One afternoon in May 2020, Julia Allison sat in a hot spring near Joshua Tree National Park, crying. A media strategist and tech-world socialite — who in her former life as a New York City journalist and media personality pioneered the sort of internet-driven microfame that we now call “influencing” — Ms. Allison was going through yet another breakup. She wanted to know: What was the point of it all?

“This was not the plan,” she remembered thinking. “Thirty-nine and single. What has my life come to?”

Then Ms. Allison had an unusual epiphany, even for Joshua Tree: She needed to consult the Felix Frankfurter professor of law at Harvard Law School, Noah Feldman.

Like Ms. Allison, Mr. Feldman first rose to prominence in Lower Manhattan in the aughts, as a wunderkind constitutional law scholar at N.Y.U. (In 2003, at 33, he advised the Iraqis in writing their Constitution after the U.S. invasion.) Also like Ms. Allison, Mr. Feldman had been unlucky in love, a bachelor since his 2011 divorce.

The two had never talked, but a mutual friend had described Mr. Feldman to Ms. Allison as “the world’s most fascinating man.” Through the friend, she had Mr. Feldman’s number, which she dialed from the hot spring. He picked up, and Ms. Allison asked him the meaning of life. They spoke for 90 minutes.

“Neither of us can remember what Noah said, but I know it was so profound,” Ms. Allison said.

Now, three and a half years later, after a courtship that has been, while not precisely a secret, at least conspicuously discreet, Ms. Allison and Mr. Feldman are engaged.

On the surface, it was an unlikely match. Ms. Allison, 42, is a 10-time Burning Man attendee who had lived in California for a decade; her friends include start-up chief executives and psychedelic psychotherapists; she considers Bali her spiritual home. Ms. Allison described a period of her dating history as “10 years of relationships with polyamorous D.J.s.” (Ms. Allison said she also dated the former Democratic congressman Harold Ford Jr. when she was a college student at Georgetown.)

Mr. Feldman, meanwhile, embodies the East Coast establishment. The son of an M.I.T. professor and a Harvard lecturer who graduated first in his class from Harvard, Mr. Feldman, 53, speaks five languages, has written nine books and is a columnist for Bloomberg Opinion. (Mr. Feldman has also been a contributing writer to The New York Times Magazine.) His first wife, Jeannie Suk Gersen, with whom he has two teenage children, is also a professor at Harvard Law School and a public intellectual.

“People I dated seriously, subsequently, were people of substance,” Mr. Feldman said in a recent interview in his office. “Distinguished in their professions.”

Ms. Allison, sitting arm in arm with Mr. Feldman, smiled.

“Serious people,” she said in a stage whisper.

But Ms. Allison’s call came at a time, early in Covid restrictions, when Mr. Feldman — then nearing 50, teaching remotely and spending much of his time alone at home — was questioning the basics of human connection.

“I was not at an optimistic point in my romantic life,” he said. He remembered wondering, “Will anyone ever meet any human ever again?”

The pair said they spoke every day for three months after that first call, often for hours at a time. Mr. Feldman invited Ms. Allison to Maine, where he owns a home.

It took some convincing. Ms. Allison was ambivalent about a bicoastal romance, and about the East Coast in general. Though she felt their chemistry was obvious, she was committed to California. Ms. Allison had moved there after a half decade in the late 2000s in which she became a recurring character in the New York gossip pages and was profiled by The Times as a kind of neo-Candace Bushnell — a dating columnist whom people both loved and loved to hate. An attention economy savant, Ms. Allison was perhaps best known as a foil for Gawker, which obsessively, and sneeringly, covered her social life. In exchange, she gained a kind of toxic fame, both hyperlocal and completely global thanks to the internet, which was a harbinger of the culture to come.

“She was too early,” said Taylor Lorenz, the Washington Post tech columnist and chronicler of social media influence. “She predicted it all.”

Scarred by the experience, Ms. Allison has been living mostly out of the spotlight ever since. Early in their phone calls, she asked Mr. Feldman not to Google her.

“It’s not a representation of who I even was then, let alone now,” Ms. Allison said.

But eventually, she got on a plane. At the Portland airport, from his car, Mr. Feldman caught sight of Ms. Allison for the first time.

“I saw Julia dancing, alone, in a sundress on this tiny little triangle of grass in the middle of the airport,” he said. “It was a beautiful, moving image of somebody who was sourcing joy entirely internally.”

They spent five days together, picking out produce at the farmers’ market, lying in the grass, and, as Ms. Allison put it, “kissing on Noah’s boat.”

“I was completely magnetized by this man,” she said.

Still, there was an acculturation process — particularly for Mr. Feldman, who is not really the dance-like-no-one-is-watching type. To begin with, Ms. Allison was immersed in a scene, centered on Burning Man, about which Mr. Feldman knew nothing.

“Many of Julia’s friends have jobs I didn’t know existed until I met Julia,” Mr. Feldman said. “One is a fire dancer. She also has a friend named Purple — he only wears purple, and his métier is bodywork.”

“Noah is learning how to have fun,” Ms. Allison said. “But he’s a fast learner.”

