The “Mathematics of War” and What’s Old is New Again (and Again)

I have no doubt that Sean Gourley is a brilliant physicist, in fact, after reading over his website I well convinced of this. This is partly why I am a bit disappointed in the findings he discusses in the above TED talk.

It is worth the seven or so minutes to watch the video, but the basic finding is that the magnitude of all conflicts—as measured by the number of dead and frequency of battles—follow a power-law distribution. That is, most battles are relatively cost-less (few casualties), while very few are costly. This is interesting, but what’s more interesting is that this same result was observed over sixty years ago by a meteorologist named Lewis F. Richardson in “Variation of the Frequency of Fatal Quarrels With Magnitude.” In fact, this result was more recently regurgitated, and then again, I noted that the result was old.

To be fair, Gourley’s method for data collection, and eventual attempt to track the the evolution of the conflicts to a power-law are novel. I am not convinced, however, that this evolution toward a power-law is not simply the result of analyzing a large unbounded system; such as war. The exact same underlying dynamic occurs in large networks, where connectivity is essentially unbounded (dependent on the exact nature of the system being observed). Also, Barabasi and Albert have already proposed a well-adopted model for simulating power-law structures.


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13 comments to The “Mathematics of War” and What’s Old is New Again (and Again)

  • In the neighborhood

    Drew,

    While I think he does a very cool job with data collection, I have to agree, there is nothing like recycling social scientist literature and labeling it as a physics/math discovery. Moreover, I think his interpolation of this steady state of war misses the key dynamics. He says that there is some alpha that provides the measure of how fragmented/strong groups are, yet his prediction on whether this is a good or bad thing with respect to Iraq can go either way (i.e. large groups are easier to negotiate with or large groups can disrupt the equilibrium). There is no predictive power from this type of hypothesis and modeling and the policy implications are dubious at best.

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  • “This is partly why I am a bit disappointed in the findings he discusses in the above TED talk.”

    I am not sure what you mean. His findings was that the surge had no effect, or the insurgency is fragmented. Iraq defies the power-law distribution.

    He is saying that the surge didn’t need to happen, or the insurgencies have fragmented. The insurgencies didn’t fragment, there are more attacks that are less lethal, carried out by fewer groups.

    In that case, I think it means something like a civil war is taking place, or close to a civil war. Its as if the surge didn’t need to happen at all.

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  • His main finding is that wars follow a pattern, which happens to be the power-law. My disappointment is really in the fact that the research is getting so much attention, given the finding is so old.

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  • Did you listen to the same TED that I did?

    “given the finding is so old.”

    So we have known for sometime that the surge didn’t work, OK. But he also said directly that something was happening that he could not explain. Perhaps someone should try to explain it. The data is telling us something is up, perhaps civil war, and everyone is falling asleep listening to him.

    I guess you are correct, it is something we have heard before.

    Those troops are never leaving.

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  • Yes, we have seen much of this before. Contrary to his suggestion that the wars are so different socially, the mechanics of violence in them are actually quite similar. Almost all insurgents worldwide use basically three weapons: assault rifles, rocket-propelled grenades, and improvised explosives. This argues that we should not be surprised that the distribution of fatalities from similar weapons is similar.

    What troubles me most, though, is his attempt to model any given war with a single parameter. This represents a huge analytical simplification reminiscent of Bob McNamara’s body count obsession in the Vietnam War. Of course, at the end, he says that the Surge either did or didn’t work, which claims little explanatory power for his model. The decrease in violence and the general suppression of the insurgency in Iraq has been naturally helped by the Army and the USMC’s progress in learning HOW to fight insurgents, and the great progress made by the Iraqi Army. That said, if someone wants to claim that adding troops didn’t help, we’d need some serious analysis.

    In the end, I find this a preliminarily useful observation, if an old one. How I might apply it from here, I’m yet unsure. But I will be looking into his work further.

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  • James,

    I agree with your comment on the simplification of this dynamic into a single parameter–alpha. I have the same problem with the preponderance of the network literature that is obsessed with identifying networks that fit a power-law. What’s more interesting, to me, is what makes these networks, or conflicts, different.

    Examining just the distributions, for example, we can see that between the 75th and 90th percentiles is where all of the variation exist (about min 2:50 of the presentation). If we hope to understand the deterministic dynamics of conflict, we should hope to learn why there is variation in the relatively more deadly attacks, and what conflict-specific factors contribute to these signatures.

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  • [...] via Zero Intelligence Agents » The “Mathematics of War” and What’s Old is New Again (and Again). [...]

  • “Examining just the distributions, for example, we can see that between the 75th and 90th percentiles is where all of the variation exist (about min 2:50 of the presentation).”

