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After the attacks of Sept. 11, 2001, and the destruction of the World Trade Center, the young architect Michael Arad started thinking about how to memorialize the tragedy. A single, powerful image came to mind: two square voids in the Hudson River, with water pouring into them. He made some drawings and even a model, which he photographed on the roof of his East Village apartment building with the Manhattan skyline as a backdrop.

“As a New Yorker, I had a need to respond,” he says. No one had asked him to design a memorial, but he started thinking about one anyway. It was a kind of catharsis.

When a competition to design the New York 9/11 Memorial was announced, Arad entered his ideas, and in 2004, the then-34-year-old won the commission to create what is now one of the biggest, most expensive and most impressive memorials in the world.

It was a remarkable accomplishment for such a junior architect and even more remarkable that his basic vision has been realized with remarkably little compromise to its essential form. Although they aren’t in the middle of the Hudson River, and are surrounded by the din and chaos of construction on all sides, Arad’s voids are flowing with water, a steady cascade of rivulets plunging into pits that are each almost an acre in size. It is an extraordinary thing.

The basic vision works, in part, because it recalls ancient and deeply embedded connections among water, memory and death. Without reference to any single myth, the flowing waters suggest the River Styx, the boundary between life and death in Greek my­thol­ogy. They also suggest portals, or whirlpools, through which one might pass to some unknown beyond, or the waters of death crossed by Gilgamesh in the old Sumerian epic.

The endless passing of water over the carefully designed weirs, which separate the flow into hundreds of smaller streams suggesting individual identity near the top of the fall and a collective confusion of intermingled droplets near the bottom, also recalls the primitive but infinite power of a mighty waterfall. One corner of New York has Niagara; the city now has its own, domesticated version of watery abyss.

But perhaps the most important connection for the success of Arad’s memorial is the suggestion of Lethe, another Greek river from the underworld, the one that brings forgetting and oblivion. For all that we like to think that memorials are about remembering, they are ultimately about forgetting. New York, over the course of its history, has absorbed an astonishing amount of tragedy and loss — 19th-century epidemics that killed dozens of people a day; the General Slocum steamship explosion, which cost 1,000 lives; and disasters with names such as the Triangle Shirtwaist factory fire and the Happy Land arson. They haven’t all sunk into oblivion, but they have become safely part of the past, dumped from that part of the memory that needs periodic purging if a city (or a person) is to move on, heal and stay vibrant.

And so while the memorial designed by Arad and the landscape architect Peter Walker now has an international audience, while it is still very much owned in some important way by the relatives and friends of those who died there, ultimately its destiny is to be merely a civic object in the urban fabric of New York. And New Yorkers will determine whether this memorial becomes a living part of their city or a dead plaza with two enormous fountains.

To succeed, it must ultimately merge with the landscape of New York not as a place apart, sacred and full of sentiment, but as a place where people gather because they want to play, flirt, think, read or eat a half-smoke with everything on it.

Arad compares his memorial, which will be dedicated on the anniversary of the attacks and then open to the public (reservations required) Sept. 12, to Union Square and Washington Square Park. Both are in New York and both contain memorials (multiple statues in Union Square and a monumental arch devoted to Washington in the park that bears his name). But anyone who has visited them knows that their memorial function is now pretty much limited to names, sculpture and inscription. Today, they serve multiple functions, as a stage for performance, home to a popular green market, a refuge for the homeless and restless, a place to walk dogs, daydream and let your little monsters run wild.

So Arad and Walker have worked hard to keep the memorial site open to the city, unbounded, neither raised on a plinth nor set into a frame. Streets that were closed off decades ago to build the superblock World Trade Center are being reopened as part of the larger redevelopment of the site. And the original idea in architect Daniel Libeskind’s master plan for the redevelopment of the World Trade Center, which called for setting the memorial in a 30-foot depression, was successfully scuttled. Although the eight acres of plaza that contain the memorial and the museum (designed by the Oslo-based Snohetta firm) will eventually be hemmed in by new high-rises (including towers by S.O.M., Norman Foster, Rogers Stirk Harbour + Partners, Fumihiko Maki and Kohn Pedersen Fox), many of the most successful squares in cities around the world are hemmed in without being closed off.

