It's an idyllic summer day in Denver. Families are enjoying a festival in Civic Center Park, while residents and visitors alike happily stroll along the 16th Street Mall as a shuttle glides past. The air is filled with the sounds of people laughing and children playing.
Suddenly, there's a deafening explosion. The urban tranquility is replaced by scenes of horror: charred wreckage, collapsed buildings, bleeding victims. Horrified screams mingle with the wail of police sirens.
Aaron Clauset watches as this terrorist attack unfolds. The University of Colorado professor is visiting the Counterterrorism Education Learning Lab, a museum that opened near Civic Center Park in 2008. The nonprofit CELL is dedicated to preventing terrorism through education and empowerment, but judging from its centerpiece exhibit — a multimedia display that uses video projections and hidden speakers to make visitors like Clauset feel as if they're experiencing a terrorist event in the middle of Denver — that education and empowerment comes with a heavy dose of anxiety and hysteria. At the end of the simulation, an ominous message lingers on the wall displays: "Terrorism: It could happen anywhere. It could happen here."
"The intent here is to scare you," says Clauset. "This is exactly what the public discourse around terrorism looks like." The underlying message of the CELL and other institutions devoted to terrorism is that it's the great horrific unknown. Terrorism is something that can happen anywhere, at any time, to anyone. Terrorism is something that should be feared, something that should be fought against, but not something that can be fully understood.
Clauset knows that the truth isn't so simple. The unassuming 34-year-old data-sciences whiz kid, dressed in a T-shirt and shorts for this visit to the CELL, understands terrorist attacks better than almost anyone. An assistant professor of computer science, Clauset is based at the BioFrontiers Institute, CU's state-of-the-art bioscience hub, even though he hasn't taken a biology course since tenth grade. This August he'll be presenting some of his newest, most provocative research at the American Statistical Association's Joint Statistical Meetings, the largest and most prestigious gathering of statisticians in North America, though he's never taken a statistics course. And his research on terrorism, which has caught the attention of national-security experts (if not many security officials), provided the basis for a chapter on violent conflict in superstar statistician Nate Silver's bestseller The Signal and the Noise — despite the fact that Clauset attended a small college devoted to the Quaker ideals of peace and consensus.
"In this game, I don't know anyone else like him who has made the contributions he's made to the world of data science across such really, really different disciplines," says James Martin, Clauset's computer-science department chair.
The reason that Clauset's research interests are so disparate — from player dynamics in online video games to the evolutionary forces that determine animal sizes — and his findings so attention-grabbing is because he's dealing with the promise and challenge of "Big Data," the phenomenon in which we now have more information about nearly everything than we have tools with which to understand it. "The science of the 21st century will be understanding complex data," says Clauset. "Today we are pretty good at producing huge amounts of this kind of data, but data alone isn't useful. How do we translate this information into something worthwhile, something scientifically useful?"
Clauset has proven to be exceptionally gifted at turning this data into knowledge, especially in the area of human violence. He's uncovered a statistical pattern behind the frequency and severity of all terrorist attacks, an underlying structure that connects small, isolated bombings half a world away to the catastrophe that was 9/11. The discovery could prove a boon for policy planners around the globe, especially since it doesn't involve any of the private Internet, phone and financial data-tracking for which the National Security Agency is currently under fire. Clauset's work adds a level of scientific objectivity to the guesswork and strong emotions that usually surround the topic of terrorism. But his research also hints at what sort of terrorist attacks might lie in the future — and some of his findings could be more frightening than anything at the CELL.
Aaron Clauset's world is defined by data. The walls of his research lab at CU are covered with dry-erase boards tattooed with lengthy equations and dashed-off graphs, and his conversations with students focus on things like data-mining the complete works of Shakespeare in order to uncover the structural similarities between the plays. "He's always finding fun excuses to look at the world using mathematical tools," says Abigail Jacobs, a third-year Ph.D. candidate in computer science.
