Wednesday, July 13, 2005

Yet another power curve

From news @
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.

Recently, the same kind of power laws were found to hold for terrorist attacks over the past four decades or so. But the precise form of the power law depends on the type of country to which it relates. Terrorist attacks in Western industrialized nations are rare but tend to be large when they happen. Terrorist attacks in the less-industrialized world tend to be smaller, more frequent events.

[Neil Johnson, a physicist at the University of Oxford] says that the bomb attacks on London's public transport system on 7 July, in which more than 50 people were killed, fit this statistical picture. 'They absolutely fall into line,' he says.
I don't understand how a death toll of 50 falls into line in this picture. London is an industrialized city. Terror attacks there should should be infrequent (which they are) and large (which this one wasn't, at least in terms of number of people killed).

Here is the abstract from "From old wars to new wars and global terrorism"
The frequency-intensity distribution of fatalities in 'old wars', 1816-1980, is a power-law with exponent 1.80. Global terrorist attacks, 1968-present, also follow a power-law with exponent 1.71 for G7 countries and 2.5 for non-G7 countries. Here we analyze two ongoing, high-profile wars on opposite sides of the globe - Colombia and Iraq. Our analysis uses our own unique dataset for killings and injuries in Colombia, plus publicly available data for civilians killed in Iraq. We show strong evidence for power-law behavior within each war. Despite substantial differences in contexts and data coverage, the power-law coefficients for both wars are tending toward 2.5, which is a value characteristic of non-G7 terrorism as opposed to old wars. We propose a plausible yet analytically-solvable model of modern insurgent warfare, which can explain these observations.

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