“Most people who interpret their work take it as metaphorical,” Professor Ihde added.

Lawrence Marek, a Manhattan architect who helped steer the house through the construction process, disagreed. “Arakawa does believe that if you build things the way he says to build them, life will be prolonged,” he said. “I don’t know if it will or not.” But, he added, “the house has a way of making people happy  it’s a feeling you don’t get from many buildings  and we should be studying how that happens.”

Image The couple also built nine reversible destiny loft-style apartments in Mitaka, Japan. Credit... Masatako Nakano

ARAKAWA, who dropped his first name more than 40 years ago, grew up in Nagoya, Japan, studied medicine and art in Tokyo, and moved to New York in 1961, when he was in his 20s. In his pocket, he said, were $14 and the phone number of Marcel Duchamp, who was then living in Greenwich Village. Duchamp, he said, became his patron.

Two years later he enrolled in art school in Brooklyn (for the visa, he said, not the education). There, he met Ms. Gins, a fellow student, who had grown up on Long Island. At the time, she said, “I was deeply alienated from society, which I didn’t see as having any answers.”

Within days they had become a couple and begun making art together. Over the next several decades, living in a loft building on Houston Street, they produced a body of work that includes poetry, philosophy, paintings and conceptual art. From the start, Ms. Gins said, the central theme of their work was “how to reverse the downhill course of human life.”

One of their first built architectural projects, a park in central Japan called “Site of Reversible Destiny,” was completed in 1995. Made up of acres of warped surfaces, it offers visitors advice, in a handout leaflet, like “Instead of being fearful of losing your balance, look forward to it.” (Several people who are said to have broken bones there might wish the name of the park were literally true.)

In 1997 the SoHo branch of the Guggenheim Museum put on a retrospective of the couple’s works. Roberta Smith, writing in The New York Times, noted that “their philosophical or linguistic puzzles can stretch the mind in briefly pleasant ways,” but did not applaud their efforts to build real-world buildings: “Theoretical follies, one of the plagues of contemporary architecture, have their place, and it’s on paper,” she wrote.

For the couple, though, “one building is worth a decade of theoretical exploration,” Ms. Gins said. In 1998 they won a competition, sponsored by the city of Tokyo, to build a vast housing project on 75 acres of landfill. The project was never realized, but a group of supporters in Tokyo arranged to build nine loft-style units, which in many ways resemble the house in East Hampton. More recently, they said, they have been trying to find backers  an effort that has included failed overtures to Russian oil billionaires  for a reversible destiny hotel.