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All the elements of classic filmmaking play out in Paul Thomas Anderson’s “The Master.” The acting, particularly that of co-leads Joaquin Phoenix and Philip Seymour Hoffman, is spectacular. The cinematography is brilliant. The score and song selection are superb. The post-war sets are perfect. And yet the story itself is disjointed, ambiguous and ultimately, unsatisfying.

The first scene sets a pattern. In it Mr. Phoenix, as troubled World War II veteran Freddie Quell, peeps out from behind a wall, apparently spying on some unsuspecting soldiers. It is an arresting image that signals something about a man who is hidden, lurking and troubled.

Trouble runs deep in his family: His mother has been institutionalized. He drinks too much, is volatile and hears voices. After being discharged from the Navy, Quell lurches from job to job struggling to hold his life together. Desperate and on the lam, he stows away on a yacht commandeered by the charismatic and domineering Lancaster Dodd (played with brilliant subtlety and pinpoint precision by Hoffman), whom nearly everyone refers to as the Master.

“Who are you?” Quell asks when they meet, intrigued and a little frightened by this force of nature bent on developing a new approach to the human psyche and the quest for perfection.

“I am a writer, a doctor, a nuclear physicist and a theoretical philosopher,” Dodd answers. “But above all, I am a man, a hopelessly inquisitive man, just like you.”

It is the nature of their relationship that is central to the movie. Nearly every scene features one or both men, grappling with their demons and passions. They are, in a sense, funhouse mirror images of each other. Dodd is sunny, confident, cocky, corpulent; Quell is, dark, emaciated, twisted, and misshapen, like a drunken scarecrow. He is Richard III as played by Montgomery Clift. Both performances by Mr. Phoenix and Mr. Hoffman are Oscarworthy.

Quell becomes the Master’s acolyte and servant, mixing his drinks and getting drunk with him, deploying crude violence against his critics, and becoming a tormented subject for the Master’s primitive psychological “process.” The latter entails lengthy and probing interview questions and exercises in mind-numbing repetition designed to break down a subject’s defenses.

The story is loosely based on the early years of Scientology, with Dodd as Scientology founder L. Ron Hubbard. And while some scenes subject Dodd and his system to ridicule – the Master claims to treat illnesses that may have originated “trillions of years ago” and explains his work with a mixture of bravado and mumbo jumbo – nevertheless, the movie does not seem bent on critiquing Scientology so much as exploring the men’s relationship and examining spirituality, human nature and false messiahs, all framed in the context of how post-war society looked to and affected Americans.

Those are big, meaty topics, and Mr. Anderson, the director of some of the most interesting American movies of the last generation, including “Boogie Nights” (1997), “Magnolia” (1999) and the Oscar-winning “There Will Be Blood” (2007), is one of the few American directors working today equipped to tackle them.

But there is no real story development or conclusion. While it is never boring and does not seem long, “The Master” runs 140 minutes and could have been a lot shorter, crisper and to the point, if there is one. Further, there is never any explanation as to what binds Dodd to Quell: The viewer will wonder whether he is a father figure, a messiah, a buddy, a trusted adviser or something else. But as portrayed by Mr. Phoenix, Quell is so flawed, vacuous and self-hating that none of these explanations makes sense.

Still, there are many compensating attractions. Most of the movie was shot on 65mm film stock, versus the usual 35, and even though Chicago has no movie theaters that use 65mm projection, even compressed to 35mm it looks brilliant in its detail and color saturation. To watch this movie is a great pleasure, even if watching it leaves the viewer puzzled and dissatisfied.