Ever since Chinese general Sun Tzu penned The Art of War, some 2500 years ago, military experts have known there are fundamental strategic principles that apply to all armed conflicts, large or small.

But there also appear to be fundamental rules governing the scale, spread, and duration of wars: ones that are only now being ferreted out … not by generals, but by physicists.

To study this, Edward Lee, a graduate student in theoretical physics at Cornell University, US, used data collected by a non-profit group called the Armed Conflict Location & Event Data Project (ACLED), which catalogues “conflict incidents” of all sizes throughout the developing world.

Limiting his focus to Africa, Lee grouped more than 100,000 incidents into clusters he calls “conflict avalanches”. Some were brief; others dragged on for decades.

He then tabulated four types of statistics for each of these wars: duration, geographic scale, number of incidents, and number of fatalities, presenting his team’s results last week at a meeting of the American Physical Society in Boston, Massachusetts, US.

For each statistic, he then tallied how frequently wars of any given size occurred.

Not surprisingly, he found that low-fatality conflicts are more frequent than high-fatality ones. In fact, he says, it has long been known that the frequency of wars drops exponentially with their size, with a 35% reduction in occurrence rate for each doubling in the number of casualties.

But it turned out that similar maths also apply to Lee’s other three variables – with wars also falling off exponentially in frequency according to their geographic scale, duration, and number of incidents. And, just as in the case of fatalities, this appears to apply over a very large range of conflict sizes.

“It’s not just the fatalities,” Lee says. “It seems that all of these other things are behaving very similarly. For us, that’s interesting as physicists, because wars are very complicated and the emergence of a regularity like that is very interesting.”

It’s also of practical value, he adds, because it means that if you are missing data on one variable, it’s possible to use what you know about the others to predict it.

For example, he explains, “if we know how long [the war lasted] and how far [it spread], but not how many died, this provides a way of filling in that blank”.

That’s a particularly important blank to be able to fill in, because fatalities are often poorly reported.

“If you know even a little bit about what it is like to count the number of people who have died in a conflict, [you know] it’s really hard,” he says.

But Lee didn’t stop there. Because the ACLED data treated each day of a conflict as a separate incident, he was also able to calculate statistics on how each war evolved through time.

What he found was surprising.

One might think that all wars follow different paths, with, for instance, the Libyan civil war having little in common with the ongoing conflict in Somalia.

But it turns out, Lee says, that wars of all sizes progress similarly, with the total number of “events” – whether they be conflict incidents or fatalities – rising linearly over their entire course, whether 500 or 5000 days.

The same also applied to the rate of geographical spread. “It looks like they all progress in a very similar way,” Lee says.

Historically, the spread of wars has often been compared to the spread of forest fires. Just as summer heat dries out timber, tensions rise, but nothing happens until a spark ignites the conflagration. (The assassination of Archduke Ferdinand at the start of World War I is a good example.)

Then the conflict spreads, like flames though tinder-dry forest, until eventually it burns itself out.

It’s a logical model, but not consistent with Lee’s data, which shows no signs of slow starts, rapid expansions in the middle, or gradual petering out at the end.

In fact, wars of all sizes appear to defy the forest fire model. Instead, they all show the same linear trend, whether it’s in the rate of conflict incidents, fatalities, or geographic spread.

“These are similarities between conflicts between conflicts that lasted 100 days and conflicts that lasted over 10,000 days,” Lee says.

“I think that’s remarkable – it’s so counter to our intuitive narrative.”

Interestingly, he adds, his data show that the same maths apply not only to wars, but to the spread of riots, protests, and violence against civilians.

“It suggests they’re related, [but we’re] not sure why,” he says.

Ultimately, he notes, it may be possible to draw from the physics of natural processes such as earthquakes and neural networks to enhance our understanding of how wars evolve.

Among other things, he says, “if you see the beginning of a conflict, you could maybe predict how big it gets”.

If so, the results would be of more than academic interest. “Despite the fascinating statistics,” he says, “the human costs of armed conflicts are anything but statistical. People are living through this every day.”