Movie lovers step into theaters hoping to tap into a power said to hover there, something rumored to fulfill even desires that can’t be named; and sometimes the characters who come and go on screen engage in a similar folly. I recall the men, grotesque and flailing surrogates of moviegoers, who venture into the indefinable Zone of Andrei Tarkovsky’s Stalker, where they expect their dreams will mysteriously become real; and now, welcoming examples in a sunnier mode, I greet the children in Hirokazu Kore-eda’s I Wish (opening in New York City on May 11), a film that gently endorses magical thinking by offering a touch of wonder of its own.

The gentleness should not be taken for granted. I Wish is a movie about kids knocking around by themselves; and the last time Kore-eda showed that sort of thing, in Nobody Knows, the story was devastating. Here, too, the potential for catastrophe is always near. It drifts visibly into the opening shots of I Wish in the form of smoke and ash, which billow from a neighboring volcano into the city of Kagoshima, in the far south of Japan. Koichi (Koki Maeda), the chubby, brush-haired boy who is the story’s instigating character, cannot understand how everybody calmly goes about living under this continual threat. “I don’t get it,” he says in his characteristic phrase, and also doesn’t get why his parents split up; why he can’t ever see his younger brother, Ryu (Ohshiro Maeda); why he has to be stuck with his mother (Nene Ohtsuka) in a nothing town like Kagoshima; and why his grandfather (Isao Hashizume) obsesses over an improbable scheme to go into business selling flavorless pastries.

Financial hardship, provincial stultification, loneliness, domestic rancor: these ongoing troubles are introduced early in I Wish, along with the all-encompassing menace of natural disaster. Were Kore-eda to be truthful about them in the manner of Nobody Knows, the worst would happen. But this time he’s out to affirm a different truth: that most children somehow grow up despite everything, in a process that might not fulfill many wishes but is nevertheless (to cite the Japanese title of I Wish) something like a miracle.

The trick is to make that miracle visible to the audience—or, rather, to get Koichi to notice its dailiness (as ghosts learned to do in Kore-eda’s masterpiece, After Life). The problem is that Koichi’s sight is blocked by his habit of being glum, ungainly and dutiful. By contrast, Ryu (here the movie jumps lightly, with the speed of a cellphone call, to the city of Fukuoka) is impish and piping but equally blinkered, in his case by a determination to seem happy no matter what. Little Ryu has to stay cheerful; he looks after himself, in conditions that approach squatterdom, while his dad (Joe Odagiri) goes on failing in a career as a rock musician. So Ryu chatters on energetically, even when his mother is weeping to him over the phone, while Koichi (in the time-honored fashion of quiet, deeply thoughtful boys) constructs a shrine to the volcano and prays for it to obliterate Kagoshima so he doesn’t have to live there anymore. Nobody’s observing much of anything.

The vehicle that opens the boys’ eyes, and those of their friends, is the new bullet train, running on a line that has just reached southern Japan. According to information circulating in Koichi’s school, the wave energy generated when bullet trains pass one another is so intense that whoever witnesses this intersection of forces will be granted a wish. So Koichi schemes with his buddies to cut school and conspires to meet Ryu and his friends at a promising spot along the line. Each kid has a wish to pursue, confessed to Kore-eda’s camera in quasi-documentary style—seven kids in all. Taken together, with their backpacks and bobbling, irregular heights, they are a wave of energy in themselves, one that continually clusters, disperses and reassembles (often trailed by a hand-held camera), flooding I Wish with youthful hope and transforming the whole second half of the film into a nonstop smile.

I can reveal that the children get to see the bullet trains pass, but how this experience opens Koichi’s eyes, I cannot say, because under the pressure of the moment Koichi himself is speechless. His words drop away; his story drops away. Only the things he’s seen remain with him. These images, which you too have seen before, now stand alone, each complete in itself, even though they’re being shuffled out of order in Koichi’s head; and despite the rush of excitement that passes with the trains, each feels as if it would be good for an eternity. Why this montage sequence works as beautifully as it does is the secret of an extraordinary filmmaker. What it means, Koichi can express only later. He sums it up as “the world.”

Outside the movie theater, in what I ordinarily call the world, disappointments and worries tend to clutter my vision. It’s a normal consequence of adulthood. But inside the theater, having looked at things through the awakened eyes of Koichi, I was so reluctant to let go of the movie that I sat all the way through the final credits—and I don’t read Japanese. The miracle that I Wish achieves may be small, but it’s real enough.

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Although there was no shortage of published opinion, almost all of it favorable, when Nanni Moretti’s latest film opened in the United States a few weeks ago, I think the occasion still merits a few words. We have seen the release over the years of many comedies about runaway brides, but Moretti’s is the first about a runaway pope.

We Have a Pope (Habemus Papam) says the movie’s title and Franco Graziosi, here impersonating the cardinal charged with announcing the new pontiff from the balcony overlooking St. Peter’s Square. After several false starts, God’s will has become manifest. The papal conclave, meeting in a splendid simulacrum of the Sistine Chapel built and painted at Cinecittà studios, has solemnly elected Michel Piccoli to head the Church. Now Piccoli has to step forward and show himself to a billion of the faithful. But he doesn’t. He howls in agony, clutching at his eyes as if he’d just been blinded, then staggers back through the halls of the Cinecittà Vatican to hide in the chapel.

After that, he escapes entirely and wanders through Rome for a symbolic three days, dressed in nondescript street clothes. Like the runaway bride who abandons her wedding gown, he might be expected to learn something about people’s lives and return stronger, wiser and ready for a real, if possibly different, commitment—but not quite. The pope, after all, is not Claudette Colbert, nor can the Roman Catholic Church, for all its ceremony, be reduced to a show-biz enterprise (a point that We Have a Pope makes repeatedly, with barbed humor). It is the imperative that the pope go beyond play-acting that torments Piccoli in We Have a Pope and turns him into a fond, foolish old man.

