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NEWS that AT&T, Verizon and BellSouth
gave customer records to the National Security Agency has set off a heated debate
over the intricacies of espionage law. But legal or not, this sort of spying
program probably isn't worth infringing our civil liberties for because it's
very unlikely that the type of information one can glean from it will help us
win the war on terrorism.
If the program is along the lines
described by USA Today with the security agency receiving complete lists of
who called whom from each of the phone companies the object is probably to
collect data and draw a chart, with dots or "nodes" representing
individuals and lines between nodes if one person has called another.
Mathematicians who work with pictures like
this are called graph theorists, and there is an entire academic field, social
network analysis, that tries to determine information about a group from such a
chart, like who the key players are or who the cell leaders might be.
But without additional data, its reach is
limited: as any mathematician will admit, even when you know everyone in the
graph is a terrorist, it doesn't directly portray information about the order
or hierarchy of the cell. Social network researchers look instead for graph
features like "centrality": they try to identify nodes that are
connected to a lot of other nodes, like spokes around the hub of a bicycle wheel.
But this isn't as helpful as you might
imagine. First, the "central player" the person with the most
spokes might not be as important as the hub metaphor suggests. For example,
Jafar Adibi, an information scientist at the University of Southern California,
analyzed e-mail traffic among Enron employees before the company collapsed. He
found that if you naοvely analyzed the resulting graph, you could conclude that
one of the "central" players was Ken Lay's ... secretary.
And even if you manage to eliminate all
the "central players," you may well still leave enough lesser players
that the cell retains a complete chain of command capable of carrying out a
devastating terrorist attack.
In addition, the National Security
Agency's entire spying program seems to be based on a false assumption: that
you can work out who might be a terrorist based on calling patterns. While I
agree that anyone calling 1-800-ALQAEDA is probably a terrorist, in less
obvious situations guilt by association is not just bad law, it's bad
mathematics, for two reasons.
The simplest reason is that we're all
connected. Not in the Haight-Ashbury/Timothy Leary/late-period Beatles kind of
way, but in the sense of the Kevin Bacon game. The sociologist Stanley Milgram
made this clear in the 1960's when he took pairs of people unknown to each
other, separated by a continent, and asked one of the pair to send a package to
the other but only by passing the package to a person he knew, who could then
send the package only to someone he knew, and so on. On average, it took only
six mailings the famous six degrees of separation for the package to reach
its intended destination.
Looked at this way, President Bush is only
a few steps away from Osama bin Laden (in the 1970's he ran a company partly
financed by the American representative for one of the Qaeda leader's
brothers). And terrorist hermits like the Unabomber are connected to only a
very few people. So much for finding the guilty by association.
A second problem with the spy agency's apparent
methodology lies in the way terrorist groups operate and what scientists call
the "strength of weak ties." As the military scientist Robert Spulak
has described it to me, you might not see your college roommate for 10 years,
but if he were to call you up and ask to stay in your apartment, you'd let him.
This is the principle under which sleeper cells operate: there is no
communication for years. Thus for the most dangerous threats, the links between
nodes that the agency is looking for simply might not exist.
If our intelligence agencies are
determined to use mathematics in rooting out terrorists, they may consider a
profiling technique called formal concept analysis, a branch of lattice theory.
The idea, in a nutshell, is that people who share many of the same
characteristics are grouped together as one node, and links between nodes in
this picture called a "concept lattice" indicate that all the
members of a certain subgroup, with certain attributes, must also have other
attributes.
For formal concept analysis to be helpful,
you need much more than phone records. For instance, you might group together
people based on what cafes, bookstores and mosques they visit, and then find
out that all the people who go to a certain cafe also attend the same mosque
(but maybe not vice versa).
While researchers at Los Alamos National
Laboratory have used this tool to sift through hundreds of terrorism-related
reports and find connections that human analysts could not have found easily
it's still dangerous to rely on the math.
This is because, as Kennedy and Lincoln
assassination buffs know, two people can be a lot alike without being the same
person. Even if there is only a 1 in 150 million chance that someone might
share the profile of a terrorist suspect, it still means that, in a country the
size of the United States, two people might share that profile. One might be a
terrorist, or he might be Cat Stevens.
This isn't to say that mathematicians are
useless in fighting terrorism. In September 2004 10 months before the bombing
of the London Underground Gordon Woo, a mathematician and risk-assessment
consultant, gave a speech warning that London was a hotbed of jihadist
radicalism. But Dr. Woo didn't anticipate violence just using math; he also
used his knowledge of London neighborhoods. That's what law enforcement should
have been doing then and should be doing now: using some common sense and
knowledge of terrorists, not playing math games.
Math is just a tool. Used wisely, math can
indeed help in warfare: consider the Battle of Britain, won in part by breaking
the German codes. But use it unwisely as seems to be the case here and your
approval ratings might just hit a new all-time low.