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Mathematicians offer help in terror fight
(Agencies)
Updated: 2004-10-11 08:08
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.
A Filipino soldier
practices as U.S. soldiers look on during training for close quarter
battle dry fire at Fort Magsaysay army camp, Nueva Ecija province,
northern Philippines, in this Feb. 24, 2004 file photo. Despite some
successes in hunting down terrorist, high-profile targets remain free by
sticking to familiar terrain where they can quickly blend in or slip away
with support from sympathizers. [AP] | It almost seems ridiculous for people who inhabit a world of concept lattices
and partially ordered sets to think 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.
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-Qaida's attack on New York City and Washington, D.C., three years
ago. It required a force of only 20 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," said terror expert Gordon Woo.
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 lifesaving."
The new Homeland Security Institute has a mandate from Congress to do just
that, said Gary G. Nelson. 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 in order to disrupt communication between the top dogs and the
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 the University of Southern California,
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 percent of a terrorist
group's members as "known" and challenges the program to find the rest. Right
now, the system misses 20 percent 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. Mass
detentions by law enforcement authorities have often snared too many innocent
people, Woo said. Britain has arrested more than 600 people on suspicion of
terrorism since the Sept. 11 attacks, and convicted only 15 of them. By some
counts, the United States has detained more than 5,000 foreign nationals under
the provisions of the Patriot Act, alienating them and their families.
"Part of the war on terrorism is winning hearts and minds," said Woo, an
analyst in the London office of Risk Management Solutions. The Newark,
Calif.-based consulting firm assesses catastrophe risks for the banking and
insurance industries.
Minds are the specialty of Vladimir Lefebvre, a cognitive scientist at the
University of California in Irvine. The Russian-born researcher has spent his
career developing ways of reducing human decision-making to mathematical
equations. The work stems from a top-secret Soviet research project that
Lefebvre worked on during the 1970s.
"I can compute feelings," he said with a grin.
Lefebvre's ideas are so obvious that you wonder if he might be kidding. Every
person, he argues, has a view of the self that he or she uses as a tool for
making decisions. That view can be influenced by the outside environment.
So in principle, there ought to be things we can do to make terrorists feel
less sure about themselves or less ardent in their beliefs. The right strategy
might even make them think of themselves as something other than terrorists.
Lefebvre believes human decision-making is so straightforward that simple
equations can describe how an individual's behavior arises from his or her
self-image as it is shaped by other people and the environment.
Stefan Schmidt, a New Mexico State University researcher who has worked with
Lefebvre, offered a hypothetical example. Suppose, he said, terrorists were
considering three points of entry into the United States — one in the Pacific
Northwest, one in the Southwest and one in the Northeast. Looking at the level
of security on the various borders, and considering other factors such as
remoteness, terrorists might decide on the Southwest as the best place to cross.
Assume that border agents, on the other hand, are heavily guarding the
Northeast border. They would benefit by making the Southwest seem more heavily
patrolled than it really is, and the Northeast appear relatively unprotected. If
they did a credible job, the terrorists would incorrectly choose the most secure
border as their best bet and run a much higher chance of being caught.
Conceptually, this kind of reasoning is no different from military strategy.
If you can plant an inaccurate idea in your opponent's head, you will have an
advantage on the battlefield.
But actually doing that — at least for the time being — requires a
combination of brilliance, instinct and luck that few people possess. Lefebvre
would reduce the process of outwitting your opponent to a computer program.
In some ways, researchers at Carnegie Mellon University have done just that.
Computer scientist Kathleen M. Carley heads a lab that tries to simulate all
kinds of social groups, including terrorist organizations.
The lab has built simulations of Hamas and al-Qaida by dumping newspaper
articles and other publicly available information about the organizations into a
computer database. A program then takes that information and looks for patterns
and relationships between individuals. It finds weak and strong figures, power
brokers, hidden relationships and people with crucial skills.
Then another program can predict what would happen if a specific individual
were removed from the organization. After Israel's assassination of Hamas
founder Sheikh Ahmed Yassin in March, the program correctly predicted he would
be succeeded by hard-liner Abdel Azziz Rantisi.
Three weeks later Israel assassinated Rantisi as well. Carley's lab predicted
that Hamas political director Khaled Mashaal would succeed him, and posted its
pick on the Internet.
This time, Hamas declined to reveal who had taken power for fear he too would
be assassinated. But eventually it became known that Mashaal was indeed the one.
At that point, Carley said, "we were told to quit putting such predictions on
the Web" by federal officials.
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