    The advantage I have for being an idiot on this subject is that I can ignore stuff like this. I just thought it was the RMS of the wave, and I am sort of correct. We think of waves forming a sine going from negative to positive,but pulses are waves also (the term frequency as in number of incidents instead of length of wave). It must be like a wave in the intensity of the pulse (from one pulse to the other).

    These pulses(commands) induce movement, by force, into the displacement (people) of the insurgency and induce them to act.

    Of course the people don’t have to act (they have control) because the force of command is mostly perpendicular to their force and their velocity could carry them around instead of into the sun (sorry from another post I did on newsvine), but they judge it to be in their interest to act.

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  • Antonio

    Gourley is doing what others with his training have done before: apply strong analytical skills to very complex problems. Unfortunately, they also tend to overlook some “human factors”. And, in this particular case, it seems that he also overlooked issues of data collection and data quality.

    Power laws are indeed old news by now, and it has been shown that they apply to many networked systems: from the Internet to biological systems at the cell level. What all these examples have in common, though, is that there are no humans on the loop.
    This does not mean the tools is bad, only that is not being used appropriately. Huberman (HP Labs) has done work on networks of users of social sites; power laws are also observed there. His conclusions are also more measured -and still very interesting.

    I’d suggest that the big difference here is that this is an adversarial situation, and that changes some of the rules. For instance, there is a strong dynamic element, in which actions on one side provoke reactions (adaptation, etc.) on the other. This seems completely missing from the analysis here, and it has become a keystone for people who uses game theory to analyze such conflicts (and if you want to see extreme claims, find Bueno de Mesquita’s talk!).

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  • Antonio,

    Agreed, in fact I think (as I say in the post) that the data collection method is useful. Although, upon further consideration I think there is going to be some serious selection bias by basing the analysis on media reports.

    I would take your point about adversarial dynamics one step further, and note that this–as all insurgencies–is a very asymmetric conflict. Power-law structures are defined by an underlying asymmetry, so this result is then highly predictable.

    As for the BDM talk, I discussed it a few weeks ago here: http://www.drewconway.com/zia/?p=507

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  • [...] know the answers, but stated we should be looking at the structure of the insurgency for answers. Drew Conway, a military-centric analyst, cautioned those at SWC to not be too impressed with the information; [...]

  • If I understand your point, the higher variability in the casualty outcomes of the larger attacks can be explained by the context, armor and explosives. Over the war years vehicles are progressively hardened, while the mine sizes are increased and augmented by EFP technology. So a near miss by a large charge that would have injured some in 2004 hopefully doesn’t kill any troops protected in MRAPS or Strykers. But a direct hit on a Striker might kill 8 men, while a hmmv, armored or not, only held half as many.

    The linear alpha, success vs effort, relatively flat (2.5) across many conflicts, seems too averaged and one-dimensional to be useful. The cost or value an attack can also be measured as perceptual- column inches and broadcast minutes- and perception of past defeat or victory changes over time. Time has both positive and negative value. Or in relative value – if the suicider is the village drunk, and our men were recruited and trained and deployed at a cost of millions each. Replacement rates favor local fighters, and determine if a strategy of attrition can succeed, or be sidestepped. Many an insurgency has been demolished in detail, only to re-emerge in a few years, if the underlying ideology, the perceived motivation remains strong. Territory is a biggie. Leadership tenacity, a Washington or William Wallace that perseveres or martyrs.

    The command truism is that battle is calculus, not geometry. Coming from a politico-historical perspective, it says ‘don’t predict outcomes using logistics and accounting’.

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  • Drew

    Thanks for the interesting video. Sorry for the late comment, I just saw the link in the recent comments section.

    His talk reminds me of a story General Powell told of his first tour in Viet Nam. A top secret research group examined the frequency etc. of mortar attacks all hush hush high powered systems analysis. The result came out. Most of the mortar attacks occurred in at about the same time of day. Which every one who had been taking cover from them knew, a little to well.

    FM 101-10 publishes the experience tables of casualties for types of operations. It is WWII data but it holds up pretty well. Usually a little on the high side but it used order medical supplies so that may be an intentional bias. For example Fullajah (2004) and Hue (1968) had similar ratios of casualties. The mechanics of a firefight are pretty much the same no matter the cause or type of war, that there is the constant he found should be expected.

    His last graph on Iraq is interesting for the context he missed. At about the time the Graph makes the sharp upturn a number of armed groups who had been sitting out the fighting joined in. Since there were more of them they were more fragmented. The surge caused the minor groups to drop out or combine so we were fighting a more unified and dedicated opposition. The opposition was broken up by the surge so there were more fragmented groups. That the last phases of the surge were Iraqi run operations is an important datum that does his methodology does not allow for.

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