The Mathematics of War: Sean Gurley Discovers Common Patterns in Attacks Across the Globe

The PopTech science fellow started by looking at attacks in Iraq, then studied conflicts in different parts of the world, and discovered the same mathematical patterns.

U.S. Department of Defense

Sean Gourley: When we sat down and looked at a conflict like Iraq, we saw that there were very strong mathematical patterns in size of attacks. And then when we looked at a conflict in a different part of the world, fought for different reasons, like Colombia, these same mathematical signatures were emerging again.

Sean Gourley of the University of Miami is a PopTech science fellow for 2010. He’s talking about what some have called “the mathematics of war.” His work – published in the journal Nature – suggests that mathematics can help predict the timing and size of attacks in certain types of war – those in which an insurgent group is trying to overthrow an authority power – regardless of where, and why, these attacks are taking place.

What we’re looking at with conflict is saying, how many attacks kill one person? How many attacks kill two people? How many attacks kill ten people? When we plot that out, we get this equation known as a power law.

In other words, they see a mathematical pattern. Gourley and his team collected data from more than 54,000 attacks across eleven recent wars.

Because we know that the probability of an event of size x in time occurring in period t is given by this equation, we can actually start to make predictions about the likelihood of an attack occurring during a one week period in a certain neighborhood in Baghdad.

Gourley said the U.S. military is looking at his research. He said that although today’s wars seem chaotic, patterns emerge because there are only a few ways to fight an authority power.


It’s actually very difficult for an insurgency to come together and fight a much stronger opposition. The reality is that an insurgency needs to evolve towards a certain state. And when it evolves towards that state, it can actually compete.

Gourley and his colleagues examined insurgent groups as if they were an “ecosystem” – meaning, the interactions of insurgents follow certain patterns, depending on what’s going on around them.

When we look at the equation we’re looking at group dynamics – how people form groups, and how they break apart. When we look at formation of groups, we find that it’s biased toward large groups – they attract more resources, they attract more people.

He said on the other hand, large groups are also more prone to break apart, as larger groups are a more likely target for the opposition. And when a large group breaks up, it doesn’t just divide, it shatters into hundreds of small groups. With this information, Gourley said, a model can help predict the reactions of insurgent groups to certain events.

We can actually start to say, if I want to bring a change, what is likely effect of my actions going to be? If I want to put more troops in Afghanistan, is likely that going to decrease or increase the length of conflict? And we can take our model, and start to run simulations with different numbers of troops, and see what the expected likelihood of the conflict ending is.

Gourley said that because wars don’t happen in a vacuum – meaning, the circumstances surrounding wars aren’t perfectly controlled by these mathematical patterns – no model can truly predict when an attack will happen. He said that his model predicts the likelihood of an attack with reasonable accuracy.


Of course, you’re dealing with a noisy and chaotic system. Being reasonably accurate may still only be 20%. But that’s still better than anything else that can be done.

Sean Gourley is a 2010 Poptech Science and Public Leadership Fellow, addressing a need for socially engaged scientists as public communicators.

Written by Lindsay Patterson

[Photo by DVIDSHUB]


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