# Rules of engagement - modelling conflict

The mathematics of warfare - Scientists find surprising regularities in war and terrorism

[http://www.economist.com/science/ The mathematics of warfare (Subscription required and on Lexis Nexis)

The Economist July 23, 2005

Is terrorism the next format for war? (Nature)

Academics Neil Johnson from the Univ. of Oxford and Michael Spagao from Royal Holloway College London are using the patterns of casualities to model the development of wars. They are attempting to monitor the casualties of the conflict in Iraq, using data from a database called IraqBodyCount.

The Nature article says:

All wars and conflicts seem to generate a common and distinctive pattern of death statistics. Fifty years ago, the British mathematician Lewis Fry Richardson found that graphs of the number of fatalities in a war plotted against the number of wars of that size follow a relationship called a power law, where all the data points fall on a straight line if plotted logarithmically. This power law encodes the way in which large battles with large numbers of deaths happen very infrequently, and smaller battles happen more often.

The Economist article also gives a nice summary of power law relationships

Power-law relationships are characterised by a number called an index.

For each tenfold increase in the death toll, the probability of such an event occurring decreases by a factor of ten raised to the power of this index,

which is how the distributions get their name.

The Johnson and Spagao paper suggests a difference between conflicts inside and outside G7-countries based on their index value.

A more worrying statistic comes from another paper on the same topic by Clauset and Maxwell at the British Institute of Physics who suggest that we can expect another attack at least as severe as September 11th within the next seven years.