Investigation and Popular Education, so he could look for
patterns in the con;ict. Johnson hoped the numbers could
tell them something about how the individual particles—in
this case, insurgents rather than electrons—functioned
when put together in large groups.
Soon the new team had a database that included more
than 20,000 separate incidents from two and a half decades
of FARC attacks. Johnson and Spagat expected that the
success of the attacks, measured in the number of people
killed, would cluster around a certain ;gure: There would
be a few small attacks and a few large ones as outliers on
either end, but most attacks would pile up in the middle.
Visually, that distribution forms a bell curve, a shape that
represents everything from height (some very short people, some very tall, most American men about 5' 10") to
rolls of the dice (the occasional 2 or 12, but a lot of 5s, 6s,
and 7s). Bell curves are called normal distribution curves
because this is how we expect the world to work much of
the time. But the Colombia graph looked completely different. When the researchers plotted the number of attacks
along the y, or vertical, axis and people killed along the x,
or horizontal, axis, the result was a line that plunged down
and then levelled off. At the top were lots of tiny attacks;
at the bottom were a handful of huge ones.
That pattern, known as a power law curve, is an extremely
common one in math. It describes a progression in which the
value of a variable (in this case, the number of casualties) is
always ramped up or down by the same exponent, or power,
as in: two to the power of two ( 2 x 2) equals four, three to the
power of two ( 3 x 3) equals nine, four to the power of two
( 4 x 4) equals 16, and so on. If the
height of Americans were distributed according to a power law curve
rather than a bell curve, there would
be 180 million people 7 inches tall,
60,000 people towering at 8' 11",
and a solitary giant as tall as the
Empire State Building. Although
power laws clearly do not apply to
human height, they show up often
in everyday situations, from income
distribution (billions of people living
on a few dollars a day, a handful
of multibillionaires) to the weather
(lots of small storms, just a few
In Colombia’s case, decades of
news reports con;rmed that the
number of attacks formed a line
that sloped down from left to right.
In general, an attack that causes
10 deaths is 316 times as likely as
one that kills 100. The larger the
event, the rarer it is.
At ;rst the pattern seemed too
clear and simple to be true. “
Immediately I thought, ‘We need to look
at another war,’” Johnson says.
With the U.S. invasion of Iraq in full
One might use the math
to argue that the 9/11 attack
was bound to happen. And there
is reason to believe that an even
bigger one is on the way.
swing, he and his collaborators had an obvious second test.
In 2005, using data gleaned from sources like the Iraq Body
Count project and iCasualties, a Web site that tracks U.S.
military deaths, they crunched the numbers on the size and
frequency of attacks by Iraqi insurgents. Not only did the
data ;t a power curve, but the shape of that curve was nearly
identical to the one describing the Colombian con;ict.
Around that time, a Santa Fe Institute computer scientist
named Aaron Clauset was applying the same approach
to what seemed like a distinctly different problem. Rather
than looking at speci;c guerrilla movements, Clauset was
examining total deaths caused by global terrorist attacks
since 1968. When he plotted nearly 30,000 incidents on
a graph, they formed a curve to the power of – 2. 38. (The
power number is negative because it re;ects a decrease
rather than an increase in the number of events as death
tolls rise.) With its characteristic downward slope, the
curve was eerily similar to those generated by Johnson
and Spagat for Colombia and Iraq.
To rule out coincidence, Johnson, Spagat, and University
of Oxford physicist Sean Gourley gathered data on nine other insurgencies. One after another, the curves clicked into
place: Peru’s Shining Path guerrilla movement: a curve with
a power of – 2. 4. The Indonesian campaign against rebels
in East Timor from 1996 to 2001: – 2. 5. The Palestinian second intifada: – 2. 55. Fighting against Afghanistan’s Taliban
from 2001 to 2005: – 2. 44. By contrast, traditional con;icts
in which two armies squared off against each other (such
as the Spanish and American civil wars) yielded graphs
that looked a lot more like bell curves than power curves.
Although the politics, religion, funding, motives, and strategies of the insurgencies varied, the power trends did not.
In an age of biological weapons and dirty nukes, the
implications are chilling. Although truly massive power-law
events—like the Great Depression or killer storms—are
drastically less common than smaller disruptions, they still
occur. In the normal distribution of a bell curve, you never
get such extremes, but the pattern underlying the power
curve enables a few rare events of extraordinary magnitude.
One might use the math to argue that the 9/11 attack that
killed more than 2,700 people in New York City was bound
to happen. And there is ample reason to believe that an
even bigger one is on the way, sooner or later.
For Johnson, a Cambridge- and Harvard-educated physicist who has studied stock markets and other apparently