Math latest weapon in war on terror
By Katherine Harvey
Stanford Daily
Thursday, November 17, 2005
Lattice theory — a branch of abstract mathematics that studies order and hierarchy — could be used to break up terrorist cells and give law enforcement and intelligence agencies more accurate assessments of U.S. vulnerability to future terrorist attacks, according to Prof. Jonathon Farley, a Center for International Security and Cooperation (CISAC) science fellow at Stanford.
A crowd of approximately 20 gathered Tuesday afternoon to hear what the science fellow, Summa Cum Laude Harvard graduate and Fulbright distinguished scholar recipient had to say about countering terrorism in a talk entitled “Beauty and Terror: Does Mathematics Have a Role to Play in Winning the Shadow War?”
Farley began his talk with a short clip from the movie “A Beautiful Mind”, the Oscar-winning film that portrayed the life of mathematician John Nash. Nash’s work in game theory, which was later applied to military strategy during the Cold War, was Farley’s inspiration, he said.
“That is where it all started,” he said, referencing the film’s opening line: “Mathematicians won the war.” Farley said he wondered whether lattice theory — his mathematical field of expertise — could similarly be applied to help fight the war on terrorism.
Intrigued, Farley set out to create a program based on lattice theoretical models that would calculate the probability that a terrorist cell has been disrupted. In Farley’s program, terrorists are represented as dots on a graph. The program sifts through current intelligence data on individual terrorists and terrorist activity, searching for patterns between individuals, locations and events that would link one terrorist to another. If enough patterns are discerned, the program would literally “connect the dots,” and establish members of a terrorist cell.
While databases drawing on similar mathematical concepts and calculations are used by intelligence agencies today, Farley said these existing databases “ignore the fact that terrorist cells have hierarchy,” something that his lattice model takes into account.
“Ideally, we want to capture everyone in the terrorist cell,” Farley said. “But that’s not realistic. But let’s say we capture four of the 15 terrorists in the cell. We want to know the probability that the cell has been disabled.”
Existing databases, Farley explained, would interpret these results without taking into account the captured terrorists’ rank in the hierarchy. If all four of the captured terrorists were in the lowest rank of the hierarchy, the terrorist cell would not necessarily have been broken, but the old model might lead intelligence officials to believe it had.
With the old model, Farley said, “We would feel safer than we would have a right to.”
Farley’s model, on the other hand, would take hierarchy into account, calculating the probability that a terrorist cell had been disabled based on the number of terrorists captured in a given cell and their hierarchal ranking in the cell. Farley said the model would also help intelligence officers identify the most efficient way to disable a cell by identifying which terrorists had to be removed from the cell in order to break the chain of command.
Many attendees asked questions about the model, which Farley fielded after his presentation. US Army Col. Bill Hix, a national security affairs fellow at Hoover Institution, asked Farley about the model’s ability to adapt to the new global terrorist threat.
Hix pointed out that terrorist networks and communications systems have become quite complex, adding, “It is not something imminently apparent on how you can approach it.”
“The model just deals with actual cells or groups,” Farley responded, “not some kind of spiritual realm.” He said he didn’t know the precise structure of terrorist cells, adding “the model has to be applied by people whose expertise is in that field.”
For Farley, the program represented a jumping-off point, a basic model that could be later refined.
“I have presented a stripped-down version of the program, and it is important to ask where we can go from here,” he said.
Stanford Daily
Thursday, November 17, 2005
Lattice theory — a branch of abstract mathematics that studies order and hierarchy — could be used to break up terrorist cells and give law enforcement and intelligence agencies more accurate assessments of U.S. vulnerability to future terrorist attacks, according to Prof. Jonathon Farley, a Center for International Security and Cooperation (CISAC) science fellow at Stanford.
A crowd of approximately 20 gathered Tuesday afternoon to hear what the science fellow, Summa Cum Laude Harvard graduate and Fulbright distinguished scholar recipient had to say about countering terrorism in a talk entitled “Beauty and Terror: Does Mathematics Have a Role to Play in Winning the Shadow War?”
Farley began his talk with a short clip from the movie “A Beautiful Mind”, the Oscar-winning film that portrayed the life of mathematician John Nash. Nash’s work in game theory, which was later applied to military strategy during the Cold War, was Farley’s inspiration, he said.
“That is where it all started,” he said, referencing the film’s opening line: “Mathematicians won the war.” Farley said he wondered whether lattice theory — his mathematical field of expertise — could similarly be applied to help fight the war on terrorism.
Intrigued, Farley set out to create a program based on lattice theoretical models that would calculate the probability that a terrorist cell has been disrupted. In Farley’s program, terrorists are represented as dots on a graph. The program sifts through current intelligence data on individual terrorists and terrorist activity, searching for patterns between individuals, locations and events that would link one terrorist to another. If enough patterns are discerned, the program would literally “connect the dots,” and establish members of a terrorist cell.
While databases drawing on similar mathematical concepts and calculations are used by intelligence agencies today, Farley said these existing databases “ignore the fact that terrorist cells have hierarchy,” something that his lattice model takes into account.
“Ideally, we want to capture everyone in the terrorist cell,” Farley said. “But that’s not realistic. But let’s say we capture four of the 15 terrorists in the cell. We want to know the probability that the cell has been disabled.”
Existing databases, Farley explained, would interpret these results without taking into account the captured terrorists’ rank in the hierarchy. If all four of the captured terrorists were in the lowest rank of the hierarchy, the terrorist cell would not necessarily have been broken, but the old model might lead intelligence officials to believe it had.
With the old model, Farley said, “We would feel safer than we would have a right to.”
Farley’s model, on the other hand, would take hierarchy into account, calculating the probability that a terrorist cell had been disabled based on the number of terrorists captured in a given cell and their hierarchal ranking in the cell. Farley said the model would also help intelligence officers identify the most efficient way to disable a cell by identifying which terrorists had to be removed from the cell in order to break the chain of command.
Many attendees asked questions about the model, which Farley fielded after his presentation. US Army Col. Bill Hix, a national security affairs fellow at Hoover Institution, asked Farley about the model’s ability to adapt to the new global terrorist threat.
Hix pointed out that terrorist networks and communications systems have become quite complex, adding, “It is not something imminently apparent on how you can approach it.”
“The model just deals with actual cells or groups,” Farley responded, “not some kind of spiritual realm.” He said he didn’t know the precise structure of terrorist cells, adding “the model has to be applied by people whose expertise is in that field.”
For Farley, the program represented a jumping-off point, a basic model that could be later refined.
“I have presented a stripped-down version of the program, and it is important to ask where we can go from here,” he said.
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