appalling amounts of hooch. Nor can I imagine an actor this year who does more to inhabit his role than Joaquin Phoenix. Without a single remaining ounce of flesh to fill out his haggard face, emotions ripple across it, forcing him to hunch his back all the more under the weight of guilt and defensiveness. This film will not answer any questions for you; you’ll walk out, as we did, bouncing questions off one another (what was it about the singing? what about forcing Freddie to walk back & forth across the room?) until gradually your conversation helps you wrangle this id of a film into a more manageable shape. Oscar contenders: this is a shot across the bow.