A cityscape is also a timescape.

And a visit to New York City is time travel. Roll the tape forward and back, and see the time-lapse version of the city, from the hard antediluvian schist that crops up in Central Park to the latest high-rise office complex.

We tend to think of America as a place that eats up its past, tearing down the old and erecting the new with no regard for history. And New York certainly has an energy that feeds on tomorrow.

But it is surprising how much of the past is still there, just left alone, standing in a multi-era crowd, with a brownstone wedged between a modern glass tower and a Beaux Arts library.

I suppose all of us who love the city have our defining frames in the time-lapse film. There is the fedora-topped bustle of New York in the 1940s, the World’s Fair gleam fighting the decay of the 1960s, the rhinestone Trumpification of the 1990s.

The city you remember best depends on how old you are and which version you first came to love.

But all of the versions are still there.

I first knew the city in the 1950s, and my memories are of Con Ed steam erupting from the streets in winter, diesel fumes filling the Port Authority Bus Terminal at 42nd Street like color fills a Titian, the squeal of the AA train (now the C train) as it fought the big curve between 168th and 175th streets. When I was a boy, we ice-skated at Rockefeller Center and window-shopped at Macy’s.

When I go back now, the subway still squeals, and the fumes are still the glorious aroma of the city, the garlic in its stew.

My city is still there, a little buried maybe, its face turned away.

That is not to say there aren’t chunks missing: Penn Station is gone; the Horn & Hardart Automat is gone; the current Madison Square Garden is a generic shadow of the old one; the Coliseum has been replaced by the gaudy Time Warner Center. Others, such as the Edward Durrell Stone Gallery of Modern Art, at Columbus Circle, have been given a new set of clothes.

Even Yankee Stadium has been torn down — Yankee Stadium, which I expected to last as long as the Roman Colosseum. (No such longing for Shea Stadium.)

Although some of the carcasses still exist along the Hudson River, the great ocean-liner piers are dusty, sagging, hollow or demolished.

And these don’t include the most obvious loss.

When I flew cross-country in 2005, the plane passed over Manhattan, and, from 30,000 feet, the missing place of the World Trade Center looked like nothing so much as the empty socket of a pulled tooth.

Yet, much of what I knew of New York when I grew up is still there.

Four decades ago, I stopped at a coffeehouse just outside Columbia University. It was when coffeehouses, not Starbucks, were the natural accoutrements of student life. You had to step down from the sidewalk to the below-grade tables. Someone was playing folk songs on guitar. It was called Cafe Ole. Two years ago, I accidentally found the same spot when I stopped for breakfast. It’s now Camille’s, but the uneven brick floor was still there, and the steps. Forty years squeezed together like an accordion.

You didn’t have to be born there: New York has a historical presence for most of us. We saw it in the movies and newsreels, in gallery photographs and paintings.

The New York of the mind comes from seeing King Kong, Breakfast at Tiffany’s and The French Connection.

Not to mention the best evocation of the city ever transmuted to celluloid: Woody Allen’s Manhattan, that cinematic mash note:

“He adored New York City. He idolized it all out of proportion — er, no, make that: He romanticized it all out of proportion. Yes. To him, no matter what the season was, this was still a town that existed in black and white and pulsated to the great tunes of George Gershwin.”

That New York of the mind is largely black and white. Or shades of gray. Even the snow in winter is gray. Like statuary, New York expresses form more than color.

Times Square sits in the mind like the black and white of Alfred Eisenstaedt, who photographed the famous V-J Day kiss there in 1945. The Staten Island Ferry does, too, and the crowds of people you pass on Sixth Avenue. (It will always be Sixth Avenue.)

Enough people fill a block there, as lunch hour begins, to populate a ballpark, but most of them might as well be alone in the wilderness that Manhattan once was. People avoid colliding but never seem to make an effort to miss each other. There’s a subliminal awareness of the crowd, but you can see in their eyes that they aren’t primarily aware of the here and now: They are thinking of the meetings they are required to attend today or whether their husband has remembered to buy the potato salad for dinner tonight. Pairs or trios walk along talking, but they are leaves floating together downstream in a current.

