Mathematics and war


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Ranged combat: aimed fire and Lanchester’s square law

We know that people vary in their abilities to perform any task, which of course includes insurgency; therefore, we must control for any exogenous or endogenous factors that could contribute to this variance as to avoid inserting into our analysis the belief that all insurgent are created equally. Once a reasonable number of theoretically justifiable control variables are identified, we may be able to get at this question at both a micro insurgent and macro insurgency level.


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Next, there has been quite a bit of research on the duration of wars , including state-on-state, civil and insurgency. For this research, a critical hurdle has always been how to overcome bias in the data collection and reporting when attempting to approximate how various factor contribute to the curation of a conflict. Sean uses open-scource media accounts of attacks to develop his data, and because most of these media outlets are primarily motivated by profit it is difficult to view this data as unbiased.

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This problem, however, can be dealt with by various sampling techniques and control varaibles. Of greater concern are the eventual conclusions drawn by attempting to match conflict patterns in this manner. Unfortunately, as previously discussed, all manner of conflicts follow this pattern.

If two conflicts have a near identical power-law distribution when observed in the long term, but upon examination we find that one is an insurgency and other a state-on-state conflict, what insight have we gained? This categorical approach, therefore, may be significantly limited in its explanatory value.


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There are likely many elements of this research that I am missing, and as such all of the above concerns may have already been addressed. Search for:. Firstly, a brief explanation. Up until relatively recently — the last coupla decades, really — warfare has been a more traditional affair. Two sides, lined up against each other, having it out. And game theory more specifically, Nash equilibria was able to adequately help model how such conflicts might go.

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Things are now different. Because govts like to keep them to themselves. So, how to get the data he wanted? The answer: open source intelligence. Open source intelligence is, simply, the information that one can gather from citizen reporting, the news, NGO stats and so forth. Data, in other words.

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Perhaps the classic story about open source intelligence and second order effects is about the Alliance. Unable to be directly sure whether they had successfully bombed bridges in Germany, they looked at the price of oranges in cities, which had to be imported. Spikes in the price of this acidic, vitamin C-containing fruit corresponded to bridges going down.

So yes. Gourley and co.

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What they found was interesting — when deaths were plotted against cumulative frequency for a number of conflicts on a log-log graph, the resulting line looked an awful lot like something adhering to the power law , with an alpha slope hovering around 2. Or, to put it more simply: the data suggested that insurgent conflicts fought in different places, for different reasons around the world might cluster around this value. For those of you not terribly comfortable with the equation, not to worry. Of more interest is what it means.

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Basically, it looks like the number of people killed in an attack is correlated with the strength of the attacking group. A smaller group of people with oodles of moolah and weaponry is going to do more damage than a larger group with less moolah and weapons. So one could look at alpha as the distribution of attack strengths, which leads us towards an organisational structure. There are a couple of possibilities — one might be taking the whole force, and dividing it up equally.

But the attacks that come out of that look more like a Gaussian distribution, not a power law distribution. Instead, the organisational structure which best fits what Gourley et al observed, was that each group would have a small number of groups which killed lots of people, lots of groups which killed very few people per attack , and a bunch of groups in the middle.

Mathematics and War

And that multiplying exponent seems to stay as one looks at different conflicts. With coalescence, there can be a formation bias towards the formation of large groups or towards the formation of small groups. And the actions can be geographic i.

The interaction between these factors gives rise to different distributions — an understanding of how allowed Gourley et al to start looking at which structures best fit insurgencies. Who would then attack them.

Said insurgent group would proceed to shatter rather than factionalise. So interesting patterns around alpha — 2. But what happens when alpha is higher or lower? If one can drive alpha higher, then one drives the insurgency towards fragmented, fluid groups, and more groups basically, more towards the guerilla feel. These tend to peter out eventually.

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