During the three years he has spent in Russian exile, Edward Snowden, the N.S.A. contractor turned whistle-blower, has maintained a surprisingly steady presence in American culture as a kind of virtual trans-border eminence. He appears via “Snowbot” and video link at conferences, in museums, and in theatres. He delivers lectures at universities and grants interviews to reporters, including, in 2014, a virtual interview with The New Yorker’s Jane Mayer. This past July, he turned up at Comic-Con, at a secret screening to promote “Snowden,” the new film directed by Oliver Stone, which comes out on September 16th. Snowden’s digital omnipresence has an ironic quality: he’s a ghost in the screen, a disembodied conscience, a spy in the sky. Yet in his most defining appearances to date, Snowden’s voice has come to us in mediated form, shaped by the artists and journalists whom he has engaged as collaborators—and sounding quite different depending on who is in the editing bay.

For the public, the Snowden story began with a short film by the acclaimed documentarian Laura Poitras, which later became the basis for her Academy Award-winning documentary “Citizenfour.” The footage, shot in a Hong Kong hotel room where Poitras and the Guardian journalists Glenn Greenwald and Ewen MacAskill arranged to meet with Snowden, in 2013, showed a pale and unshaven twenty-nine-year-old in rectangular spectacles, explaining eloquently, and with eerie calmness, why he had chosen to reveal the existence of an extensive domestic-surveillance program in the United States, and then to reveal his own identity. He described the system that he helped build as “the architecture of oppression,” and said that he could not go on “living unfreely but comfortably,” paid well to spy on unwitting Americans.

The tale, many said, was straight out of a John le Carré novel, especially when Snowden, charged by the United States Department of Justice under the Espionage Act, had his passport revoked en route to Ecuador and spent thirty-nine days in Moscow’s Sheremetyevo Airport, before being granted temporary asylum in Russia. In his best-selling book “No Place to Hide,” Greenwald recalls thinking to himself that the Snowden story was “a surreal international thriller.”

That line must have been a red cape snapping in the faces of Hollywood packagers. Sony secured the rights to Greenwald’s book. Stone, on the other hand, optioned “Time of the Octopus,” a novel by Anatoly Kucherena, the Russian lawyer who negotiated Snowden’s asylum, which recounts the adventures of an N.S.A. whistle-blower named Joshua Cold, including his extended stay in Sheremetyevo Airport and his dealings with journalists named Boitras and Greywold. According to a long process piece recently published in the Times Magazine, it was Kucherena who approached Stone, offering access to his client in exchange for the rights to the book, for which a Wikileaks data dump revealed he charged Stone a million dollars. (Stone says that he never intended to use the material.) Turned down by numerous studios, Stone got distribution through Open Road, an independent production company that last year won an Oscar for “Spotlight.”

Stone’s “Snowden” follows the title character, played by Joseph Gordon-Levitt, from a patriotic impulse to enlist in the Special Forces after 9/11, through a stellar intelligence career and an odd-couple romance with a liberal acrobat and pole-dancer named Lindsay Mills, to his current state of exile. Many scenes re-create Poitras’s hotel-room documentary almost to the frame—in one case, literally, when one side of Snowden’s rectangular eyeglasses, jutting past his face, distorts the field of view. (Melissa Leo plays Poitras; Zachary Quinto plays Greenwald; Shailene Woodley plays Mills.) Stone, who is known for his anti-establishment character studies that engage with recent American history—and for conspiracy-theory politics—portrays Snowden’s choices as the inevitable actions of a person of conscience. He and his co-writer, Kieran Fitzgerald (grandson of Robert), have named the overreaching spy boss (played by Rhys Ifans in the film) after the zealous Thought Policeman O’Brien in “1984.”

In an interview with The Hollywood Reporter, Stone described the film as a close cousin to “Born on the Fourth of July,” his 1989 movie starring Tom Cruise as Ron Kovic, a paralyzed Vietnam veteran who becomes an antiwar protester. Much like Kovic, Snowden wanted to serve his country, was repelled by what that service entailed, and then found a purer form of patriotism by speaking out against the actions of those in power. As in “Born on the Fourth of July,” the Snowden character is ennobled by his transformation from insider to outcast; the drama, driven by the hero’s disgust and disillusionment, centers on his change of sides. In Stone’s hands, the man who signed his anonymous e-mails to Poitras “Citizen” is not a character playing ethics chess, as in le Carré, but a hero of apostasy—an American archetype as old as the nation itself. When, in the movie’s final moments, the real Edward Snowden appears, in a gauzy cameo that the Times Magazine reports was shot in Anatoly Kucherena’s dacha, we are meant to see him as the ultimate patriot.

Gordon-Levitt, like Snowden, was born in the early eighties. A former child actor, he retains an eager boyishness—not enigmatic so much as blank-slate. In last year’s Robert Zemeckis bio-pic “The Walk,” he portrayed the French high-wire artist Philippe Petit with what Richard Brody characterized as the “antic perkiness of a salesman.” As Snowden, the actor’s innate jauntiness is suppressed; he’s watchful, grim, and courteous. To prepare for his role, he spent several hours with his subject in Moscow; he found him to be polite and slightly formal, in a Southern way. (Snowden is from North Carolina.) When Stone called him about the part, Gordon-Levitt knew little about Snowden. Since then, he has become an evangelist for Snowden’s cause, donating most of his acting fee for the film to the A.C.L.U.—the organization for which Snowden’s American lawyer, Ben Wizner, works—and embarking on a collaboration between HitRecord, an online collaborative community that he started a decade ago, and the A.C.L.U. to explore the role that technology should play in a democracy.

Not long ago, I went to see Gordon-Levitt at the HitRecord offices, a loftlike space in a suburb of Los Angeles. It was lunchtime, and employees were gathered around a communal table eating takeout. HitRecord brings together half a million animators, editors, writers, filmmakers, musicians, and other content generators, who collaborate on various kinds of projects, some prompted by Gordon-Levitt and his editorial team. (The team also produced an Emmy-winning television show, “HitRecord on TV,” for the millennial-oriented network Pivot.)

Gordon-Levitt, who was wearing khakis, Pumas, and a T-shirt, led me over to a quiet seating area and eased into an armchair. He said that, when he met with Snowden in Moscow, he discovered that the two have common ground. Like Snowden—who, according to Vanity Fair, spent his late adolescence online—Gordon-Levitt, a native of the San Fernando Valley, grew up around computers. His dad, who runs a small software business, had a Commodore 64; Gordon-Levitt got his first e-mail address in high school. “I don’t think I ever thought of computers or the Internet as something that could be leveraged to the detriment of the human race,” he told me.