Ms. Allison took Mr. Feldman on several pilgrimages — acid tests, really — to make sure he could loosen up. First the pair went to the Indonesian island of Bali, where Ms. Allison lived for a year from 2017 to 2018 doing what she referred to as a “yoga and meditation sabbatical,” and which she said she paid for with earnings from her investments in cryptocurrency. (Mr. Feldman was familiar with the island in part through the work of the anthropologist Clifford Geertz, who wrote about the social dynamics at play in Balinese cockfighting.) Mr. Feldman was tense at first, but cycling the village roads north of Ubud, he began to feel himself pleasantly removed from the rigidly intellectual culture of Cambridge, Mass.

“It may be as far away as you can go from Boston,” he said.

Next, in the fall of 2022, came the final exam: Burning Man, the weeklong event where tens of thousands of people gather to camp and revel in the Nevada desert, and worldly accomplishments aren’t supposed to matter.

“To say Noah was having trepidation about Burning Man would be a major understatement,” Ms. Allison said. “He understood it was a requirement. If you’re going to be with me, you have to go to Burning Man. He was vibrating with anxiety.”

There, it was Ms. Allison’s turn to behold Mr. Feldman. The law professor had agreed to M.C. some events for Ms. Allison’s camp, which she described as a “matriarchy.” One session featured a woman in a large headdress leading the audience in a mind-body therapy that involved rapidly tapping certain points on the body. As Ms. Allison entered the tent, she saw Mr. Feldman in front of the crowd, tapping himself and repeating the mantra, “I love and accept myself unconditionally.”

“It was the best moment of my life,” she said.

Still, for all the changes Mr. Feldman has made, it was Ms. Allison who agreed to pull up stakes. She moved to Cambridge in November of 2021, and last month, she began a master’s program at the Harvard Kennedy School. She said she hoped to work on issues that matter to her: environmental justice, gender issues and animal rights.

Because of her course load, she missed Burning Man this year for the first time in a decade — possibly a sign of kismet in and of itself.

And she has moved into Mr. Feldman’s 5,000-square-foot mansard-roofed home, which she has, with her fiancé’s intermittently enthusiastic participation, redecorated.

“It was a sad, beige house for a sad, beige bachelor,” she said.

Ms. Allison’s changes include whimsical pink wallpaper with a pattern of monkeys and leopards; thick velvet drapes; Balinese statuary; antique chandeliers throughout the house; and a formidably deep, blue velvet couch in the living room, intended to encourage a kind of sensuous lazing that is not typically associated with Cambridge.

Now, Ms. Allison calls the house “the Bohemian Embassy,” and she sends guests a mission statement ahead of time. “Our home is more than dwelling,” the message reads. “It is a confluence of diverse minds and spirits, a space of exploration and enlightenment.” Ms. Allison hopes to turn the house into a place where the free-spirited sensibility of Burning Man can mix with the cerebral culture of Cambridge.

“Noah is a sharp edge that needs to be softened; he is a square that needs to be rounded,” Senator Cory Booker, Democrat of New Jersey, said of his longtime friend. (The two have been close since they were Rhodes scholars together at the University of Oxford.)

“This woman is a gift to him, a guy who has been walking a narrow pathway toward extraordinary success all his life,” he continued. “And she was on the side of the road in this wondrous field, filled with wildflowers, and she got him off the path, to dance.”

On a recent, humid August evening, the couple hosted a Shabbat dinner to put those hopes into practice. (Mr. Feldman, who is working on a book about the nature of contemporary Judaism, grew up modern Orthodox. Ms. Allison said that she planned to “join Judaism.”) The guest list featured friends of Ms. Allison’s — among them a professional intimacy coach, an entrepreneur who built a high-tech chair for meditation and a professional relationship coach — as well as two friends of Mr. Feldman’s, a physicist and a sociologist.

After a dinner of plank-grilled salmon, prepared by Mr. Feldman, and several glasses of Pouilly-Fuissé, the group retired to the living room. Mr. Feldman, wearing a rakishly unbuttoned pink oxford shirt, reclined on the sofa, where the meditation chair entrepreneur draped her legs across his lap. (Ms. Allison’s Burning Man friends place a premium on physical touch and soft surfaces, a phenomenon they refer to as “bringing the squish.”)

Ms. Allison sat on her heels on the floor in front of them, her full-length pink floral dress gathered around her. Topics of conversation included the potential for MDMA to treat trauma, the 19th-century German sociologist Max Weber and the nature of love.

Starielle Hope, the intimacy coach, said that at first she had been skeptical about the match.

“To me they were so different,” she said. “He is a man who is part of a hierarchical system, and she is a woman who is seeking an unconventional life in balmy climates.”

Ms. Allison laughed. “These two worlds could do so much together,” she said.

The physicist, reclining in an oxblood Eames lounge chair, offered that the hippies had saved physics, to murmurs of assent. As the evening progressed, he performed sleight of hand.

This summer, Mr. Feldman and Ms. Allison went on a four-country trip to Europe to scout wedding locations. But the couple hasn’t yet set a date. Ms. Allison said that she was simply too busy with school to properly focus on the wedding she envisions.

“I have to plan an event worthy of waiting until 42 to get married,” she said.