# Mathematical structure of terrorism

#### PIT2

ABSTRACT
We report a remarkable universality in the patterns of violence arising in three highprofile ongoing wars, and in global terrorism. Our results suggest that these quite different conflict arenas currently feature a common type of enemy, i.e. the various insurgent forces are beginning to operate in a similar way regardless of their underlying ideologies, motivations and the terrain in which they operate. We provide a microscopic theory to explain our main observations. This theory treats the insurgent force as a generic, self-organizing system which is dynamically evolving through the continual coalescence and fragmentation of its constituent groups.

http://xxx.lanl.gov/abs/physics/0605035

These are the only rules of the model, and they turn out to work just fine. After the population is allowed to evolve for a long time, the result is a power law distribution of group sizes with an exponent of exactly –5/2. Since group size is proportional to attack strength, this distribution also predicts the frequency of attacks causing a given number of fatalities. It is also interesting that the result of this model depends only on the probability of fragmentation. As long as this probability is reasonably small, the distribution of attacking groups will settle into a steady state with a power law distribution.

Is this new ‘Law of Terrorism’ really universal? “Power law patterns will emerge within any modern asymmetric war being fought by loosely organized insurgent groups.” Johnson speculates, “Although future wars will provide the ultimate test.” J

http://www.physorg.com/news67524254.html
I wonder if they can tell if this means the war is lost, or if they will be able to defeat the insurgents by manipulating this 'law of terrorism'.

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#### Bystander

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What's it mean? It means a group of statisticians haven't had anything to do for the past year or two.

How did they entertain themselves? They rediscovered "Statistics of Fatal Quarrels." (Ain't gonna dig out the author right now.) See also, Quincy Wright, A Study of War, which has been rehashed by a half dozen or so people under the auspices of "COWPAT" U. of Chi.. (oh, all right --- Causes of War Project at U. of Chi.).

Have they discovered anything new? No.

Did they sneak one past the peer review process? Yes.

#### Tojen

Isn't "terrorism" just a modern, sexy term for guerilla warfare?

--Guerrilla (also called a partisan) is a term borrowed from the Spanish "guerrilla" meaning little war, and used to describe small combat groups and the individual members of such groups. Guerrilla warfare operates with small, mobile and flexible combat groups called cells, without a front line. Guerrilla warfare is one of the oldest forms of asymmetric warfare. Primary contributors to modern theories of guerrilla war include Mao Zedong, Abd el-Krim, T.E. Lawrence, Wendell Fertig, Regis Debray, Vo Nguyen Giap, Josip Broz Tito, Michael Collins, and Che Guevara.

--The -illa term accepts the unequal fight between civilians against an organized State Army.

--Guerrilla tactics are based on intelligence, ambush, deception, sabotage, and espionage, and an authority through long, low-intensity confrontation. It can be quite successful against an unpopular foreign regime: a guerrilla army may increase the cost of maintaining an occupation or a colonial presence above what the foreign power may wish to bear.

http://en.wikipedia.org/wiki/Guerilla_warfare
The only new thing about terrorism that I can think of is possibly suicide bombing, and I'm not sure about that. There's nothing new about "propaganda", though.

#### jgruszynski

Terrorism can be Guerilla or not

Strictly terrorism is the use of terror to achieve political or social goals. Guerilla warfare's primary characteristics is stealth and a tendency toward a networked organization structure. Terror can be a useful tactic for guerillas. Guerilla techniques can be useful for terrorism. I claim they are different, however. Terrorism that is "state-sponsored" is less likely to be purely or at all guerilla. Guerilla warfare need not use explicitly created or intended terror though its strengths may foster terror in conventional forces. Al Qaeda does clearly practice guerilla tactics so perhaps the point is moot.

Since guerilla combat is often network organized and most social networks follow a power-law scaling, the referenced paper's results are not surprising. The specific -2.5 value is intriguing. It might mean something very significant.

A secondary result that would be expected from power-law scaling is that guerilla forces can never be suppressed completely. This is akin to work on influenza and HIV transmission in a power-law network - there is no possible way to achieve a "cure", i.e. infected population = 0.

