“He's handsome,” says my friend Elaine, looking at the photograph I’ve slipped from my wallet. Not much bigger than a postage stamp, the portrait rests in the palm of my hand as we sit on a bench by the swift tidal strait that is New York’s East River.

On the opposite shore, glassy-bright under a pale, shining winter sky, are the towers of Manhattan’s skyline; a stolid orange ferry sets out for Staten Island, and out in the bay Liberty lifts her torch in spite of all. We warm ourselves with coffee from the deli just off Cranberry Street, behind us in the Heights, and look back through time into the clear grey gaze that meets ours.

The photograph is of a young man with a firm jaw and a well-shaped brow; his coat is buttoned to the neck and he wears a crushed, peaked cap set with the emblem of Abraham Lincoln’s Union Army. There is, in his look, both caution and resolve. He would need both. The picture was taken in 1861 when its subject was 24 years old. During the American Civil War he would rise from private to lieutenant-colonel; he would fight at Gettysburg, Bull Run, Chancellorsville and Antietam. His name was Washington Augustus Roebling, and when he was done with the war he would give 14 years of his life to building the Brooklyn Bridge. “Let’s walk,” I say to Elaine.

The Brooklyn Bridge is no secret. The greatest suspension bridge ever built when it was completed in 1883, it is still one of the most famous spans in the world, though there are now many bridges that exceed it in length and height, and it is a New York landmark on a par with the Empire State Building or Central Park. Want to buy the Brooklyn Bridge? That’s how the story goes. And yet – because it is not only a handy way to move between Brooklyn and Manhattan but also a work of art – it is my secret, too. All true works of art are secrets, because they communicate uniquely with each person who chooses to open themselves to what they may give and how they may speak.

In 1878 Walt Whitman visited the near-completed bridge and declared that his visit provided “the best, most effective medicine my soul has yet partaken – the grandest physical habitat and surroundings of land and water the globe affords – namely, Manhattan island and Brooklyn, which the future shall join in one city – city of superb democracy, amid superb surroundings.”

Take the subway and see for yourself that he was right then and right now. If you’re coming from Manhattan, there’s the C train to High Street/ Brooklyn Bridge, or the 2 and 3 to Clark Street. Either way, when you ascend into the light, you’ll find yourself in the now fashionable neighbourhood of the Heights, and even without the wonder of the bridge there would be plenty to keep you entertained in these cobbled, tree-lined streets with their wooden houses, warehouses, and the feel of old New York.

There’s the best pizza in the city, for one thing, at Grimaldi’s (get there when they open or you’ll queue for an hour) and the best ice-cream at the Brooklyn Ice Cream Factory, housed in an old fireboat house just in the shadow of the span. Stand with your cone (as big as your head) and imagine the days before the bridge was begun in 1869, when, in the winter, the river would choke with ice and cut off the ferry traffic, isolating what were then still two cities.

When Elaine and I leave the promenade, we walk the few blocks to Cadman Plaza to duck underneath the roadway for the stairs that rise to the wooden walkway. Washington Roebling was not this bridge’s designer, although he was its chief engineer.

The work was conceived by his father, John Augustus Roebling, a Prussian-born engineer and one of the men who made the modern suspension bridge possible. At the time the Brooklyn Bridge was begun, bridge-building was a risky undertaking; one in every four bridges built would eventually fail. Yet John Roebling believed in the possibilities of wire rope, of strong construction, of stone foundations sunk deep in the river’s mud. He was killed in an accident just as the task was begun; his son, by then 32 years old, was the only man in the world equipped to finish the job.

That he did, at the cost of his health and with the help of his remarkable wife, Emily. I stand on the walkway and run my hand along one of the four great cables that support this structure. Thousands of miles of steel wire run back and forth across the river so the bridge was spun like a web. I take hold of one of the narrow descending cables, the cold steel against my warm skin, and feel the vibration in the wire, for this bridge – though it looks as solid as the ages – is never still. Stone in compression and steel in tension, the bridge lives across the river, which glitters and shivers far below as a bright red tugboat passes underneath our feet.

Once upon a time, there were twin towers visible on the Manhattan skyline, but New York has twin towers still: the stone towers of this beautiful place, a place that is no place, that is between, that is itself. Standing on it – as I love to do at dawn, at dusk, at any hour of the day in any weather – is a testament to possibility and the power of belief. The engineers who made this bridge had faith in themselves, in the power of their work, in the harmony that progress would bring. We, their inheritors, may no longer feel that “progress” brings such unalloyed benefit, yet it’s impossible not to feel hope as you stand here, held over the river, safe.

Here, you may go forward, you may go back. The choice – and which is which – is entirely yours.

Here’s a man and his daughter standing, pointing, discussing the city’s landmarks; here’s a cyclist in yellow and black Lycra sweeping down the incline towards Park Place. Here are tourists and commuters and you may notice, as I do sometimes, that more of them than you’d think are smiling, and I know it’s because of this bridge.

When my friend and I left the bridge we parted; I headed up into Chinatown and Little Italy, a half a mile or so away; I bought sweet mozzarella and San Daniele prosciutto at the Alleva Dairy and artichoke ravioli, made fresh every day, from the Piemonte Ravioli Company. A walk across the Brooklyn Bridge will restore your appetite, if you’ve lost it; your appetite not just for food but for life itself. The span of a bridge, the span of life. Quotidian beauty, useful beauty, in the strong, light works of the engineers. A secret for everyone, just for me, and just for you. Let’s walk. Erica Wagner’s novel Seizure is published by Faber & Faber (£10.99).

Where to eat near Brooklyn Bridge

Grimaldi’s, Brooklyn Bridge Pizzeria, 19 Old Fulton Street (tel. 718 858 4300)

Brooklyn Ice Cream Factory, 2 Old Fulton Street, Brooklyn (tel. 718 246 3963)

Alleva Dairy, "The Oldest Italian Cheese Store in America", 188 Grand Street (tel. 212 226 7990)

Piemonte Ravioli Company,190 Grand Street, (tel. 212-226-0475)

Further information: www.visitbrooklyn.org

Where to stay
Will Hide

Marriott, Brooklyn Bridge
Many Brits think of Brooklyn being to Manhattan as Slough is to London, but fear not. The nearest subway station to this large hotel is Borough Hall, and you can reach southern Manhattan in minutes, or walk to Brooklyn Esplanade near by for skyline views. The location means rates are lower than uptown. Details: 001 718 246 7000, www.brooklynmarriott.com. Doubles from £105.

Pod Hotel
On East 51st, between 2nd and 3rd Avenues in east Manhattan, this hotel offers good value, with bunk rooms that sleep two (from £73) as well as regular singles and doubles. Many have shared bathrooms, but there are iPod docking stations plus free wi-fi. Details: 212 355 0300, www.thepodhotel.com. Doubles from £101.

Bed and Breakfast on the Park
This Brooklyn B&B, in an old “brownstone” building in Prospect Park West, was built in 1895 and is filled with period antiques. There are seven rooms. The F train subway is two blocks away and will get you to 34th Street in Manhattan in about 20 minutes. Details: 718 499 6115, www.bbnyc.com. B&B doubles from £141.

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