So it’s conceivable that one day not so far in the future someone new to New York, some aspiring banker or editor or new immigrant, might happen on the memorial by accident, pass by the thousands of names cut into the bronze panels that line its vast pits, marvel at the giant sheets of water that seem to plunge into an abyss, and think, simply: Cool.

At which point, one can say of the memorial: Job well done. If that seems cavalier about the meaning of Sept. 11, the loss of life, the grief of families, it’s worth remembering that the actively healing part of a memorial often has little to do with its form or design. Today, with America defined by fractiousness and anger, the healing is all in the fight that precedes the construction. It is the controversy, the anger, the recriminations and ad hominem attacks that help many people move past grief.

Over the years it took to design and build the memorial, Arad and his team had to contend with enormous conflicts. They fought off efforts to clutter the plaza with skylights and large air vents serving the acres of space underneath, including the waiting room and tracks for a new transit hub designed by Santiago Calatrava. They had to compromise on cost concerns and security worries, and abandon their initial plan to open up a gallery behind the waterfalls underneath the plaza, where the names would be displayed. Even so, the memorial and museum complex will cost some $700 million, and someday, when passions have cooled, it will be reasonable to ask: What kind of society spends this much money on memorials?

But perhaps most contentious was the anger of survivors, who couldn’t agree on how the names of the dead should be listed. Should first-responders, who served heroically, be displayed more prominently or be grouped together? Should people be grouped by where they worked? Where they died? Should the names of the companies who lost staff be included?

One prominent relative of a fallen firefighter feared “an attempt to establish a hierarchy of loss.” But many of the family members were enraged by Arad’s initial plan to list the names randomly. “The haphazard brutality of the attacks is reflected in the arrangement of names,” wrote Arad and Walker in their 2004 design statement. “No attempt is made to impose order upon this suffering.” Instead, they proposed using “meaningful agencies,” grouping names in ways that reflected bonds of friendship, family or collegial relations.

But it seems that “imposing order on suffering” is exactly what people want, or need, and that one way to feel that order has been imposed is to impose one’s will on other people. The families fought back, and eventually a compromise, suggested by New York Mayor Michael Bloomberg, was reached: Names would be grouped by which tower people worked in or which flight they were on when the planes crashed, with first-responders grouped together. “Meaningful agencies,” worked out with a complicated computer algorithm that processed more than 1,200 requests for proximity filed by family and next of kin, were then found among these large subgroups.

Arad’s initial idea was better, but now it’s over, and the names have been cut into bronze. Heating and cooling elements keep the plates at a comfortable-to-touch temperature year-round. Lights and mirrors underneath make the names glow at night. The bronze panels have been carefully arranged and sized so that people in wheelchairs should have a reasonably good view of the water voids, which descend in two stages, 30 feet into a granite-lined basin, and then into a smaller 30-foot shaft, almost to the bedrock beneath Manhattan. From the top of the plaza, it seems the water is descending to infinity.

Soon, the fight over the names, and someday even the endless squabbles over the larger World Trade Center redevelopment, will be forgotten. All the lost opportunities, the hope that there might be a cultural center at the site rather than just office space and a museum, will no longer feel so bad. Eventually, even the names of the dead will be mostly forgotten, as anonymous as the names on an old marble obelisk marking the Civil War dead in small towns over much of America.

If the fountains of Arad’s memorial are still running — and given how balky and complicated to maintain fountains is, that’s a big if — they will probably inspire feelings of awe, and pride, in people who know the events of September 2001 only as a few paragraphs in the history books. The plaza where the twin towers once stood will have been deeded back to its rightful owners, who will look at the enormous waterfalls and think: Is this a great city, or what?