THE FIRST TIME we see Freddie Quell, the dipsomaniac drifter sex-fiend cult-devotee hero of Paul Thomas Anderson’s new film The Master, he’s peering out over the bow of a ship. All we see of him are his eyes and forehead, shadowed by the brim of a combat helmet. It’s just a flash. We don’t know what he’s looking at or what he’s about to face, whether he’s about to land on an enemy shoreline or go off on leave, just that its wartime in the Pacific. But whatever happens to Freddie in the war certainly leaves a mark. The next time we see him he’s on a beach and clearly strung out, chopping coconuts with a machete like he has a mind to lop off his own hand. He celebrates V-J day by drinking ethanol out of torpedo engines. While the other sailors wrestle, Freddie simulates sex with a woman sculpted out of sand and masturbates into the surf. Back home, he flunks out of an early version of PTSD screening by claiming every Rorschach blot he’s shown is either a cock or a pussy or a cock going into a pussy. At this point we start to wonder, why are we following this creep around? Wasn’t this supposed to be a movie about Scientology?

The Master is P.T. Anderson’s sixth film. Over the past 16 years, he’s put together a body of work that has made him stand out as one of a handful of bona fide American auteurs — directors with a discernible vision, a recognizable visual style, and a commitment to the medium as an art form. Beginning with Hard Eight in 1996, he’s made a suite of films in an array of genres and moods: a perfectly executed noir short story, a sprawling Altmanesque group portrait, a haphazard (and to my mind, somewhat curdled) paean to chance, a slim, darkly funny novella, and a return to the DeMille-Griffith fire and brimstone epic. All of them are held together by a fascination with a place (Southern California) and certain types of character (obsessed loners, orphaned children, surrogate fathers). Of all of these, The Master is his strangest and most elusive work. Hard Eight and Punch Drunk Love were genre pieces, however off-kilter. Boogie Nights is an exquisite ensemble piece, but it’s hardly mysterious. Magnolia and There Will Be Blood were driven by clear, if sometimes overly schematic, clashes. The Master is harder to characterize. It’s a play on film history, an unresolved love story, a statement about conformity and rebellion. Above all it’s a struggle between two characters and two epochs, a duet in which nothing resolves or comes to a conclusion. It’s as wide-open and complex a masterpiece, and as ambiguous and puzzling a film as has appeared in America since David Lynch’s Mulholland Drive or Todd Haynes’s Safe.

Freddie is what sticks with you as you leave the theater. He’s like Robert De Niro’s characters in Mean Streets and Raging Bull — as long as he’s on screen you can’t relax because something might happen to him, or he might do something terrible to someone else. You feel like you’ve gotten too close to his mania and his tics and you want to push him out. If you’ve ever been crazy, or known someone who is, you also recognize the terrible energy, like black electricity, which threatens to consume him and which he works so hard to deaden and contain. But even as Freddie is the most surprising and indelible thi...