Clauset applies those same tools to his personal life. He tries to remain as analytical as possible when he discusses the time in 2004 when he was cajoled into trying out for a reality show and ended up doing a short-lived stint on Average Joe, in which he and a bunch of other regular guys vied for the affections of a model. "I went in thinking this would be a unique experience and fun and weird and an opportunity I shouldn't say no to," he says thoughtfully. "The best thing that came out of it was how much joy it provided to my friends and family."
On his personal blog, Structure + Strangeness, Clauset posted a recap of 2012 based solely on statistics. Papers of his that were published or accepted: four. New citations of his past papers: 1,495. New research grants he was awarded: three, totaling $1,379,260. Pages of student work he graded: 5,282 (103 pages per student). Movies and shows he watched via Netflix: 132. Jigsaw pieces he assembled: more than 5,000. Houses he purchased with his wife, Lisa: one. Babies born to the two of them: one. Baby photos taken: 683.
"He's one of these people who looks at the world around him and asks interesting questions about it," says Mark Newman, a physics professor at the University of Michigan who's a friend and frequent academic collaborator. "A lot of people would see a video game and say, 'This is a fun game.' He thinks that, but he also says, 'There are really interesting scientific questions about this.'"
Clauset's analytical approach is in his blood: He was born in North Carolina to a schoolteacher father and a mother who worked on the computer systems that would become the basis for today's airline reservations systems. "Academic curiosity was just a given in the household," says his mother, Rebecca Harris. "We all liked learning new things. We all hated being idle and bored."
"Having two parents who were both scientifically minded was a huge thing for me," Clauset says. "They encouraged my curiosity without telling me what to be curious about."
Clauset's curiosity led him to pursue his undergraduate degree at Haverford College, a small liberal-arts college in Pennsylvania founded by Quakers. He planned to double-major in physics and sociology, but quickly realized that the latter's abstract, theoretical approach wasn't for him. "I became frustrated by the social sciences," he says. "They seemed squishy and focused on inherently ambiguous ideas. I wanted the mathematical rigor and predictive power that I saw in my physics classes. A clear and scientific explanation of how the social world worked." So he majored in physics with a concentration in computer science, fields deluged by a whole lot more hard data about hitherto "squishy" aspects of everyday life, thanks to the Internet and new technologies like cell phones. As noted in The Signal and the Noise, IBM calculates that the world is collectively generating 2.5 quintillion bytes of new data every day.
The Big Data flood is so great that some people believe it will eventually preclude the need for any scientific analysis at all. But others have the opposite opinion: that now, more than ever, the world needs people who can make sense of all of this information. And that's exactly what Clauset set out to do. "This is an exciting new direction for science," he says. "Learning how to understand these big piles of data. To work out the physics of society."
He decided to take a macro-level view of the data, working to find large-scale patterns that are often missed when researchers drill down into minutiae. This top-down strategy went against the sort of science that had dominated the twentieth century, with researchers tackling ever more specific areas of interest. But the complex systems that interested Clauset — systems like social networks and biological evolution and international relations — could never be fully understood by studying their pieces in isolation. "All of these systems are hard to understand," he says. "Taking them apart and studying their pieces one by one won't help you understand how the whole thing works."
Clauset's focus on big-picture data science led him to the University of New Mexico, where he obtained his Ph.D. in computer science. It's also where he met his future wife, Lisa Mullings, a nutrition educator. In 2006, he moved on to a post-doctoral fellowship at the nearby Santa Fe Institute, the nonprofit operation founded by Los Alamos National Laboratory scientists to conduct interdisciplinary theoretical research. Since its start in 1984, the academic powerhouse has been integral in fields ranging from chaos theory to artificial intelligence.
Working at the institute "was like coming home," Clauset says. "Everyone there was intimidatingly intelligent, but open-minded and willing to talk to you about crazy ideas in a serious way." He found himself banging around crazy ideas on everything from conflict dynamics in primate societies to the social mechanisms of poverty to the physics of financial markets.
In 2010, Clauset moved to Boulder to take a computer-science professor slot at the new BioFrontiers Institute. The institute, housed in a 330,000-square-foot facility on CU-Boulder's east campus, is dedicated to cutting-edge research in bioscience and biotechnology that fuses the expertise of chemists, computer scientists, mathematicians, physicists, engineers and faculty from other disparate disciplines. "I liked that they were really pushing the idea of lowering boundaries between disciplines," he says.
