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Science Forum Index » Anthropology - Paleo Forum » [Fwd: The Mathematical Structure of Terrorism]
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| Roger Bagula |
 Posted: Sat Feb 17, 2007 1:40 pm |
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-------- Original Message --------
Subject: The Mathematical Structure of Terrorism
Date: Sat, 17 Feb 2007 16:16:07 GMT
From: Roger Bagula <rlbagula@sbcglobal.net>
Organization: SBC http://yahoo.sbc.com
Newsgroups: sci.fractals,sci.nonlinear
Posted by: "V.Z. Nuri" vznuri@earthlink.net vznuri
Fri Feb 16, 2007 2:03 pm (PST)
Quote: this is some very cool research I learned about in the relatively
new science magazine Feed, which seems to be significantly increasing
in quality.
Professor Neil Johnson of Oxford University has found a very interesting
power law that underlies insurgent warfare relating to incidences of
casualties
over time. he seems to have a simple explanatory model. profiled in
various
places for its obvious right-now significance/
relevance.
I hope to see more research like this that applies to large-scale human
dynamics. in particular, I think the field of economics still lies
largely
unexplored for many similar, simple laws of collective behavior.
maybe someone will eventually "derive" the result, war==hell. maybe the
american warmachine will eventually be reigned in from its current
wild unleashing.
http://www.physorg.com/news67524254.html
The Mathematical Structure of Terrorism Discussion at PhysOrgForum
The complex patterns of the natural world often turn out to be governed
by relatively simple mathematical relationships. A seashell grows at a
rate proportional to its size, resulting in a delicate spiral. The
gossamer network of galaxies results from the simple interplay between
cosmic expansion and the force of gravity over a wide range of scales.
As our catalogue of natural phenomena has grown more complete, more and
more scientists have begun to look for interesting patterns in human
society.
The nature of war is a question of great interest to everyone,
especially as the era of large-scale conflicts recedes into the past.
The wars of today tend to be lopsided affairs, where guerilla forces,
insurgent groups, and terrorists oppose incumbent governments. Instead
of a few large-scale battles, this situation leads to an apparently
random series of small-scale attacks against vulnerable targets of
opportunity.
While affected governments collect records of past attacks, the random
nature of such wars means that these data are of limited use in
predicting future attacks. When classified according to their frequency
and intensity, however, the events of any insurgent war appear to follow
a power law. It should come as no surprise that weaker attacks are more
common than stronger attacks, but a power law distribution makes a much
more specific prediction. It turns out that if individual conflicts (for
example, a terrorist attack or a guerilla raid) are classified according
to the resulting number of fatalities n, then the number of such
conflicts occurring in any given year is proportional to n raised to a
constant power.
Let’s look at a specific example. In the case of the Iraq war, we might
ask how many conflicts causing ten casualties are expected to occur over
a one-year period. According to the data, the answer is the average
number of events per year times 10–2.3, or 0.005. If we instead ask how
many events will cause twenty casualties, the answer is proportional to
20–2.3. Taking into account the entire history of any given war, one
finds that the frequency of events on all scales can be predicted by
exactly the same exponent.
Professor Neil Johnson of Oxford University has come up with a
remarkable result regarding these power laws: for several different
wars, the exponent has about the same value. Johnson studied the
long-standing conflict in Colombia, the war in Iraq, the global rate of
terrorist attacks in non-G7 countries, and the war in Afghanistan. In
each case, the power law exponent that predicted the distribution of
conflicts was close to the value –2.5.
What’s more, in the case of Colombia and Iraq he was able to show that
the exponent seemed to be evolving towards that value; Colombia from
above, and Iraq from below. Does this hint at a simple underlying
pattern driving the behavior of modern wars?
Johnson thinks so, and has even developed a model that predicts a power
law distribution of casualties with the correct exponent. In his model,
the insurgent force consists of a fixed number of attack units (a
general term which may include equipment or even information, as well as
people) which may group together to form larger units. Each unit on its
own is assigned a ‘strength’ of one, meaning that a conflict involving
that unit will result in one death. Coalitions of units pool their
strength, and cause proportionally more deaths.
The key ingredient in this model is the evolution of groups over time.
Terrorist organizations, for example, typically function in relatively
small units. When an opportunity comes up that demands more resources,
they may band together. When the authorities grow too close for comfort,
on the other hand, they may split up. In time these competing pressures
can create a stable arrangement of groups, with a fixed distribution of
different sizes.
Johnson’s model adopts a very simple dynamic to model this evolution. In
any given time step, one group of attack units is randomly chosen. Each
group's chance to be chosen is proportional to its size, but the many
small groups still see much more activity than the few large groups. The
group selected is given a small probability (1%) of disbanding into
individual units; if it doesn’t disband, then it joins up with another
randomly chosen group.
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.” Johnson’s research continues with the
analysis of data from other conflicts, such as Senegal, Indonesia,
Israel, and Northern Ireland.
Citation: Neil Johnson et al. 2006, “Universal Patterns Underlying
Ongoing Wars and Terrorism”, http://xxx.lanl.gov/abs/physics/0605035
By Ben Mathiesen, Copyright 2006 PhysOrg.com |
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