Studying these cells could lead to new treatments for diseases ranging from gastrointestinal disease to diabetes.
The man who keeps the hit TV show "Numb3rs" mathematically honest is also using a rarified math theory to correct a flaw in standard counterterrorism thinking. A recent visiting professor of mathematics at MIT and a Hollywood math consultant, Dr. Jonathan D. Farley realized that experts could make potentially grave errors by overestimating their effectiveness at breaking up terrorist cells. "They're asking the wrong question and getting the wrong answer," Farley explains.
It's an easy mistake to make, since most government operatives don't use lattice theory to analyze social networks. Lattice theory, which includes Boolean algebra, is Farley's favorite conceptual realm, and his talent at it has earned him great acclaim. (In 2003, he solved a problem posed by MIT's Richard Stanley in 1981.)
He used to joke that it has no practical purpose whatsoever, but after the Sept. 11 terrorist attacks, Farley wondered if pure math actually could save lives. He remembered the opening line in the movie "A Beautiful Mind" about John Nash: "Mathematicians won the war." And, he remembered Palestinian leader George Habash's words: "Terrorism is a thinking man's game."
Being a thinking man, Farley says, "it's better to fight smarter, not harder," and fighting Al Qaeda with abstract theory could more accurately assess our vulnerability to future attacks than current methods. As a bonus, it could also prevent financial resources from being wasted on phantom fears at the expense of real dangers.
"People often view terrorist cells as a graph, with members as nodes connected to each other if they have a direct communications link," Farley says. "But they're leaving out the most important part, the hierarchy," he says. "Terrorist cells have chains of command (partially ordered sets) from leaders to midlevel operatives to the workers who carry out orders."
As simplified examples, the graph theory would conclude that blocking four intersections along Massachusetts Avenue between Kresge Auditorium and Harvard Square could prevent MIT students from driving to the square. But students could use side streets to bypass the blocked intersections.
Likewise, the graph theory would show that capturing four members of a 15-member terrorist cell arranged as a binary tree gives a 93 percent chance the cell has been disabled. Even without knowing the captives' positions in the hierarchy, it's still possible to plug in the "cut sets" that could break the command chain into a probability formula, and that probability is, unhappily, only 33 percent. "Lattice theory won't tell you how to fight the terrorists, but it might tell you if you've won the battle," Farley says.
Farley's hypothesis, published in late 2003, interests several military researchers, including Rebecca Goolsby of the Office of Naval Research. "With covert missions, there's a lot of missing data, and some of it is wrong," she says. "Jon came up with a new approach and drew up good questions" for approaching these "very muddy" issues in an analytical way.
An associate professor of mathematics at Vanderbilt University, Farley was a Dr. Martin Luther King Jr. Visiting Professor in the MIT Department of Mathematics from January 2003 to December 2004. He is also the co-founder of a mathematical modeling consulting firm. "Our ultimate goal is to develop software so that law enforcement experts without these rigorous mathematical skills can ask--and answer--these same analytical questions about security."