It was a Thursday night at Frim Fram Jam, right in the middle of the Tranky Doo.

Caleb Wiese was doing a Suzy Q — “literally, in the middle of the song,” his partner, Katherine McClintic, said — “and he’s looking at me and he stopped and said, ‘I need to talk to you.’ ”

Mr. Wiese is a mathematician. Ms. McClintic is a dancer “slash sales” who works at a software start-up. The night in question was Aug. 1, 2013, hot and wet in the city. Mr. Wiese had brought avocados and mangos. They were friends, just friends.

If summer romance in New York is a geography of tipping points, this was theirs. As Mr. Wiese put it, “I had my solution in my head and I needed to apply it.”

His solution, as Ms. McClintic remembered it on a recent afternoon, nearly two years later, was this: “He just said, ‘I like you.’ ”