To what extent can we hold Mr. Bloomberg responsible for these gulfs? For the fact that the poverty ratio has remained essentially unchanged in New York since his first days in office, with roughly a fifth of the city’s residents living below the federal poverty level?

Certainly, some of the disparity would exist without him, and the poverty rate has been more or less intractable for the past 30 years. But it is easy to envision that we might have arrived at a better place with someone who had paid more visceral attention to inequity than with someone who felt the need to sue the City Council to block a measure mandating a living wage (the suit was thrown out of court).

And still, it is not fair to paint the mayor as a Dickensian ogre who utterly ignored the poor. His Young Men’s Initiative, to which he contributed $30 million of his own money, seeks to improve the lives of young underprivileged black and Latino men. The administration’s efforts to expand education and job training in Brownsville, Brooklyn, for example have led to higher high school graduation rates and lower rates of unemployment. A network of organizations and agencies called NEON, an innovation of the Department of Probation, puts probation offices in neighborhoods where rates of incarceration have been high so that those in the criminal justice system are saved long commutes to mandatory meetings with their officers. Instead they are encouraged to use their time productively.

What’s striking about a recent report delivered by the Furman Center for Real Estate and Urban Policy at New York University, which examines demographic data neighborhood by neighborhood, is that poverty actually declined between 2000 and 2011, though by no means hugely, in some of the most afflicted places in the city — in Brownsville and in various enclaves of the South Bronx.

Where poverty has crept up are those places where income levels hover around the city’s median of $55,000 — neighborhoods like the Fresh Meadows, Hillcrest and Elmhurst sections of Queens and Stapleton and St. George on Staten Island. Job losses, rent increases and foreclosures have brought those previously able to sustain themselves to precarious new lows.

One legacy of the Bloomberg era is that it has redefined our economic and social categories — giving us a universe of superrich that have assumed a great share of our psychic space, and replacing a working class with an artisan class. The mayor spoke this month on his fiscal legacy at the former Pfizer pharmaceutical factory in Brooklyn, making this explicit.

The building had served as a manufacturing plant for 150 years, the mayor told his audience. Five years ago, executives closed it. “But today, as you can see, this is once again a manufacturing hub,” he continued. “Only now it’s an incubator for a new generation of craftsmen and women, who are making everything from furniture and fashion designs to kimchi and cookies, to software and 3-D printers.”