Kirsten Luce for The New York Times

It would be hard to overstate the level of preposterousness that surrounds Jon Gnarr, the punk rocker-turned-comedic actor-turned mayor of Reykjavik, Iceland. Mr. Gnarr was elected in 2010 after he formed a quasi-satirical political party, the Best Party; his campaign promises included putting a polar bear in the city zoo and offering free towels in the swimming pools — as well as a promise to break all his campaign promises.

Given that degree of personal absurdity, his appearance in New York on Saturday, to speak at a small conference dedicated to the future of radio, would qualify as merely unlikely. Mr. Gnarr was the keynote speaker of the first Radiovision Festival, a three-day conference put on by the radio station WFMU; other guests included representatives from Twitter, Kickstarter, the Web site Know Your Meme and Makerbot, which produces 3D-printers.

“Being a free-form station, I thought it was fair to put together a bit of a free-form conference,” said Benjamen Walker, Radiovision’s organizer. The festival was concurrent with the popular WFMU record fair, now in its 18th year.

Mr. Gnarr agreed to participate on a whim. “I met Benjamen in Lyon, in France, in a similar thingie,” he said, “and he told me about this event and there was just something — a kind of intuition. I just said yeah, I’ll do that.”

The mayor arrived with Heida Helgadottir, his general secretary – a title Ms. Helgadottir, the only paid member of the Best Party, said was purposely invented to sound stuffy. Mr. Gnarr, in a black sweater, black jeans and the kind of buzzed, slicked-back haircut that would not look out of place on an aging British rocker, and Ms. Helgadottir, who sometimes served as his translator, dug right in.

“The Best Party was the first anarcho-surrealist party in the world,” Mr. Gnarr began. “The party doesn’t have any sort of aim or philosophy,” he continued. “It’s based on pure nonsense. The thing is, I believe in nonsense.”

“Comedy is my religion,” he added, as the audience laughed. There were fewer than 100 people in the room, and several left during Mr. Gnarr’s talk. (“I came for Ira Glass,” Gabe Pittleman, a Princeton University senior and music director of the campus radio station, explained on his way out.)

But much of the crowd was delighted by Mr. Gnarr’s appearance. He discussed the vagaries of the currency market (the Icelandic króna is “crap,” said Mr. Gnarr, who prefers the dollar — “the euro is simply not cool”); whether Iceland should join the European Union (Turkey should get in first; it’s only polite, Mr. Gnarr said, as they’ve been waiting longer); and answered questions about the challenges of being mayor.

“One of the most difficult things you can do in life is changing a school system,” he said. “It’s a bit like moving a cemetery. You don’t get any help from inside.”

In office now for over a year, Mr. Gnarr admitted it had been occasionally boring, adding that he was surprised his staff members, many culled from Iceland’s punk rock scene, had not quit. But he noted that being a political tourist, as he called himself, was an asset in getting things done.

“I don’t really care if people like me or not,” he said. He has led Reykjavik’s gay pride parade dressed in drag and made a Christmas video as Darth Vader in a Santa hat. “One of my personal goals is to damage this image of the leader,” Mr. Gnarr said. (Ms. Helgadottir, who met Mr. Gnarr through a friend who directed a documentary, “Gnarr,” about his campaign, nodded her agreement.) Mr. Gnarr even showed off a calendar he keeps, counting down to his final moment in office. “I have 959 days, 3 hours, 30 minutes and 8 seconds left,” he announced.

But he is far from flip: in an interview backstage, perched on an audio equipment case, he appeared thoughtful and sincere in his vision. “We are having a unique opportunity to disrupt and think things over and make them better,” Mr. Gnarr said. “And I think we have to; the whole thing with politics, it’s over, politics are dying. The sure death will take some time, and something extraordinary will come instead.”

In Mr. Gnarr’s view — and in his life — comedy can be exalting. “I believe that humor and happiness is a power in itself that can solve things,” he said during his talk. A “South Park” fan, he had wanted to see “The Book of Mormon” in New York, but thought the tickets were too expensive. So Mr. Gnarr went to Occupy Wall Street instead, dressing for the occasion in a black suit jacket and an orange-haired orangutan mask.