Clauset was well-suited to such an innovative, boundary-pushing environment. An academic who couldn't stand to watch violent movies and sometimes felt faint discussing gruesome accidents, he'd decided on a whim to delve into a subject in which he had no background whatsoever: terrorism.
His trip into terrorism started in early 2003 with a series of heated student listserv discussions on the lead-up to the invasion of Iraq. Everyone on the forum seemed to be arguing about what was known about the situation, what was unknown, and how it was all connected to the War on Terror. It was exactly the kind of squishy, imprecise dialogue that rankled Clauset, so he wondered if he could nail down some of the issues with data.
Clauset and another computer-science student, Maxwell Young, started looking for that data. They found it in a database of global terrorist attacks maintained by the Memorial Institute for the Prevention of Terrorism in Oklahoma City, a homeland-security education and training institute founded in the wake of the 1995 Oklahoma City bombing. Once they'd built a computer program that could extract and parse the database's records on the nearly 30,000 terrorist attacks in 187 countries worldwide since 1968, they started looking for patterns.
Clauset's goal wasn't to solve the world's problems; it was just to answer the latest interesting question that had caught his fancy. "I'm fairly opportunistic, not motivated by the moral imperative," he explains. "If something seems interesting or weird, I might dive right in, looking for data, building models and teaching myself what's known and not known."
Clauset and Young were far from the first scholars to dive into the subject of human conflict. Since before the ancient Greek historian Thucydides penned The History of the Peloponnesian War in the fifth century B.C., people have been trying to figure out why and how humans kill one another. Not surprisingly, over the past decade, much of that scholarship has focused on terrorism. "Before 9/11, terrorism was not a hot research topic," says Victor Assal, political-science professor at the University at Albany-SUNY and director of the university's homeland-security concentration. "But since then, there has been an explosion of research. The government has poured a lot of money into the public and private sectors to study it."
The vast majority of scholarship on violence, terrorist-related or otherwise, has focused on the cause and effect of violent incidents: the motives and ideologies involved, the social and political repercussions that followed. But Clauset wasn't interested in digging into details — he wanted to look at the big picture.
And when he and Young looked at the big picture of terrorism, comparing the severity of attacks with their frequency, they noticed something interesting. "This looks like the same pattern as earthquakes," Clauset remembers thinking. The size and occurrence of earthquakes follows what's called a power-law distribution. There are usually lots of small earthquakes, a few mid-sized earthquakes and one or two powerful quakes. It's more common for statistical information to follow a normal or bell-curve distribution, in which most data points fall near the average. Human running speed, for example, has a bell-curve distribution, with most people running at about the average speed. If running instead followed a power-law distribution, Clauset explains, "there would be a small number of people who could run so fast they could launch themselves into orbit."
But terrorist attacks seemed to follow a power-law distribution: There had been lots of small attacks, killing one or two people; a few mid-sized attacks, like the 1995 Oklahoma City bombing, which killed 168 people, and the 1988 Lockerbie plane bombing, which killed 254; and one really large attack — 9/11, which killed nearly 3,000. Before the two could announce their discovery, though, they had to be sure they were right. "We were just grad students," says Clauset. "This is about terrorism, and we don't want to stick our necks out there and be wrong."
As it turned out, there was no standard statistical measure to determine whether a given mathematical pattern really followed a power-law distribution. So Clauset set about creating one, and sure enough, the terrorism data passed the power-law test.
Another concern remained: The data was too clear, the pattern too obvious. "Surely, someone has thought of this before," Clauset recalls thinking. But the only example they could find of similar research was the work of Lewis Fry Richardson, an English mathematician and Quaker pacifist who drove an ambulance in World War I. Along with doing major work in the fields of weather forecasting and fractals, Richardson would go on to analyze all the wars from 1815 to 1945 and conclude that they followed a power-law distribution; he found the same pattern in gang killings in Chicago and Shanghai.
