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Insurgent Attacks Follow Mathematical Pattern
Hugh Pickens writes "Nature reports that data collected on the timing of attacks and number of casualties from more than 54,000 events across nine insurgent wars, including those fought in Iraq between 2003 and 2008 and in Sierra Leone between 1994 and 2003, suggest that insurgencies have a common underlying pattern that may allow the timing of attacks and the number of casualties to be predicted. By plotting the distribution of the frequency and size of events, the team found that insurgent wars follow an approximate power law, in which the frequency of attacks decreases with increasing attack size to the power of 2.5. This means that for any insurgent war, an attack with 10 casualties is 316 times more likely to occur than one with 100 casualties (316 is 10 to the power of 2.5). 'We found that the way in which humans do insurgent wars — that is, the number of casualties and the timing of events — is universal,' says team leader Neil Johnson, a physicist at the University of Miami in Florida. 'This changes the way we think insurgency works.' To explain what was driving this common pattern, the researchers created a mathematical model which assumes that insurgent groups form and fragment when they sense danger, and strike in well-timed bursts to maximize their media exposure. Johnson is now working to predict how the insurgency in Afghanistan might respond to the influx of foreign troops recently announced by US President Barack Obama. 'We do observe a complicated pattern that has to do with the way humans do violence in some collective way,' adds Johnson."
The vast majority of casualties are from insurgents targeting other civilians, not from insurgents targeting multi-national forces. It hasn't been a war since June of 2003... just an extended police action versus a religious or nationalist insurgencies.
It's actually a much simpler equation for non-guerilla (ie. traditional) warfare.
Take the War in Iraq, for instance. It basically boils down to:
(Crazy Corporate-Controlled Republicans) + (Lust for Oil) + (Mercenaries) + (Hatred for Brown People) = Unprovoked Invasion and War
Cosma Shalizi rants a lot about scientists' (often physicists') claims about having found a power law description of some empirical phenomenon (upshot: finding a straight line on a log-log plot isn't enough). See the following:
http://cscs.umich.edu/~crshalizi/weblog/491.html
http://cscs.umich.edu/~crshalizi/notebooks/power-laws.html
Research is what I'm doing when I don't know what I'm doing. -- Wernher von Braun
the way in which humans do insurgent wars — that is, the number of casualties and the timing of events — is universal
Did anyone else find it ironic that human solidarity was found in acts against human solidarity?
I wonder what mathematical laws are in play that results in the reported number of insurgents killed during any attack by coalition forces weirdly hovering around 30. Google "30 Taliban killed", or "30 insurgents killed", or "30 militants killed" and you see a lot results going all the way back when the wars were started. See this blog entry http://securitycrank.wordpress.com/2009/12/07/winning-the-war-30-taliban-at-a-time/ for more discussion.
Excellent point. But it make me question his definition of an insurgency.
Apparently, an insurgency that's crushed quickly doesn't count as an insurgency. And an insurgency that grows into a civil war doesn't count as an insurgency.
Only if the counter-insurgency is somewhat effective in reducing but not eliminating the number of attacks does he include it in his data set. In conclusion (and most remarkably) the data in his data set show a strong correlation across "insurgencies".
The value of the exponent is interesting. If one assumes that the smallest attacks happen roughly once a day then the attacks that are an order of magnitude larger happen about once a year. This implies that there may be some sort of calendar event that triggers these larger events. If these events can be identified then it may help avoid some of the large attacks. It would be interesting to check this by looking at the timing of the largest attacks in the data set that was used for this study.
Just because you are paranoid does not mean that no-one is out to get you.
Yea, who would have thought that war follows a predictable (even mathematical) pattern.
http://en.wikipedia.org/wiki/The_Art_of_War
Living in Chile
Hmm, well shame on me, I saw the talk existed but expected just a verbal representation of the article.
I had missed the point about stability around alpha. I have to admit the graphs of alpha vs events like the surge or elections are pretty interesting.
Equally interesting though is the rapid return to alpha=2.5. I guess the real question at this point would be: Can repeated examinations of alpha be used to measure the positive effect of a strategy or is it merely a measure of the temporary perturbation and inevitable return to 2.5 because humans are after all humans and 2.5 merely represents the steady state of humans desire for coalescence vs fragmentation.
In short it's a question of cause and effect. Would a different species have a different alpha that's just as stable because it's a reflection of their physiology and psychology.
The research is certainly more interesting than I originally credited, thanks.
There is a whole cottage industry of trying to fit power laws to data and being amazed whenever it fits. I guess I don't understand this one though; it sounds like they're just saying small attacks are more numerous than large attacks, which would seem obvious. What am I missing?
I'm not even sure that a major premise of their pattern is correct. From the submission: the researchers created a mathematical model which assumes that insurgent groups form and fragment when they sense danger, and strike in well-timed bursts to maximize their media exposure.
One could probably form a strong argument (perhaps even with a valid mathematical basis) that suggests that so-called "insurgent" actions have worn out their welcome, and news of them floats in a featureless sea of similar actions. It doesn't help the "insurgents'" cause that they have little record for being nice to their own people, so they can only garner support from the most polarised of those they choose to leave alive.
Power laws are ubiquitous in human affairs - almost everything we do as a group involves power laws. This works for the size of cities and the sale of books and traffic to web sites, so I am not surprised it also happens in insurgent attacks.
Whether that will actually result in the effectiveness of Army tactics is another question, and, frankly, I am dubious. The sale of hit records follows a power law, but knowing that doesn't make me into a better musician.
So World War Two didn't start when Germany took over Poland with almost no resistance? Good to know.
I think a lot of comments above miss a more important point, that knowing the attacks follow a power law distribution (for argument's sake) still doesn't help predict individual events. Really, unless you're placing bets on terrorism (google for "futures market terrorism Poindexter") this won't help you much.
"Restate my assumptions: One, Mathematics is the language of nature. Two, Everything around us can be represented and understood through numbers. Three: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature. Evidence: The cycling of disease epidemics;the wax and wane of caribou populations; sun spot cycles; the rise and fall of the Nile. So, what about the stock market? The universe of numbers that represents the global economy. Millions of hands at work, billions of minds. A vast network, screaming with life. An organism. A natural organism. My hypothesis: Within the stock market, there is a pattern as well... Right in front of me... hiding behind the numbers. Always has been."
The reason the basic idea sounds familiar to not just you but everybody here is that it is the characterizing property of fractals. I wouldn't go so far as to relate this idea to biology per se, however. It commonly occurs in physics as well.
Intuitively, fractals (and therefore power laws) ought to arise whenever a finite resource is split among a large number of independent processes, which are all identical and have no limit on resource consumption. So if you look at your examples, there's a resource limit. But if you look at other examples, such as the wealth of individuals within a country, then there is a power law because there's (approximately) no limit to how much an individual can accumulate, but the total amount of money in the economy is still a finite resource.