In his tiny 1949 book, Here Is New York, E.B. White wrote, “New York blends the gift of privacy with the excitement of participation; and better than most dense communities, it succeeds in insulating the individual (if he wants it, and almost everybody wants and needs it) against all enormous and violent and wonderful events that are taking place every minute.”

Stop at a storefront McDonald’s on a rainy November day and see the hordes lined up, warm against the cold outside, rubbing their hands as 40 people wait in ill-defined lines to be served. It’s noisy, yet quiet: The heat is steamy, the floor is worn. The bustle is enough to keep your ears electrified, but there is not much language to be heard outside the giving of food orders. The din is a roar of accelerating buses on the street, car horns, subways below the sidewalk grates and the incoherent susurrus of private conversation at tables.

It’s surprising how well people get on in New York, given the wide variety of types, ethnicities, politics and interests. The city makes room for all of them. Or, more precisely, the city takes equal lack of notice of all, so there is a kind of equality built in, an equality of negligibility.

It hasn’t always been that way. In the 1960s, the city seemed to be coming apart at the seams. The tourism slogan was “New York Is a Summer Festival,” but everyone in the city remembers it as “New York Is a Summer Fistfight.”

But now, allowing for the fact that you have 8 million people squeezed onto 300 square miles of land, the city is notably amicable: It has the lowest crime rate of the 25 largest U.S. cities, according to FBI statistics.

It is a city of diversity, and one that enjoys that about itself.

The last time I left the city, the hotel concierge phoned for a cab to take me to the airport. The cabbie was a large, bearded man with a black suit and an Eastern Europe accent; he drove a shiny black limo. Two blocks from the hotel, he pulled over. Another cab pulled over in front of us.

“If you please, my brother take you rest of way,” he said in a thick Boris Badenov voice. We emptied my bags into a second black limo.

The “brother,” who spoke with a Spanish, not Russian accent, explained as we drove that only one car in their fleet of cabs was authorized to pick up customers at the hotel, and so the first cab spent his day going from hotel to hotel, picking up customers and then redistributing them like a kindergarten teacher handing out cookies.

You come to expect such things in the city. It has always been this way.

What single image can catch the essential persistence of New York? The subways, the cabbies, Mott Street? For me, it is the wooden water tanks on the roofs of high rises. One would think they would have been replaced by something modern, something in stainless steel, perhaps. But they haven’t: All over the city, roofs are defined by their wood-slat water tanks, sitting on the tops of buildings like the acroteria on Greek temples.

A tourist will never run out of things to catch his attention, or his dollar. But the Statue of Liberty, the Guggenheim and The Lion King are not the images that boil up in memory for me. It is the water tanks.

My essential New York is built of alleys between apartments on the upper West Side, their trash cans waiting to be emptied.

It is the elevated train station at 125th Street, looking like some obsolete, alien spacecraft landed on stilts in the gully called Manhattan Valley.

It is the George Washington Bridge, which my grandfather worked on as an engineer in the 1930s.

There is no better way to enter the city than to walk across the GWB. You get the sense of crossing some large space that defines the difference between the comfortable world you know and the beehive world of the city. The bridge is a behemoth, covered in a putty of silver paint, with leopard spots of rust. The noise of the traffic as it passes blots out awareness; it is a constant ear-splitting surf.

But you arrive at 178th Street, and the neighborhoods begin. It is important to recognize that New York isn’t a single city; it is hundreds of individual communities, each with their life-support drugstores, groceries, shoe stores, churches and pizzerias. The city may not be as medievally immobile as it used to be, when most New Yorkers rarely left their two- or three-block turf except to go to work, but those neighborhoods are still the hearts of local patriotisms, each an axis mundi.

The two-story 1920s frame houses that line the streets of Queens, the brownstones of Brooklyn, the awning-beaked apartments of 59th Street in Manhattan — each neighborhood has its flavor, its architecture, its private history.

I look at my life and I know that although I am a grayhair 6 decades old, the 10-year-old kid who watched the Macy’s Thanksgiving Day Parade is still there somewhere, and so is the college graduate who came back to the city, and the married man who vacationed there, and now the senex who encompasses them all. And just as my whole life is a single long memory — a single speck of meaning — the city is the same: Everything that ever happened there is still there.