Clauset and Young's results appeared to fit perfectly with Richardson's work; in the scale of human conflict, terrorism usually falls between murders and wars. So when the two, joined by University of Essex political-science professor Kristian Gleditsch, published their terrorism findings in the Journal of Conflict Resolution in 2007, they proposed what they called Richardson's Law, the conjecture that all deadly human conflicts, from random murders up to world wars, follow a simple power-law distribution.
Clauset still isn't sure why violent incidents such as terrorism follow this pattern, with lots of small attacks and a few very large ones. One explanation is that the power-law distribution arises from terrorists preferring to target locations with higher population densities, like markets or coffee shops, rather than choosing targets at random. Another possibility is that big terrorist attacks are just a lot harder to pull off. Small, violent strikes involve minimal planning and manpower, so it's fairly easy for terrorist organizations to accomplish a lot of them. Major attacks like 9/11, however, require lots of personnel and years of planning, so only a small number make it to deployment without falling apart or getting exposed.
Clauset and Young did more than just find interesting patterns within the data, however; their work could help change the way people think about future terrorist attacks. The common view among policy planners is that there is a difference between "big terrorism" and "little terrorism." Little terrorism, like abortion-clinic bombings or shootings in the Middle East, is often written off as unsurprising, meaningless violence, perhaps because there are so many incidents. Big terrorism like airplane hijackings, on the other hand, is deemed much more important, but also inherently unpredictable. "The implicit assumption is that big events are beyond understanding and could strike anywhere, at any time," says Clauset.
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."
And after a lengthy delay, the Department of Homeland Security turned down a grant proposal to develop prediction tools based on his research — in part, Clauset says, because "the reviewer thought the tools would be too complicated for the typical DHS worker to understand."
The complex nature of Clauset's work could indeed be part of the problem, says LaFree: "He's working in a pretty rarefied atmosphere in terms of mathematics and statistics. A lot of policymakers don't speak that language." Then again, Clauset's findings don't mix well with the shortsighted nature of most policy work. "This isn't going to be useful to help say what Homeland Security should do next month or next year," LaFree explains. "It is more of a long-term tool."
And Clauset and his colleagues continue to drill into terrorism data. For example, they've determined that explosive devices account for nearly half of terrorism-related deaths. While the finding isn't earth-shattering, it drives home the importance of trying to limit would-be terrorists' access to bomb-making materials. More surprising was their discovery that while larger, more experienced terrorist groups generate a lot more attacks than smaller, unsophisticated groups, when you compare individual attacks, the smaller groups are just as effective at generating casualties. In other words, while focusing resources on defeating major terrorist networks might curtail the overall number of terrorist strikes, it won't necessarily stop major attacks from occurring, since tiny terrorist cells are just as likely to pull off a major catastrophe.
In 2010, Clauset, Young and Gleditsch, along with Lindsay Heger, a political scientist now working at the Broomfield-based One Earth Future Foundation, narrowed in on a specific violent struggle: the ongoing Israeli-Palestinian conflict. And what they've found by analyzing the 3,017 terrorist events associated with this conflict since 1968 could prove relevant to both sides in the struggle. They determined that a tit-for-tat strategy of violent countermeasures sometimes used by the Israeli military was ineffective in quelling violence, and discovered that suicide attacks orchestrated by Palestinian groups were similarly impractical, since they did little to improve the operations' approval ratings among their constituents.
And Clauset continues to consider the underlying promise of terrorism's power-law pattern: its ability to help predict the frequency and severity of future attacks. A 2005 preliminary draft of his original power-law paper caught media attention because it predicted another 9/11-scale attack within seven years — but Clauset and his co-authors removed the prediction from the final version because they believed it wasn't accurate enough. At the prestigious Joint Statistical Meetings this August, however, Clauset and Woodard will return to the prediction issue: They will present new research concluding that if the level of terrorism violence remains stable — as it has, more or less, for decades — there's roughly a 30 percent chance of an attack similar to 9/11 in the next decade. To hedge their bets, they'll also note that if terrorism violence begins to ebb, that chance drops to just 7 or 8 percent. But if terrorism gets worse, the chances of another 9/11 increase significantly — to 80 percent.
