A mathematical model to predict the growth of deadly terrorist attacks was published on 1 July 2011 in Science along with an estimate of when attacks may occur in the future. Using a study of public data regarding human losses in Afghanistan and Iraq over 7 to 10 year periods, the scientists conclude that terrorist attacks follow mathematic schemas already known to social sciences and applicable to human activities more generally.
Neil Johnson is director of the ‘Complexity’ interdisciplinary research group in the department of Physics of the University of Miami. Complex systems, nerve cells, ant colonies and financial systems are all systems that bring together a large number of agents interacting by means of nonlinear reactions. Their evolution cannot be predicted through physics equations. In fact the only way to model complex systems is to deduce the laws of evolution by observing real systems.
This study was financed by the Joint Improvised Explosive Device Defeat Organization (JIEDDO), an entity within the US Department of Defence whose goal is to reduce and eliminate the effects of IEDs (Improvised Explosive Devices) used against American and coalition forces. The MITRE corporation, an American not-for-profit association that manages federal funds for national defence research technology also funded the study.
The study of human losses in Afghanistan and Irak
The ‘complexity’ research group recently published a surprising article in Science based on the study of attacks conducted by terrorist groups that resulted in the death of members of the military . The data studied can be found on www.icasualties.org/, an Internet site in the public domain. The site gathers official data on human losses that occurred in military campaigns in Afghanistan and Iraq between 2001 - 2010 for the former, and 2003 - 2010 for the latter.
According to the conclusions drawn by the site, the number of deaths occurring during a terrorist attack remains relatively consistent throughout a given conflict. This suggests that a terrorist group’s strategy will be – if they have the means at their disposal – to increase the frequency of attacks. It also implies that the time between two consecutive attacks will diminish. Here we can see the extent to which these scientific publications extend beyond applied mathematics.
A model that predicts terrorist attacks
In this study, scientists next applied a mathematical model that in normal times describes the level of success of many different activities. They adjust the curb representing the time reduction between terrorist attacks during a conflict using a power law:
where ‘t’ represents the time between the (n-1)th and the (n)th attack. The coefficient ‘b’ is the level of the increase in violence. This leads them to conclude that the frequency of terrorist attacks in a conflict is probably governed by the same rules as ‘human activities generally’. This allows them to analyse a conflict using a simple social system…
Even more surprising, these scientists have traced a linear law between the ‘b’ coefficient and time t1 between the two first attacks occurring in different regions of Afghanistan (Kaboul, Kandahar…) and Iraq (Baghdad, Diyala…). The generalisation of the model continues with regards to the type of weapon used (home made bombs, bombing suicides and terrorism generally). As with any scientific publication worthy of its name, the margins of error and the results spread are ‘analysed’, as is any correlation between parametres such as the increase in the number of ‘targets’ (here a target refers to soldiers on the ground) as well as the geographic data of the attacks.
After two terrorist attacks in one region, we could use this model to estimate the increase of attacks over the following days. What is more, the greater the number of attacks, the better the prediction will be.
One might argue that analyses of this kind are useless once publicly known, because they can be invalidated by insurgents’ free will. However, we believe this will not happen for the same reason that all commuters know that a traffic jam will appear every day at rush hour on a certain route, yet many still end up joining it. Science 333, 6038 (2011)"
At the border between mathematics, biology, physics and social sciences then, the study of complex systems is sometimes applied to systems such as attacks by groups of terrorists. Beyond this, to suggest that such a study could reveal the dates and size of terrorist attacks is surely both exaggerated and utopic. The validity of such a study is an ethical question – a question not considered in this publication. It is however ‘interesting’ to know what use is made of the numbers of human losses during a conflict, associating human losses in conflict with an epidemic or the functioning of an ant colony.
As the atypical career of a physicist Neil Johnson attests, physics is a science essential to understanding the world that surrounds us, from the application of complex biological and physical systems, to the modelling of financial transactions and terrorist attacks… But what were the selection criteria for this article to appear in the scientific journal Science? Innovative subject? Scientific applications? Technical applications? Something else entirely?
 Pattern in Escalations in Insurgent and Terrorist Activity, N. Johnson, S. Carran, J. Botner, K. Fontaine, N. Laxague, P. Nuetzel,J. Turnley, B. Tivnan, Science 333, 6038 (2011), http://www.sciencemag.org/content/333/6038/81.abstract
Find out more:
1) Predicting random violence by mathematics, D ; Braconnier, physorg.com, 2011, http://www.physorg.com/news/2011-07-random-violence-mathematics.html
2) The mathematical structure of terrorism, B. Mathiesen, physorg.com, 2006, http://www.physorg.com/news67524254.html
3) Mathematical Methods for Destabilizing Terrorist Activities, 2012, http://www.springer.com/computer/theoretical+computer+science/book/978-3-211-99440-5