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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."
I saw this on "Numb3rs!"
Sean Gourley shows that if the exponent is larger or smaller than 2.5, the war becomes unsustainable and ends fairly quickly. http://www.ted.com/talks/lang/eng/sean_gourley_on_the_mathematics_of_war.html
I don't see what it is they think they've discovered. If you take a loose collection of 5000 people with a weak desire to cooperate you're going to get way more groupings of 10 than 100 than 1000. The desire for safety in numbers is offset by the risk of exposure by size. In fact I'd have drawn almost exactly their curve if somebody had asked what the distribution would look like.
If the likelihood of an event is a coupled with critical mass of groupings then the event distribution will follow pretty much the same curve.
If somebody understands what it is these folks found could you explain it.
Insurgent: "Hey, chief, there's a big column of Americans coming! Let's skank 'em!"
Chief: "Hold on, let me get out my calculator . . . damn it! I should have paid more attention to the Linear Programming and Game Theory courses at the Madrasah! Go ahead and attack . . . then turn on CNN to see if we got any media exposure. And please bring me some more pencils and paper . . . this mathematically based insurgency strategy *really* sucks!"
Schroedinger's Brexit: The UK is both in and out of the EU at the same time!
The result is cool, and important in the details, but is not that interesting in terms of breaking new ground. As a biologist, having measured countless number of behavioral parameters that all follow power laws, it is not surprising that yet another biological behavior, waging a particlar kind of war in this case, follows a power law. That part is ho-hum.
Similarly it would only surprise me if things like, oh, the size of undergraduate populations at different universities, the number of cars in each country, the number of stray dogs in each city, the average brain mass for each species, or the number of bullets used in any given firefight, do NOT follow a power law. It's just biology. That's the way things work.
And, to keep things in perspective, I'm just a biologist. It could be that all natural phenomena follow that sort of pattern, like the mass of celestial objects, the surface areas of land masses, the percent cloud cover at each point on Earth, etc. The basic idea of power laws -- lots of small versions of a thing, only a few big ones, and a smooth distribution between -- seems inherently universal to my small brain.
Put my fist through my alarm clock with its ding-dong death inside my ear. - The Blackjacks.
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.
'nuff said.
Let's see. It takes more energy, time, and complexity, to move into place the resources needed for a bigger attack. So, its not really surprising at all that bigger attacks occur less frequently or even obey a power law.
This is my sig.
> The total amount of attack will/power stays the same, no matter what size
> the individual attacks are? No shit? I could have told you that too.
But you did not. I am constantly amazed that every time some sort of insightful discovery is
made there is a chorus of voices saying " I could have told you that". Wake me when someone
actually does "tell me that" before someone else publishes it.
Just because you are paranoid does not mean that no-one is out to get you.
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
...if we brought them all home?
You're doing it wrong. There's no use in doing thousands of submissions if you don't follow the correct power law. An attack with ten submissions should be 316 times more likely to occur than an attack with 100 submissions.
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.
Meh. I could have told you that.
Just what we need, another mathematical model show people are numbers and the dead and wounded (wounded; not like a broken finger, but like arm GONE) are only statistics.
6.8SPC TR of 550, l xwind at 6, drift rt at 26" drops 77". AT has 503 ft-lbs at 1403 fps. FT 0.86
Of course, you are correct. Thanks for the additional input.
My position was though was that the randomness instead of being 50-50 like the coin flip might instead be 60-40 or even 70-30 but still a large unknown exists to predict with any sense of integrity of accuracy.
Perhaps if it collapsed nearer to 100% such as 95-5 or 98-2 then I could see a usefulness for predicating a potential.
It does remind me of the old adage "Figures lie and liers figure"
And in the end, the love you take is equal to the love you make
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.
What they are saying is that regardless of culture, location, enviroment decade, reasons behind the conflict, etc., the relation between large and small attacks appears to be a constant.
That wasn't obvious at all.
Solid post. This comment
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.
is about the best "correlation vs. causation" post I've seen lately.
Correlation vs. Causation has turned into an overused meme IMO-- not around here, just digg and reddit.
Sir you are under arrest for a crime you would be committing in an hour. Our equation said so.
"They confiscated everything, even the stuff we didn't steal!"
"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."