This is one of the "strengths" of guerilla combat. In the Lanchester asymmetric model this comes from that fact that the identity of being a guerilla or convertable sympathizer can never be determined with 100% certainty short of 100% genocide. In practice, guerilla identity certainty tends to be less than 1%. Sympathizer identity is higher but highly deniable and if the conventional practices draconian techniques (e.g. torture, death) it only increases sympathizer creation and conversion. Attempting genocide as such tends to create significant conversions of civilian population to the guerilla cause long before it ever becomes effective militarily.

Further other studies have shown that conversion of only 3-4% of the population is sufficient to topple any totalitarian governments (based on historic examples). This range seems likely to apply in an asymmetric conflict which only differs in who the conventional force is (domestic vs. foreign occupation). Historically massive conversion tends to be discontinuous (cusp catastrophe) and tends to come from a large sympathizer population (inversion population ? laser population inversion follows Bose-Einstein distributions which is closely related to power-law distributions so it may not be so farfetched) which converts due to some trigger event. This bodes poorly for the US given the 71% Iraqi opinion the US should leave within 12 months or less poll results.

Another strength is that guerilla combat can eliminate the symmetric conventional force square-law advantage. This is simulataneously similar to the conventional advantages of using technology or stealth to counter square-law advantage (e.g. US vs. USSR - USSR had a significant square-law advanage which was balanced or eliminated by technology and stealth) which essentially gives a conventional force some guerilla-like features.

The biggest example of this effect is to look at the relative operational costs of Al Qaeda vs. US in the WOT. Numerous US govt sources put Al Qaeda costs for 911 as no more than $1M, and combined with all the operations back to 1991(USS Cole, East Africa, etc.!!) no more than$2M total. Compare this to the operational costs of Afghanistan and Iraq which are both justified as efforts against AQ being in $100B-$10T. Spending 10,000x-1,000,000 against an "enemy" that is unkillable as the flu and that will always have that cost advantage can't be sustainable. The US number doesn't even count indirect economic costs like TSA-derived inefficiencies in air travel.

Some of the ways the cost differential occurs is simply due to the operational inefficiencies of standardization across a broad range combatants (aka military discipline and standardization) and hierarchal economic and information inefficiencies compared to dynamic power-law networks in a changing environment.

About the only thing a conventional force can do is to try to pull the guerilla combatant back into symmetric operation, militarily, politically and socially. The first means making them be like a state and holding territory - the early success in Afghanistan and Iraq are examples of what happens. The problem is that there are strong forces to drive organizational evolution toward asymmetric conflict - its simply safer, cheaper and more effective - the same theaters predictably show the same! The second technique (political symmetric) involves operating within the rule of law and diplomacy. The last involves social efforts to remove the sympathizer and conversion incentives.

Ignoring "symmetric pull" make WOT loss for the US almost a foregone conclusion. Time to think about getting dual citizenship if you're a US citizen.

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Welcome to PF! Wonderful for you to start with such an informative post! That "inversion population" comment was tremendously interesting.

I don't see, though, why a power law distribution would be assumed for a subset of a population, since the appropriate model is not a network but some nearest neighbor model like the Ising model? So in that case the Bose distribution would not be unexpected.

#### jgruszynski

Thanks for the comment...

I'm assuming you mean the part about "Further other studies..." The part about population inversions is suggested by research such as Francisco's "Dictator's Dilemma". The metaphor of population inversion is purely an associative hypothetical on my part, hence the smiley and "?". Francisco models the effect with an insect outbreak DE which may fit his data but might not be the true relationship.

Bianconi & Barabasi in "Bose-Einstein condensation in complex networks" suggests that a 2nd order phase change a la Ising is part of the continuum within complex networks. Scale-free and 2nd order phase changes are different but related parametrically in their model ( Bose-Einstein mapped to network/graph theory). Interestingly their model is essentially a "nearest neighbor" model but with a slightly different slant than most Ising derivations I've seen.

BTW both papers are available online.

"Mathematical structure of terrorism"

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