Please create an account to participate in the Slashdot moderation system


Forgot your password?
BLACK FRIDAY DEAL: Trust the World's Fastest VPN with Your Internet Security & Freedom--A Lifetime Subscription of PureVPN at $48 with coupon code "BFRIDAY20" ×
Math The Military Technology

Insurgent Attacks Follow Mathematical Pattern 181

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."
This discussion has been archived. No new comments can be posted.

Insurgent Attacks Follow Mathematical Pattern

Comments Filter:
  • by Kagura ( 843695 ) on Saturday December 19, 2009 @10:03AM (#30498490)
    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.
  • by Anonymous Coward on Saturday December 19, 2009 @10:13AM (#30498538)

    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: [] []

  • Human Solidarity (Score:3, Interesting)

    by psnyder ( 1326089 ) on Saturday December 19, 2009 @10:34AM (#30498654)

    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?

  • by Anonymous Coward on Saturday December 19, 2009 @10:35AM (#30498660)

    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 [] for more discussion.

  • by tomhath ( 637240 ) on Saturday December 19, 2009 @10:58AM (#30498786)

    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 2.5 Exponent (Score:4, Interesting)

    by mrsquid0 ( 1335303 ) on Saturday December 19, 2009 @11:03AM (#30498806) Homepage

    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.

  • The Art of War (Score:3, Interesting)

    by cenc ( 1310167 ) on Saturday December 19, 2009 @11:14AM (#30498858) Homepage

    Yea, who would have thought that war follows a predictable (even mathematical) pattern. []

  • by belthize ( 990217 ) on Saturday December 19, 2009 @11:28AM (#30498954)

    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.

  • Re:The 2.5 Exponent (Score:3, Interesting)

    by mrsquid0 ( 1335303 ) on Saturday December 19, 2009 @11:45AM (#30499072) Homepage

    That is certainly true, but it would be interesting to see if there is some sort of periodicity, particularly considering that there are many different annual events and cycles that could affect insurgencies and the way that they plan and carry out attacks. The 2.5 exponent may be completely unrelated to the year, but it is interesting that it does roughly correspond to an order of magnitude larger attack on roughly annual timescales.

  • Re:Uhuh (Score:3, Interesting)

    by timeOday ( 582209 ) on Saturday December 19, 2009 @11:46AM (#30499078)

    Warning - a lot of things look like they follow a power law.

    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?

  • Re:Uhuh (Score:5, Interesting)

    by BrokenHalo ( 565198 ) on Saturday December 19, 2009 @11:59AM (#30499176)
    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.
  • Re:The 2.5 Exponent (Score:4, Interesting)

    by mrsquid0 ( 1335303 ) on Saturday December 19, 2009 @12:37PM (#30499474) Homepage

    Yes, we would see the same timescale regardless of the base that was used. The only difference would be the value of the exponent. The value of the exponent itself is not the key, it is the timescale that the exponent (in combination with the base) implies. The timescale may very well be a coincidence, but if it does merit some consideration to see if there is any evidence to suggest that the timescale is real. Fortunately, there are many tests that can be made to see if there is any evidence for some sort of periodicity or pseudo-periodicity. OF course, this whole idea falls apart if the timescale for the smallest attacks is significantly different from one day, which is another test of the hypothesis.

  • by mbone ( 558574 ) on Saturday December 19, 2009 @12:47PM (#30499560)

    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.

  • by greyhueofdoubt ( 1159527 ) on Saturday December 19, 2009 @12:49PM (#30499576) Homepage Journal

    Ehhhh... I don't think so.

    A series of searches of "x insurgents killed" yields:

    2= 14,700
    3= 30,700
    4= 164,000
    5= 20,000 results
    10= 160,000
    15= 64,000
    20= 306,000
    25= 41,000
    30= 58,400
    31= 10
    32= 75,400
    33= 4,460
    34= 26,400
    35= 36,000
    40= 57,000
    41= 484
    42= 28,400
    43= 9
    44= 1
    45= 9,180

    I think it would be difficult to draw any conclusions about how many insurgents are killed at once. How do you decide when an incident starts and ends? Operations can last days. How close do they have to be to each other when they die? I can almost guarantee that we are taking out insurgents one by one or two by two for the most part. They don't run around in packs of 30, they sneak at night in pairs.

    That's just my experience, though. Keep your fun little "23" theory.


  • Re:The 2.5 Exponent (Score:5, Interesting)

    by greyhueofdoubt ( 1159527 ) on Saturday December 19, 2009 @01:01PM (#30499652) Homepage Journal

    These may be useful to you: [] []

    I can't speak of afghanistan, but in iraq the insurgent attacks were higher and more effective:

    -when the ground was dry (moving around in iraq during the rainy season is a nightmare)
    -lots of blowing dust in the air, drastically reducing visibility
    -around dusk
    -toward the end of ramadan

    That's just a taste of all the factors that you'd have to account for to get an accurate map of insurgent behavior. Even then, I think it'd be pretty useless, since they are not a regular army and do not usually coordinate among cells. Maybe they want to attack, but the shipment from libya isn't here yet, so they wait for that but now the americans are getting suspicious so they launch all 20 of their libyan mortars at once and high-tail it out of there. Seems like a major, coordinated attack when in reality things are very different.

    Guaranteed to make your brain hurt.


  • by Anonymous Coward on Saturday December 19, 2009 @01:16PM (#30499728)

    So World War Two didn't start when Germany took over Poland with almost no resistance? Good to know.

  • How does this help? (Score:2, Interesting)

    by Primitive Pete ( 1703346 ) on Saturday December 19, 2009 @02:35PM (#30500126)
    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.
  • Patterns... (Score:2, Interesting)

    by Erinnys Tisiphone ( 1627695 ) on Saturday December 19, 2009 @04:32PM (#30500634)
    "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."
  • Re:Just Biology (Score:3, Interesting)

    by martin-boundary ( 547041 ) on Saturday December 19, 2009 @08:17PM (#30501560)

    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.

    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.

  • Re:The Art of War (Score:3, Interesting)

    by cenc ( 1310167 ) on Sunday December 20, 2009 @08:23AM (#30503450) Homepage

    yea, the guys with this study likly failed at both. I am not sure I would want to be the guy in the field getting shot at when it turns out they got one of the variables wrong (which from the article seems like they got more than a few wrong like this B.S. about the media).

    My point was more aimed at the people that thought this was somehow a special discovery. The Art of War contains many specific (if not basic) formulas, mostly in regards to economics, about the nature of troop strengths, cost fielding troops, distance, and so on and done over 2,000 years ago.

    Military fighting forces have been crunching numbers for a long time about everything.

"The one charm of marriage is that it makes a life of deception a neccessity." - Oscar Wilde