Edwin Denby died in 1983. I met him in 2006 (he would have been 103), if reading him counts as meeting him. I was taking a dance criticism course, and my teacher, Mindy Aloff, assigned his Dance Writings and Poetry, introducing me to endlessly readable essays like “Three Sides of Agon” (even the title makes you want to hold it up, inspect the choreography) and “Against Meaning in Ballet,” which I now assign to my students.

I remember learning—unless I made this up—that Denby would struggle to finish his reviews, working right up to the last minute, refusing to let go until he absolutely had to. “And that’s why when you read him,” Mindy said, “it’s like shrugging off a sweater.” He writes as if he’s just sitting down for a chat, just telling you what he saw, like you’ve known each other for a long time.

I thought of this one night in February at “A Reading for Edwin Denby.” It was the opening of Danspace Project’s “Platform 2015: Dancers, Buildings, and People in the Streets,” six weeks of performances, classes, and other encounters inspired by Denby’s thinking, looking, writing. The title comes from a lecture that he wrote for Juilliard dance majors but never delivered (he even planned ahead for failed jokes). Many of his friends were there at St. Mark’s Church, people who really knew him, like Bill Berkson, Jacob Burckhardt, Mimi Gross, Vincent Katz, and Anne Waldman. They read from his work, talked about his life. The evening’s unofficial refrain: “Edwin taught me how to look.”

Certain basic facts about him came as revelations. He lived on West 21st Street with a space heater, a typewriter, and walls of books. To visit his loft, it seems, was a real event, something you didn’t forget. He had season tickets to the New York City Ballet and an affinity for mid-show naps: “The curtain went up, and my eyes went down.” He was tall and thin with white hair, “this luminous ghost,” Ron Padgett recalled. He wrote a romance novel, Mrs. W’s Last Sandwich. Selectively shy about performing, he avoided reading his work in public but acted in silent movies, evidently in some nutty roles. We watched The Uncle’s Return and excerpts from a few other films, all of which involved a lot of chasing and stumbling and running in circles.

“I myself like the climate of New York,” we heard him say, a sonnet illustrated by Rudy Burckhardt’s black-and-white stills. Crosswalks, rooftops, Broadway merging with Fifth. I thought about Denby’s New York—my grandparents’ New York—versus mine. Those buildings, those people. How different are we? How unchanged?

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“There’s going to be a lot of absence in the Platform, a lot of failure,” one of the Platform participants told me as we walked through the Lower East Side. He was among the 13 artists selected by the critic-poet-curator Claudia La Rocco (also my friend and former editor at this publication) to represent three “nodal points” or lineages of dance in New York, stemming from George Balanchine, Merce Cunningham, and Judson Dance Theater. In the spirit of illuminating, as Denby did, relationships between “uptown” and “downtown” dance—those persistently divided realms, if decreasingly by geography then still by aesthetics—Claudia paired artists from different traditions and essentially said, “Do anything.”

“It’s incredible. She’s reversing the traffic flow,” a friend said after a stunning performance by two of those pairs (Kaitlyn Gilliland and Will Rawls; Silas Riener and, in video form, Adrian Danchig-Waring). In the audience that night, another friend, a “downtown” choreographer (I wavered over those quotes), bumped into an old classmate whom she hadn’t seen since ballet school a decade ago.

A more disgruntled colleague: “I like to know what I’m getting, for ballet to be ballet, downtown to be downtown, you know?” He made little box shapes with his hands. I couldn’t tell if he was serious.

I think the traffic-flow-reversal is thrilling: not just novel but actually productive, doing the work of building connections where few exist, or uncovering those that do. At a panel discussion with some of the artists, Danchig-Waring, a City Ballet principal, reflected on that 67-year-old company. “It’s an institution with pretty impermeable walls, and this project has really brought them down,” he said.

Which isn’t to say that some kind of we-are-one utopia sprang up. I gather that the collaborative process wasn’t easy for anyone, from scheduling rehearsals to negotiating what the artist Yve Laris Cohen called “different lived socioeconomic realities.” The Judson-Cunningham-Balanchine triangle, he pointed out, “is not an equilateral triangle.”

Maybe it’s not even a triangle. Those points aren’t so discrete. “Am I Judson?” the choreographer Jillian Peña wondered out loud. “Yeah, I’m Judson,” but she could be all three.

Danchig-Waring also talked about his common ground with Riener, who danced for Cunningham from 2007 to 2011, with Cunningham’s death falling halfway through his tenure. Both had spent time working “in the houses of these masters who are deceased,” Danchig-Waring said. He joined City Ballet in 2002, nearly 20 years after Balanchine’s death, but the company will always worship its founder.

A lot of absence. Balanchine. Cunningham. Denby. (Judson icon Yvonne Rainer, I’m happy to report, was in the house.) But here we are, and the Platform feels like forward motion. I spent a Friday afternoon learning the opening of Serenade, the first ballet Balanchine made in America (1934), in the St. Mark’s Church sanctuary. Kaitlyn Gilliland, a former City Ballet dancer (now freelance all-star) taught it, joined by the City Ballet principal Teresa Reichlen. I pressed my right palm up to the sky, looking past my second finger. I brought the back of that hand to my right temple, peering down over my left shoulder. Observers wanted to know why Balanchine did this and that. The teachers didn’t always know, and I don’t think they need to.