And in doing so, he handed New Yorkers an unyielding standard by which to take the measure of their new mayor.

The political theater was striking, and not just because a mayor with precious little experience as an executive had set a monumental task for himself.

Mr. de Blasio was flanked during this ceremony by his two political mentors, former President Bill Clinton and Gov. Andrew M. Cuomo. They are the Great Triangulators, who most often tiptoe around raging liberal fires. Their presence cast into sharp relief Mr. de Blasio’s embrace of a new progressive zeitgeist.

President Clinton, who swore in the new mayor, deregulated the financial industry, and possibly helped to unleash the animal spirits that led to the recent Great Recession. Hillary Rodham Clinton, another exemplar of center liberalism, stood behind them.

Governor Cuomo, who once employed Mr. de Blasio, wrapped him in a bear hug Wednesday and appeared to harbor genuine affection for the new mayor. But the governor, too, is a cautious ideological sailor, tacking this way and that. He has appointed two tax commissions, one liberal and one not so much. And he has pulled up short of endorsing Mr. de Blasio’s proposal for a tax on the wealthy to pay for universal prekindergarten.

And on New Year’s Eve, the governor, who has spoken movingly of those who are serving sentences decades long for workaday drug crimes, once again declined to pardon any of the tens of thousands of convicts serving time in state prisons. Instead he pardoned three who left prison many years ago.

That exercise finished, Mr. Cuomo drove south to an inauguration, where he heard his protégé, Mr. de Blasio, talk of an "inequality crisis” and pledge a march "towards a more progressive place.”

Mr. de Blasio’s promised progressive river could lap one day against the doors of the State Capitol. There’s no assurance the new mayor will walk away the winner.

More broadly, the new mayor’s speech underlines that those conservatives who cast a querulous eye and accuse New York City of floating closer to Europe than to North America are not entirely mistaken. It can seem more akin to a Social Democratic nation-state than to a typical American city.

We have stiff antismoking and antigun laws, and a great array of hospitals, clinics and public colleges. While several speakers on New Year’s Day condemned the condition of our homeless shelters, it is worth keeping in mind that the city stands nearly alone in declaring that homeless people have a legal right to shelter.

Mr. de Blasio’s hopes are grand. "When I said we would take dead aim at the Tale of Two Cities, I meant it,” he said. "And we will do it.”

Perhaps he’s right. The coming months will offer a clearer verdict. But you suspect that his life’s experience has also taught him that chasms are rarely crossed in a single step. His long-ago employer, David N. Dinkins, is referred to, more than a touch unfairly, as having presided over a failed mayoralty.

He made mistakes, not least in his handling of the Crown Heights rioting. But Mr. Dinkins reduced single and family homelessness to record lows. He opened libraries for longer days and turned schools into after-hour social service and recreation centers. His Office of Operations pushed innovation and rode herd on city agencies to innovate. He also rehabilitated tens of thousands of units of affordable housing in the howling winds of a vicious recession.

Those rebuilt neighborhoods can be found all over New York City. In other words, seemingly small steps left footprints still seen today.

Mr. de Blasio offered a final plea to keep the faith as thin gray cirrus clouds slid across New York, harbingers of an approaching winter storm. At the Canal Street subway station, a man, homeless and enveloped in blankets, sipped chicken soup. He put it down and blew on his hands for warmth.

The metaphor was inescapable. Great hope and great challenge, and storms ahead. "Our strength is derived from you,” the new mayor concluded. "God bless the people of New York City.”