Piccoli and Moretti conceive of the character as having suddenly been made simple, his wide, timid eyes searching for guidance that doesn’t come and his lips drawn in as if now perpetually afraid to let out the wrong words. Only a single explosion of impatient anger recalls this man’s history of command. Otherwise, he’s stripped at one stroke of everything except a few memories, mostly concerning the alternative career he once wanted onstage, in the plays of Chekhov. But life has made him much grander than any retired, ailing Sorin. He’s become Lear—a ruler forced to confront his elemental frailty. That means We Have a Pope also needs a Fool, a part taken by Moretti himself as an irreligious psychoanalyst who has been summoned to the Vatican to treat the new pope and now, because of the demands of secrecy, cannot leave. With no Lear on hand, the Fool has nothing to do except preen, mutter sarcasms about the wealth and power of his hosts and (as his one useful contribution) organize a volleyball tournament among the cardinals.

Moretti’s direction in We Have a Pope is as light as the volleyball in flight. Piccoli, one of the greatest of screen actors, is at all times subtle and quizzical in his anguish—deliberately tentative, if such a thing is possible, as if Sorin had been drafted to play Lear. Best of all, the dual vision of We Have a Pope does justice to both the Fool and his master. The railery is genuinely funny; the finale, played out before the red curtains, deadly serious.

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It would be too much to call Shirley Clarke’s first feature, The Connection, an outsider film, considering that it premiered to rave reviews in 1961 at the Cannes festival and then enjoyed a New York preview screening attended by everyone from James Baldwin and Norman Mailer to Marlene Dietrich and Jonas Mekas. Excitement ran so high that the manager of the new D.W. Griffith Theatre paid $20,000 upfront—an extraordinary sum—for the right to open the film.

But an entire year had passed between the Cannes screening and the preview, and another five months dragged on before the theatrical premiere, which coincided with the theatrical closing. The State of New York immediately shut the Griffith on grounds of public indecency and had the projectionist arrested. After a court ruled in the distributor’s favor, a brief run ensued in November 1962, but it was dogged by a disastrous review from the New York Times. Since then, The Connection has been a recognized masterpiece that never broke even and is seldom seen. Prints have been out of distribution since the early 1980s. Determined cinephiles have found the film at rare museum and archive screenings, or since 2004 have tracked it down as a niche-market DVD, which is currently unavailable on Netflix (although Amazon will sell you a copy for $299.90). The Connection, at minimum, is a film maudit.

Now, though, there’s good news for the accursed. Milestone Films has paid for a new 35mm preservation negative at the UCLA Film & Television Archive (which preserved and restored The Connection in 2004 with funding from the Film Foundation) and is returning the movie to theaters, starting on May 4 with the IFC Center in New York City.

Based on Jack Gelber’s play of the same title, which the Living Theatre had introduced in 1959, The Connection both appeals to and repudiates the peephole syndrome—a desire to witness forbidden things, which Parker Tyler thought was the essential come-on of underground cinema—while gleefully mocking all social-problem dramas and attempts at documentary realism. Ostensibly set in a brick-walled, bare-floored, scarcely furnished Village apartment, where sounds of traffic filter through the grimy windows and the toilet lies behind a wooden door marked “Toilet,” The Connection purports to be assembled from footage shot during a long afternoon by a Harlem cameraman (Roscoe Browne) and his boss, a briskly officious documentarian (William Redfield) who keeps barging into the frame to urge a little more action from his subjects, a collection of sick junkies. While waiting for Cowboy (Carl Lee) to bring back the heroin that the filmmaker has paid for, these people consistently disappoint as examples of American social malaise.

At times, they won’t even talk, except to challenge the filmmaker (and the audience) for wanting to look at them. Meanwhile, the Freddie Redd Quartet, featuring Jackie McLean, puts on a show; these musicians, too, are waiting for a fix, but they are also using the apartment to rehearse. As the other addicts and the two cameras prowl about in Clarke’s flamboyantly sophisticated lower-depths choreography, the musicians tear into chorus after chorus of diamondlike hard bop: the greatest advertising soundtrack heroin ever had.

I’m sure somebody at some point will describe all this as a time capsule. To which I say, the specimens in the capsule remain very much alive—and they can hit.

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“As a moviegoer,” Shirley Clarke once said, “I personally would take the likes of Duck Soup over The Connection any day.” Honesty compels me to add, on my part, the Farrelly brothers’ Three Stooges. This, too, is lower-depths choreography, here put in the service of harmless mayhem and complete idiocy, or complete mayhem and harmless idiocy. Will Sasso gives a star-making performance as Curly, and Larry David appears in habit as a nun who mangles Magdalene into Mengele.

Other noteworthy new releases: Mia Hansen-Love’s Goodbye First Love, which has just opened, is a lovely, alert and unsentimental ride through a decade in the emotional life of a young Parisian (Lola Créton), from abject infatuation to maturity, self-assurance and just a little resignation. Payback, on view through May 8 at Film Forum in New York City, is Jennifer Baichwal’s absorbing essay film about the multifaceted nature of debt—economic, political, environmental, psychic—based loosely on a book by Margaret Atwood. The characters range from feuding Albanians to migrant farm workers in Florida to former media mogul Conrad Black; the settings, from Eastern State Penitentiary to a lecture hall in Toronto to the Gulf of Mexico during the Deepwater Horizon disaster. The film’s thesis may be hard to summarize, but I’m sure most Nation readers will agree.