Math Keeps Friends & Colleagues Together on 9/11 Memorial

At first glance — and even after deep scrutiny — the names on a new memorial to those killed on September 11, 2001, seem randomly arrayed. The names are not arranged alphabetically nor, for the most part, are they presented in labeled groups. But the memorial's layout is anything but random. The 2,983 names — etched across bronze panels surrounding two memorial pools of water, one north and one south — are strung together in a way that reflects thousands of complex interpersonal relationships forged before the attacks and, on at least one occasion, during the immediate aftermath. [Read more about the 9/11 anniversary in this in-depth report] The memorial's arrangement preserves, for instance, the terrible blow suffered by the investment bank Cantor Fitzgerald. Before the morning of September 11, the firm's headquarters occupied several floors high in the North Tower of the World Trade Center (WTC). In the first of the terrorist attacks of that day, a hijacked airliner struck the North Tower, just below Cantor's offices. The firm was devastated; 658 employees died in the attack, along with 46 contractors, food-service workers, consultants and visitors. Although no heading identifies them as such, the 704 names of those killed at Cantor Fitzgerald appear together on the memorial. Cantor's loss was so great that its portion of the memorial surrounds almost half of the north pool. Within that grouping, as elsewhere on the memorial, the placement of names also reflects numerous other social and professional connections, thanks to input from families and co-workers and some heavy lifting by a custom-built computer algorithm. The planners of the memorial, which will be dedicated this weekend where the Twin Towers once stood, solicited requests from victims' loved ones for "meaningful adjacencies" — names that should appear together on the memorial. Roughly 1,200 responses came back, asking that a victim's name be grouped with specific colleagues, with family members or with friends who also perished in the attacks. The web of meaningful adjacencies at firms such as Cantor Fitzgerald were large and complex — loved ones made half a dozen or so adjacency requests for some victims. Some requests, such as the one linking Victor Wald and Harry Ramos, were somewhat simpler. Wald, 49, and Ramos, 45, worked at financial firms three floors apart in the WTC's North Tower but had never met before September 11. As recounted in Richard Bernstein's 2002 book Out of the Blue, the two men met in the stairwell as they were both trying to escape the stricken building. Wald was sitting on the stairs at the 53rd floor, unable to continue, when Ramos and one of his colleagues, Hong Zhu, decided to stop and help Wald down any way they could. They carried him, they commandeered an off-limits elevator, and the three men eventually reached the 36th floor before Wald said he could go no further. Zhu escaped at the urging of a firefighter, but Ramos stayed with Wald, telling him, "Victor, don't worry. I'm with you." The two men died when the tower fell about half an hour later; their names appear together on panel 63 of the North Memorial Pool. The number of interlocking adjacency requests, both simple and complex, meant that laying out the names by hand would be nearly impossible. So the planners enlisted the help of a complex algorithm built by media design firm Local Projects and New York City–based software artist Jer Thorp. The names algorithm works in two stages. The first stage, really an algorithm unto itself, builds clusters of names from the adjacency requests. If person A needs to be near person B, and person B near person C, those three names will form a cluster. "That kind of results in a pile of really irregularly shaped puzzle pieces," Thorp says. Among the various indivisible bunches formed by the clustering algorithm were blocks with as many as 70-odd names. A second, space-filling algorithm takes those puzzle pieces and fits them into place within the confines of the 76 bronze panels enclosing each memorial pool. [See below for a NOVA video about the fabrication and etching of the panels.] "In general it takes the big pieces and finds a place for them, and then fills in the gaps with the small pieces," Thorp explains. He says it took about a month to get the algorithms working, followed by months of tweaks as design requirements shifted. When Jake Barton, principal of Local Projects, approached him about the project, "I told Jake I was happy to work on the project, but I didn't know if it could be done," Thorp says. ("Little did we know that two computer scientists had turned it down outright," Barton adds.) The task, after all, was not so simple as forming odd-shaped pieces and fitting them together — the arrangement of names had to obey a number of other requirements. Typographic demands, for instance, meant that some names could bridge the gap between two panels, whereas others could not. For instance, the combination of a first name ending in "T" and a last name beginning with "J" was unsuitable for spanning two panels. (Some design challenges were best left to human hands; a manual interface allowed the architects to make tweaks to the algorithm's initial layouts.) And organizational requirements imposed a nested, overarching system for the placement of names. The north pool memorializes those who were killed in the WTC's North Tower; the passengers and crew of hijacked American Airlines Flight 11, which hit the tower; and the seven victims of the 1993 bombing of the WTC. Each of those groups occupies its own section in that part of the memorial. Similarly, the South Memorial Pool carries the names of those killed in the South Tower; the passengers and crew of hijacked United Airlines Flight 175, which struck that building; the first responders who died in the attacks and their aftermath; those who died at the Pentagon in Washington, D.C.; the passengers and crew of hijacked American Airlines Flight 77, which was flown into the Pentagon; and the passengers and crew of hijacked United Airlines Flight 93, which crashed in a Pennsylvania field. Within those larger groups are subgroups representing professional affiliations, such as the 704 victims from Cantor Fitzgerald or the 11 victims from New York City Fire Department Ladder 3. And within those subgroups, finally, are the clusters built from adjacency requests. Some meaningful adjacencies join two professional groupings, such as that linking the Vigiano brothers. Firefighter John Vigiano, 36, and his detective brother Joseph, 34, were among the first responders who died in the attacks. The brothers' names appear side-by-side on panel 23 of the South Memorial Pool: John at the end of his unit, Ladder 132, and Joseph at the beginning of his police department Emergency Services Squad 2. The memorial — and the online guide that helps visitors find their way through it — freezes into place the events of that day a decade ago. In its overarching structure, the arrangement of names preserves the order behind the victims' lives — their work, their friends, their families. "You have this enormously organic, complex, human web of meaning," Barton says. At the same time, the seeming disorder in the arrangement of victims' names preserves the chaos and randomness behind their deaths. "You get this incredibly powerful sense of undifferentiation," Barton says of viewing the long chains of names on the finished memorial. "Based on the event, all these names are equal."

Constructing the 9/11 Memorial Plaques, by NOVA: Watch the full episode. See more NOVA.

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