By early 2012, the footprints of the structures on the platform’s eastern side were fixed: four towers, the Shed, shops, restaurants. Related asked for proposals from three landscape-architecture firms. The platform, only a few feet thick and heated up by idling trains below, presented a horticultural challenge. Related executives did not ask for a sculptural landmark, although they did explain the need for a few concrete vents, which could perhaps double as kiosks or cafés.

One proposal, from the firm Nelson Byrd Woltz, included a lawn, a man-made stream, and a reflecting quarter-inch skim of water that could be drained whenever the Shed’s canopy was rolled out over it. The firm also included a six-story lookout tower. This was sketched as a shaft around which two ramps spiralled in a double helix—all of it wrapped in a perforated screen of weathered steel, the rust-covered material of a Richard Serra sculpture. In its pitch, the firm referred to two rail tunnels that run beneath the site. The tunnels, dug in the early twentieth century, still transport all trains between Penn Station and New Jersey. The tower, vaguely suggesting a drill bit, would have been erected close to the point where tunnelling machinery was once lowered down a shaft.

I asked Ross about his reaction to seeing N.B.W.’s tower.

The Seed Cathedral housed two hundred and fifty thousand plant seeds at the ends of sixty thousand acrylic rods. Photograph courtesy Iwan Baan

“Ugh,” he said.

Related hired the firm, but at a meeting with Thomas Woltz, the owner of N.B.W., Ross asked for a new landscape. “I said, ‘Throw those plans out!’ ” he recalled. He described Woltz’s face falling, and added, “Nice young kid.”

If Ross had ever supported the idea of another Bryant Park, he no longer did. He took Woltz to a window at the Time Warner Center, saying, “Look at Columbus Circle, how hard it is.” There would be no grass on his plaza. “I said, ‘Forget about it.’ I mean, people with their dogs?”

The final landscape will include no lawn, no stream, no skim of water. But Ross had clearly absorbed the idea of an ornament. Jay Cross acknowledged that such a structure “wasn’t a part of our thinking until Woltz brought it up.” He added, “Once the lawn was gone, Stephen was, like, ‘We’ve got to have a piece of art.’ ” It had to be a destination, Cross said. “It had to be ‘I’ll meet you at the Whatever.’ ”

Before the 2012 Summer Olympics, Heatherwick was known in Britain for three striking but impermanent designs. His Shanghai Expo pavilion had a scheduled life of only six months. In 2002, for a site in Manchester, Heatherwick Studio had created B of the Bang, a two-hundred-foot-tall cluster of metal spikes emanating from the top of a column, to suggest a midair explosion. It was finished late and was over budget. The tip of a spike fell off just before it was unveiled. Other spikes later threatened to fall and had to be removed. The Manchester City Council sued Heatherwick and his contractors, and settled out of court. In 2009, the sculpture was dismantled.

The New Routemaster, a handsome double-decker bus designed for London’s transportation authority, went into service in February, 2012; it had an open platform at the back, echoing a classic, defunct design. It seems to have been commissioned, at the insistence of Boris Johnson, as much to symbolize the city as to serve it: a double-decker pavilion. It had advantages over off-the-shelf alternatives but cost nearly twice as much, was cramped and hot, and was more polluting than promised. The bus was discontinued.

Heatherwick Studio had submitted designs for two Olympic structures—a velodrome and an observation tower—but had failed to win the commissions. A participant in the tower competition has said that Boris Johnson asked for a design that would “match the Eiffel Tower.” The winning entry was co-designed by Anish Kapoor, the British artist best known for Cloud Gate, a seductive, seamless blob of polished stainless steel in Chicago’s Millennium Park. Nicknamed the Bean, it is now partway to achieving Eiffel-like status. Kapoor’s London Olympics tower, the ArcelorMittal Orbit, is not. A three-hundred-and-eighty-foot lattice of red steel loops around a red steel trunk, it has been likened to the site of a major roller-coaster accident.

The design for Heatherwick’s losing entry, which has never been published, was a staircase that split and split again—“like a growing plant,” he told me. In the course of his twenty-five-year career, Heatherwick has generated ideas that he has been loath to abandon; one was to adorn a design with large planters, each holding a single tree. One of Heatherwick’s former colleagues told me that, in brainstorming sessions, “tree bowls always came up.” Another favored conception was a connected set of staircases. His Olympic design echoed an unbuilt 2006 commission for a structure on a hilltop in Baku, Azerbaijan. This monument—an ascending curlicue—was “a heroic staircase,” Heatherwick wrote in 2012. “It would give people stories to tell, such as the first time their child had walked up by herself or the time that, having made it to the top, a young man went down on one knee and made a proposal of marriage.” (This is not the Azerbaijani way, but perhaps it would have become so. Related executives expect marriage proposals on the Vessel.)

Heatherwick did secure a more modest Olympic commission, the cauldron, and he made a sensation out of it. Discounting a recommendation from officials that it should have no moving parts, he provided the opening ceremony with a moment of high emotion. The cauldron looked like something that should malfunction, yet it worked. Today, the Museum of London has a permanent exhibition celebrating the design. “Each stem carried a fragment of the Olympic flame in a uniquely shaped copper piece, only burning as one when they finally and perfectly nestled together,” one caption reads.

“I grew up in a city where nothing happened,” Heatherwick told me, referring to his sense of London’s creative stagnation, at least in terms of civic space, in the seventies and eighties. But, after the Olympics, he said, “there was a window of opportunity to maybe not be cynical, and to maybe make something unprecedented.” A few weeks after the closing ceremony, Heatherwick and Joanna Lumley had their first meeting with Boris Johnson about the Garden Bridge. Earlier that year, Lumley—who had previously proposed such a bridge as a memorial to Princess Diana—had written to Johnson, saying that the project would bring “great loveliness” to the Thames. She had added, “Please say yes.” Covered with hundreds of trees, it would link an area of diplomatic missions and barristers’ chambers, on the north side, to a riverside walk, popular with tourists, on the south. Heatherwick says that he and Lumley first discussed the idea some fifteen years ago. She has always deferred to him on its design, except for a few suggestions: it should have a Christmas tree during the holidays; it should not provide a straight line of sight, encouraging pedestrians to meander; and, although the bridge’s platform would widen at two points, above thick supporting pillars, from the air its outline should not evoke a pair of sunglasses or a bra.

Bjarke Ingels, describing his collaborations with Heatherwick, recently said, half joking, “Whenever I wanted Heatherwick to like something, I would start by talking about nooks and crannies—he says ‘nooks and crannies’ constantly.” Heatherwick has described the Garden Bridge as “a series of intimate spaces in which to stop and linger.” Richard Rogers, the architect, has praised it as a likely “oasis of calm and beauty.” Lumley has imagined a place “where the only sounds will be birdsong and bees buzzing and the wind in the trees, and, below, the steady rush of water.” One can admire this optimism, after repressing thoughts of driving rain and dense crowds. But Heatherwick and the bridge’s supporters also have asked that it be valued as transportation infrastructure, and this is harder to accept. Heatherwick told me that the Garden Bridge would be built in “the biggest gap” that exists between any two bridges in central London, which wasn’t true. It would be closed at night, and cycling would be banned. According to projections, its entrances would be congested. Indeed, Heatherwick has said, approvingly, that the bridge “has the potential to be the slowest way to cross the river.”