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It’s improbable that a moviegoer will wander into a matinee of Mr. Gaga expecting a feature about Lady G. in drag. But now that we’ve established what it’s not, let’s be clear about what it is: The film is strictly for devotees of avant-garde modern dance. Not for general dance enthusiasts. Not for viewers who are unfamiliar with its subject, choreographer Ohad Naharin, but like to watch documentaries about celebrated artists. If you’re not already solidly in Naharin’s camp, the dance you’ll see here is unlikely to entertain you. Instead, it will seem weird.

The Israeli Naharin is first shown teaching a dancer to fall. It won’t be the only time. According to the choreographer, gaga—a dance style he created—is “the demand to listen to our body before we tell it what to do. And the understanding that we need to go beyond familiar limits on a daily basis.” Natalie Portman is here to comment, saying that it’s “this incredible sort of movement/theory/practice.” Yossi Yungman, a dancer himself, recalls the first time he saw an Naharin work, which involved swaying dancers lined in a row. Yungman was transfixed and commented, “There’s the essence of everything in nothing. And that’s art.”

Hmm. From the rehearsal tapes, home videos, and snippets of various works that director Tomer Heymann uses to patch together the film, gaga seems to involve jerky movements that usually increase in speed until they’re frenetic. There’s forehead-smacking. Air-punching. Arm-waving. Head-shaking. And, yes, a lot of falling to the ground, as if the dancers have suddenly lost their bones. The music is often tribal, but the rhythms never overtake the viewer; the whole package remains inaccessible, and vaguely off-putting.

Mr. Gaga also talks about Naharin’s childhood and development as a dancer. He was raised for some years in a kibbutz, where he and his mother would happily bang on things to make music and elicit movement. He started professional training very late, at age 22, the point at which he says, “I was a lot more connected to the animal I am.” Naharin danced with Martha Graham’s troupe, but wasn’t satisfied there, so he eventually returned to Israel to head the Batsheva Dance Company. His detractors included the head of Israel, who demanded that Naharin change the dancers’ costumes (basically, underwear) for a national celebration to something more modest; specifically, as a broadcast reporter describes it, “something that the religious public can live with without overthrowing the government.”

As are many artists who are labeled geniuses, Naharin is a difficult taskmaster, yelling “You’re boring me!” at dancers while they’re onstage or having rehearsals end with a dancer walking out while shouting or crying. (One dancer’s remark that his comments on attempts to please him resulted in “No. No. No. No. No. I want you to read my mind,” recall the drum teacher in Whiplash.) Yet, another dancer said, they would come back, because “twisted or not, they felt that the work was worth it.”

Mr. Gaga was eight years in the making, and though Naharin tells a lot of his story, you’ll find out that he’s not always the most reliable narrator. The film touches on his personal life, too, including his committed relationships to two of his dancers, one of whom he had a child with. (The toddler, shown at the end, finally adds a touch of humanity to a man who otherwise seems otherworldly.) And even if you don’t know what the hell a fellow choreographer means when she says, “He has that Mediterranean spine. It’s serpentine, and sinewy, and flowy, and yet articulate!” you can’t miss the joy of amateurs moving around freestyle during one of his open classes. Gaga may not be for everyone, but for those who embrace it, it seems to mean the world.

Mr. Gaga opens today at West End Cinema.