Or rather an inkling of seemingly untenable optimism; the plan relies on a rate of housing production higher than anything we have witnessed in a long time. The lauded housing initiative for low- and moderate-income New Yorkers during the Koch administration resulted in the creation and rehabilitation of about 150,000 apartments over a similar time frame, many of them born of renovations to vacant buildings in the Bronx, Harlem and Central Brooklyn that had been lost to the misery and ashes of the 1970s. There is no such analogous derelict housing stock today, which means that much of the building that will happen will be building up.

And here, as with the obvious and Olympian challenges of financing, is where so many complications lie. One of the many commendable aspects of the mayor’s plan, which is over 100 pages long, is the interest it extends beyond construction to fostering communities and facilitating economic integration. This means that commercial thoroughfares like Pitkin Avenue in Brooklyn, for example, would presumably no longer exist merely as corridors of poverty retail (a cellphone store next to a fried-chicken chain next to a purveyor of cheap tank tops). Better services would, in theory, bring more moderate-income tenants to historically troubled neighborhoods.

Implicit in this paradigm is the idea that affluent New Yorkers living in well-tended corners of the city would also open themselves up to neighbors who might be less privileged. It was telling that the mayor announced his plan in the gentrified, multimillion-dollar brownstone world of Fort Greene, Brooklyn. At every point along the spectrum, including the high end, the only way to have cheaper housing is to have more of it, an idea that many New Yorkers are happy to embrace until submission to the principles of supply and demand means looking out at a 30-story tower 15 feet away.

Within days of the plan’s release, residents in and around One Brooklyn Bridge Park, an expensive condominium complex converted from an old printing plant on the Brooklyn Heights waterfront, drafted a petition objecting to a proposal for a high-rise complex next door, where the city is considering placing middle-income housing alongside luxury properties. The dissenters appeared to see no irony in the fact that they held out the Pierhouse, a low-rise building going up in the north end of the park, where the smallest apartments are selling for $2 million and the larger ones closer to $11 million, as an example of more mindful development.

Any modicum of economic diversity left in TriBeCa, otherwise a temple of hedge-fund wives migrating between 6,000-square-foot lofts and SoulCycle, exists because of the 39-story towers of Independence Plaza North, built as a Mitchell-Lama complex in the 1970s. When the buildings aged out of the program a decade ago, tenants fought and continue to fight to keep some portion of the apartments within the reach of the artists and electricians and teachers and waitresses who live there. The legal battles are an object lesson for the city in the challenges of preserving the affordability of subsidized housing. Over the next 10 years, more than 53,000 rental units, including some in Mitchell-Lama buildings, will risk losing their subsidies and be subject to market rates.