Bollettino

Since LI has gone hardcore about the missing Osama bin Laden (day 921 since the promise of his capture), we’ve gotten some flack for putting a premium on his capture or death.

There’s an interesting story in the Chronicle of Higher Education about terrorist cells. According to Jonathan David Farley, a mathematician, the connectionist idea that was so popular in the wake of 9/11, according to which one terrorist are nodes on a graph, connected by links, understates the organizational resiliency of cells:

“When FBI agents arrest a few members of a terrorist cell, how can they know if the cell has been disabled? Several scholars have brought mathematical tools to bear on that crucial question. Social scientists have imagined individual terrorists as nodes on a graph, most of whom are connected to only one or two other nodes. Using such cellular graphs, the scholars have proposed ways of estimating whether a chain of relationships has been effectively shattered, even when some of its members elude capture. But those models are too simple and too optimistic, according to Jonathan David Farley, a visiting associate professor of mathematics at the Massachusetts Institute of Technology. In the November-December issue of Studies in Conflict and Terrorism, Mr. Farley proposes an alternative method. We should imagine terrorist cells not as graphs but as ordered sets, he says. "Lattice theory, my field, is the abstract study of order and hierarchy. In terrorist organizations, hierarchy appears to matter."

As LI understands it, there are two major kinds of networks – egalitarian networks, in which the ordering is non-hierarchical, and hubs, in which networks form around or through 1+ intersections, with a disproportionate number of short distance lengths from the intersection to other links in the network compared to other links. Farley’s idea is that using the model of weak ties between cell members as a template for rolling up terrorist groups ignores the importance of hierarchical structure in sustaining and regenerating cells.

Here’s the money shot graf:

“Mr. Farley offers an equation for calculating the probability that a given cell has been disrupted. His formula is gloomier than the "graphic" models offered recently by other scholars. In an example in
which four members of a 15-member cell have been captured, he says,
the standard graphic model would suggest a 93-percent probability that
the cell had been broken; Mr. Farley's equation yields only a
33-percent probability. "I'm not selling mathematical snake oil,
suggesting that we can actually make exact predictions," he says. The
point is instead to give law-enforcement agencies a rough idea of how
to allocate their resources.”

My guess is that Bush’s comments (rare as they have been) about having killed or captured ¾ of the Al Qaeda organization is using an extrapolation from a graph model of the kind Farley is countering. We are not mathematical enough to even pretend to compute Farley’s equation, but we can make common sense of his assumption about hierarchy – it is the old chain of being metaphor equipped with plastic explosives.

Is it true? Well, we’d guess that it is at least plausible. The NYT contains Kerry’s first shot against Bush, and it is a hopeful one. Poor Kerry – since the Dems rolled on their belly before Bush in 2002, he has to break the shell of invincibility that has been woven around Bush since 9/11 on his own. It isn’t going to sink in immediately. Let’s hope Kerry realizes that he has to keep attacking here. Bush’s unwillingness to go for the kill – in fact, his frank disinterest in the only terrorists that really threaten the U.S., since Tora Bora – could undo our woeful Childe Bush by the fifth act.