BY JACQUELINE CUTLER

New Yorkers say they live in the city.

But where they actually live is usually within a few square blocks. Sure, prepandemic, people commuted for work, but they do the bulk of their living in their neighborhoods.

This great metropolis has always been a collection of neighborhoods.

Marc Aronson’s “Four Streets and a Square” understands that. His lively book bills itself as “A History of Manhattan and the New York Idea,” and his way of telling that story is novel. Aronson divides the borough into five sectors — Wall Street, Union Square, 42nd St., Harlem and West Fourth St. — and assigns each an era, depending on its influence.

Wall Street rules over the establishment of Manhattan as an early trading post and eventual financial powerhouse. In the 19th century, as ethnic battles and labor struggles grow, we move on to Union Square.

The early 20th century and New York’s new prominence as a cultural center take us to 42nd St. The ensuing decades switch between Harlem and the Village.

Aronson begins downtown with Wall Street and the Dutch, who set out to enclose it after purchasing the wide-open island from Native Americans. A fort at one end fended off invading navies. A nearby wall fenced out the original inhabitants.

Yet, despite itself, Manhattan grew more diverse. Some of the Blacks who arrived in chains eventually bought their freedom and started small farms. The first Jews arrived in 1654, 23 Spanish refugees who first sought haven in Brazil.

Prejudiced Gov. Peter Stuyvesant didn’t like any of this. When Quakers started arriving, too, he put his peglegged foot down. But the corporate Dutch West India Co. was the colony’s true ruler, and it made him back off. Population growth was good for business.

The city’s new diversity, however, was not accompanied by equality.

“Jews could come, but not as equals,” Aronson writes. “Africans could buy freedom, but their children remained enslaved.”

That’s because the city’s true founding principle was never the defense of freedom but the pursuit of profit. Visitors only needed to look up and down Wall St. to see the proof. At one end of the thoroughfare stood the beautiful Trinity Church — partly funded by booty from the ruthless Captain Kidd. At the other end? The slave market.

Money ruled Manhattan, and no one ever questioned where it came from or what it was used for.

Although New York City was occupied by British soldiers during the Revolutionary War, it flourished after independence, when the new Erie Canal made it a central shipping hub. Between 1820 and 1860, the city’s population soared from 123,000 to 813,000.

All those newcomers had to live somewhere. New York expanded, creating housing for a flood of German and Irish immigrants and public transportation to get them to their jobs. The major train and trolley lines converged at one station, Union Square.

Soon, that name would take on a deeper meaning, as political groups took up residence in nearby buildings and took over the park for raucous rallies.

“For the first time, the center of a city was not City Hall, as it had been on the old Wall Street; was not a church like Trinity; was not an open market,” Aronson writes. “Union Square was none of these and all of these — it was where many of the forces rising, pushing, suffering, triumphing in the city all met. It was the heartbeat of a city that was about to change.”

Once again, it was immigrants who led that change. Jews fleeing the pogroms of Eastern Europe settled downtown; Blacks fleeing the lynch mobs of the South found refuge uptown. They would both soon rejuvenate and remake Manhattan’s popular culture and progressive politics.

The modern American theater was created in and around 42nd St. by the German-Jewish immigrant Oscar Hammerstein I. His namesake grandson would go on to revolutionize Broadway with “Oklahoma.” But it was the original Oscar Hammerstein who first imagined it, figuring the neighborhood, with its easy access to mass transit, would draw patrons.

“As the story goes, in 1894 or ‘95, Hammerstein stood amid the odors and mud of 42nd St. at the crossing of Seventh Ave. and Broadway,” Aronson writes. “He gazed past the parade of suspicious characters and horses relieving themselves on the street and saw what the intersection could be.”

He not only built Broadway’s first entertainment complex, the Olympia, between 44th and 45th Sts., but also pioneered the “so bad it’s good” concept by booking the Cherry Sisters, a terrible singing duo. Hammerstein strung a protective net in front of the tuneless performers, then handed out fruits and vegetables to the audience. They flung rotten tomatoes with gusto.

Meanwhile, African-Americans and Caribbean immiHarlem. grants were heading to There were 60,000 Blacks in New York in 1900; by 1930, the number was more than five times that. The literary Harlem Renaissance introduced the world to writers like Zora Neale Hurston and Langston Hughes, while in the streets, fiery orators like Marcus Garvey promoted Black pride.

Art and politics mingled freely downtown, too, but then they always had. At the turn of the century, Greenwich Village had been home to committed radicals like John Reed and his hard-drinking friend, playwright Eugene O’Neill. By the ’50s, they had given way to beat poets in coffeehouses. A decade later, they would be pushed off stage by folkies strumming battered guitars.

But if neighborhoods like Harlem, Greenwich Village, and the Theater District pushed New York forward culturally, financially the city had lost its way. It forgot that money still mattered most in Manhattan, and by the 1970s, the city was running out of it, verging on bankruptcy. There was little sympathy in Washington. “Ford to City: Drop Dead” ran the famous Daily News headline.

“New York was out of money and the president was not willing to bail it out,” Aronson writes. “Lenders were no longer willing to trust the city to make good on the billions of dollars it owed . ... As the city’s critics saw it, New York was like an angry teenager; it spent with a free hand, expecting to be bailed out while flaunting its distinct set of values.”

Appropriately, it was the city’s first neighborhood, Wall Street, that came to its rescue when investment banker Felix Rohatyn cobbled together a plan to stave off fiscal disaster. But it was a “diminished, chastened” city that emerged, one that no longer offered free college tuition or undertook ambitious public projects like Lincoln Center. The new New York was a different New York, and although it would eventually prosper, not everyone would profit equally. But that division has always been part of the city, too.

“You could see this entire pageant of New York City history as a set of dialogues between pairs of streets,” Aronson writes. “Wall Street versus Union Square — the grandees versus the people. Forty-Second St. versus West Fourth St. — commercial popular culture versus the experimental, critical artist.”

Decades later, New York’s debates, and divisions, persist. However it changes, the New York idea has remained just that, ultimately, Manhattan’s strength comes from its immigrants, openness and willingness to dream. And from these many separate little neighborhoods rises one great city.