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Factoring Equations Into the War on Terror

Mathematicians who specialize in order theory say they can help, such as by predicting the most likely suspects or winnowing intelligence.

October 10, 2004|Matt Crenson | Associated Press Writer

PISCATAWAY, N.J. — Terrorism takes brains.

You don't need political influence, military might or economic resources to plant bombs or take hostages; but without brains, terrorism is nothing more than random violence.

Consider Al Qaeda's attack on New York City and Washington, D.C., three years ago. It required only 19 men armed with box cutters, yet it was so brilliantly conceived, meticulously planned and keenly attuned to global politics that it changed the world.

"Terrorism is a thinking man's game," terror expert Gordon Woo said.

Which is why a small group of thinking men and women convened at Rutgers University last month to consider how order theory -- a branch of abstract mathematics that deals with hierarchical relationships -- could be applied to the war on terror.

It almost seems ridiculous for people who inhabit a world of concept lattices and partially ordered sets to think that they can affect a war that is being fought on the streets of Baghdad and in the remote mountains of northern Pakistan. But the war on terror is also fought in cyberspace and in the minds of people from Lahore to Los Angeles. Mathematicians are right at home in such abstract realms.

"It's not just theoretical," said Fred Roberts, director of the Center for Discrete Mathematics and Theoretical Computer Science, the Rutgers research institute where the conference was held.

Mathematician Jonathan Farley of the Massachusetts Institute of Technology said he was inspired to organize the meeting by the movie "A Beautiful Mind." The film tells the story of mathematician John Forbes Nash, whose work in game theory found application in Cold War military strategy, international trade and the auctioning of broadcast frequencies by the Federal Communications Commission.

"I'm a pure mathematician, so I'm completely useless for the most part," Farley said. "But it would be nice to take some of what we do and make it useful for some people -- maybe even life-saving."

The new Homeland Security Institute has a mandate from Congress to do just that, Gary G. Nelson said. A senior researcher at the quasi-governmental institute, he attended the conference in hopes of finding research projects for the institute to support.

Some ideas sounded promising, Nelson said. The most intriguing were those that could help intelligence agencies boil down the vast amounts of data they contend with.

Other proposals were "a pretty long logical distance" from the real world. And not everything was easy to understand, he said, even for a systems engineer.

Theoretically, Farley said, abstract math could help intelligence officers figure out the most efficient way to disable a terrorist network.

Say it's cheaper or more practical to go after a terrorist cell's "middle management" rather than its leadership. How many of those lieutenants would you have to remove to disrupt communication between the top dogs and field operatives? Are there one or two key individuals whose capture would completely cut off the chain of command?

Order theory is all about such questions.

"This helps them decide where to spend the money," Farley said.

Of course, many times, the organizational structures of terrorist groups are unknown. Mathematical techniques could also be applied to that problem by using computer programs that comb through giant databases looking for connections between individuals, locations or events. For example, a program might discover that everybody involved in a given attack attended the same London mosque. Or it might find large numbers of e-mail messages between members of one terrorist cell in Germany and another in the United States, suggesting that they may be working together.

Such data-mining techniques are nothing new. But the explosion in computing power over the past few years has spurred innovation in the field.

Jafar Adibi, a computer scientist at USC, is developing ways to find hidden links between known terrorists and their as-yet-unknown confederates.

"You're trying to detect major groups of these bad guys," Adibi said.

The technique relies on having an initial group of known terrorists. Then it analyzes things those known terrorists have in common with other people in the database, such as phone calls, places of worship, political affiliations or blood relation.

The program concludes that anybody who has enough connections of the right kind with a known terrorist probably is one also.

Adibi has tested his program using a database built from newspaper accounts and other publicly available information. He labels 20% of a terrorist group's members as "known" and challenges the program to find the rest. Right now, the system misses 20% of the remaining members, and three of the 10 people it does identify as "bad guys" aren't actually terrorists.

Adibi said he hopes to improve those numbers a bit. But even so, programs like his could help focus anti-terror efforts on the most likely suspects.

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