Clauset and his colleagues have avoided predicting the likelihood of a larger event — the sort of chemical, biological or nuclear attack that could kill hundreds of thousands of people. "We weren't confident there is enough data to build a model that could make a scientifically based prediction there," explains Clauset.
Still, just as his research drives home the fact that 9/11 should have been conceivable before it occurred, it also suggests that magnitude-9 terrorism is far from impossible. "If we believe the power law is a fundamental property of terrorism — and it appears to be so in a very robust way — it's reasonable to conclude that there may be 'really big terrorism,' this other category involving chemical, biological or radiological attacks. And almost surely, the probability of these kinds of events is much higher than people might expect," he concludes. "If we don't have some people thinking about this in the long term, we are going to be very surprised. We are going to be unprepared."
It's early morning, and the Clauset household is busy. Aaron Clauset sips warily at a cup of coffee he's holding in one hand; he's recovering from a respiratory infection, not to mention jet lag. He's just back from a conference in Zurich, and later this week, he and his family are off to Copenhagen for another series of academic talks. Parker, his ten-month-old daughter, fidgets in his other arm. She doesn't feel like eating this morning, just like she often doesn't feel like sleeping, preferring to keep her parents up much of the night. It doesn't help that their baby-food maker is currently on the fritz; in the kitchen, Lisa is trying to purée steamed pears into edible mush.
Nevertheless, Aaron remains calm, playing happily with Parker. That's the way he usually is at home. "In the academic world he might come off as all business," Lisa says, "but for me, he's really sweet and loving and understanding and warm."
The serene scene stands in stark contrast to the dreadful scenarios that Clauset explores at CU. With the hard-and-fast statistical rules he's uncovering about the way the world works, it's as if he's chipping away at the concept of free will, the concept of being able to change the future, one data point at a time. Despite billions spent on security efforts, Clauset has found that the frequency of major terrorist attacks over the past 35 years hasn't changed...at all.
But the way he sees it, the patterns he's discovering about terrorism could be comforting — even empowering. For one thing, even in his most pessimistic probability models, the chances of Clauset or any of his family members getting caught up in a terrorist attack are infinitesimal, much lower than getting in a car crash or getting hit by lightning. For another, one of the reasons terrorism is so frightening is that it appears utterly uncontrollable and unpredictable: As the CELL exhibit says, it could happen anywhere, at any time, to anyone. As Clauset has shown, though, terrorism is in fact much less random and unpredictable.
"Over the ages, humans thought earthquakes and floods were malicious, and then simply unpredictable," he points out, and because people didn't understand the way natural phenomena worked, such events would carry an added level of existential calamity. But once people realized that earthquakes follow a power-law pattern, that rivers have flooding cycles, these disasters, while still costly and deadly, no longer seemed so random or malevolent.
Clauset believes a similar perspective shift could be useful with terrorist attacks. "There is a very large cognitive difficulty in thinking of terrorism as a natural phenomenon, as a natural consequence of modern society," he says. After all, the aim of terrorism is to terrify. His research might help change that, might help to neutralize terrorism's psychological threat."Mathematics is one of the few things that allow us to be unemotional about things," he says. And the impassive lens of mathematics, which creates a big-picture view of terrorism, is what helps Clauset work on the subject without becoming overwhelmed by the trauma involved. "My work is sufficiently abstract that it doesn't have that visceral feeling," he says. Still, he adds, "a theoretical attack that kills 3,000 people is going to be a brutally gory, terrible event. If I stop and think about the details..."
He catches himself, leaving the thought unfinished. He doesn't want to start imagining the sort of horror he witnessed at the CELL. Instead, he turns his attention back to Parker, resting happily in his arms. He works hard to maintain a balance between work and home life, to rein in his data-science curiosity regarding his own family. Yes, for a while after Parker was born, he was tracking her sleeping habits and every bowel movement on his iPhone, to see what sort of interesting patterns might emerge. But after a few months, he dropped the experiment.
"You're spending time with your baby, and here you are, trying to enter all this data into your phone. What the heck?" he says with a laugh. Sometimes, it's better to leave the patterns blissfully unknown.
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