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Richardson's Law suggests otherwise. Power-law relationships all follow the same basic pattern: If you plot the information on a double-logarithmic scale, the data falls into place along a straight line, so that knowing the pattern of small events tells you something about the pattern of big ones. In the case of terrorist attacks, drawing an arrow from the large number of small attacks clustered at one end of this scale would lead you straight to the handful of large attacks at the other end. In other words, the frequency and severity of small terrorism can be used to determine the likelihood of violent incidents many times larger.
According to the big terrorism/small terrorism approach, prior to September 11, 2001, an attack killing 3,000 people seemed incredibly unlikely, since such casualty numbers were nearly six times greater than any previous terrorist event. But if policy planners had realized that attacks follow a power-law function, 9/11 would not have seemed unlikely at all. According to a paper to be published later this year by Clauset and another colleague, Ryan Woodard from the Swiss Federal Institute of Technology in Zurich, the data on terrorist events between 1968 and 1998 showed there was actually a 30 to 60 percent chance of a 9/11-scale disaster.
In The Signal and the Noise, Nate Silver uses Clauset's analyses to suggest that 9/11 shouldn't have been a complete surprise to those in charge. "The Lockerbie bombing and Oklahoma City were the equivalent of magnitude 7 earthquakes," he writes. "While destructive enough on their own, they also implied the potential for something much worse — something like the September 11 attacks, which might be thought of as a magnitude 8."
But if 9/11 was a magnitude 8 earthquake, that means we could be in store for a magnitude 9.
Students and professors have gathered in a small classroom in CU's computer-science building to hear Clauset give a special presentation on some of his latest work. According to department head James Martin, Clauset is a popular professor because of both the fascinating topics he explores and the lively way he presents his research. "Aaron has to beat the grad students away with a stick, because everyone wants to work with him," says Martin.
This particular presentation should live up to the hype, judging from its title: "How Large Should Whales Be?"
"Is that the setup to a joke?" asks one attendee.
No, Clauset replies with a smile. It's just the latest esoteric question that caught his fancy. Why is it that most mammals are relatively small, but a few species are downright gigantic? Clauset explains that he was able to answer this question without including population dynamics or environmental pressures or any of the other myriad factors ecologists usually consider when tackling such issues. Instead, he devised a simple mathematical model for the evolution of seafaring mammals involving just a few parameters, such as minimum size needed to stay warm in seawater and the tendency for larger species to die out faster than smaller ones. He'd earlier developed a similar model, with a few thermodynamic tweaks, for land-mammal sizes, correctly replicating the size distributions of 4,002 mammal species from the past 2.5 million years. His new, water-based model ended up perfectly predicting the size distribution of all 77 living cetacean species, from the diminutive La Plata dolphin to the king of the ocean, the blue whale.
These size-distribution models are more than a neat trick; they could enable people to understand the long-term mass patterns of now-extinct species like dinosaurs, or what extraterrestrial life might be like. And as Clauset excitedly informs his audience, his work also suggests that it's theoretically possible to have a monster mammal species roaming the oceans that's 3.7 times larger than the blue whale.
As the world is flooded with ever more information, Clauset's ability to slice and dice the data in eloquent, meaningful ways could become increasingly useful. An example is his work analyzing dynamics in the online multiplayer game Halo: Reach. By focusing on a few basics, such as the regularity with which someone plays the game with another person and whether or not he or she helps other players in the game, Clauset and his colleagues were able to develop a computer algorithm that analyzed 700 million games in Halo: Reach and determined whether the players interacting in the game were friends with a 95 percent accuracy. Friendship-aware systems like this could have all sorts of real-world applications, from helping online games better match players to improving a social-media site's ability to correctly recommend whom you should friend and follow. But such systems also raise privacy questions. Do we really want computer programs that can easily identify our closest acquaintances? And if such intimate information can be gleaned just from online shoot-'em-up matches, what sort of private details is the government capable of uncovering from the treasure trove of surveillance records being compiled by the NSA?
Clauset appreciates the concerns over secretive data-mining. "The fundamental ethos of the government should be transparency," he says. Still, he points out, "just because the feds have access to all that information doesn't mean they know what to do with it."
Some terrorism experts were quick to embrace Clauset's power-law discovery, and he's consulted with operations ranging from the U.S. Naval War College's Strategic Studies Group to the Office of the Secretary of Defense. "I think Aaron's work has huge implications," says Gary LaFree, director of the National Consortium for the Study of Terrorism and Responses to Terrorism, based at the University of Maryland. "It's one of these big-ideas projects, and it has interesting policy and methodological implications." But while Clauset and his colleagues used to joke that once news of their terrorism work got out, a bunch of government spooks might show up at their door, nothing of the sort occurred. "I have been surprised how few people have contacted us to follow up," says Clauset, "or express any interest in the larger intellectual questions this research brings up."