February 19, 2005


Don't panic, it might never happen: A mathematical study of terrorist attacks need not leave us fearing the worst (Philip Ball, 2/18/05, Nature)

Computer scientists Aaron Clauset and Maxwell Young of the University of New Mexico, Albuquerque, have analysed the data on terrorist attacks compiled by the National Memorial Institute for the Prevention of Terrorism in Oklahoma City. They say the numbers follow a 'power-law' relationship.

A graph of the number of attacks n plotted against their severity x (in terms of injuries and/or fatalities) reveals that n is roughly proportional to x -1.85. Put simply, this means that the frequency of attacks decreases as their size increases - which is what you'd expect - but also that this relationship holds for events ranging from those that injured or killed just a few people to those that, like the Nairobi car bomb in August 1998, produced over 5000 casualties.

This might sound like no more than a formal way of presenting the statistics, but the power-law relationship has startling implications. For example, Clauset and Young say that the statistics suggest a strong probability of an attack as devastating as that on the World Trade Center within seven years.

And the power-law relationship implies that the biggest terrorist attacks are not 'outliers': one-off events somehow different from the all-too-familiar suicide bombings that kill or maim just a few people. Instead, it suggests that they are somehow driven by the same underlying mechanism. [...]

[A] power-law suggests something about that mechanism. If every terrorist attack were instigated independently of every other, their size-frequency relationship should obey the 'gaussian' statistics seen in coin-tossing experiments. In gaussian statistics, very big fluctuations are extremely rare - you will hardly ever observe ten heads and ninety tails when you toss a coin 100 times. Processes governed by power-law statistics, in contrast, seem to be interdependent. This makes them far more prone to big events, which is why giant tsunamis and market crashes do happen within a typical lifetime. Does this mean that terrorist attacks are interdependent in the same way?

This touches on a deep, difficult and long-standing question that has divided historians for centuries: are there universal laws governing human history?

Immanuel Kant, writing in his essay Idea of a Universal History from a Cosmopolitan Point of View (1784), proposed that "Individual men, and even whole nations, little think, while they are pursuing their own purposes...that they are advancing unconsciously under the guidance of a purpose of nature which is unknown to them."

The idea that there are robust laws of social behaviour analogous to the laws of physics - laws which are beyond our power to change - is what underlay the 'positivist' philosophy of Auguste Comte in the 1830s. It moved Leo Tolstoy to ask: "What is the force that moves nations?" A belief in the 'law-like' unfolding of history and economics also provided the foundation of Karl Marx's theories, and it continues to inform the thinking of Marxist historians today.

No one of even mildly open mind will fail to discern the other philosophy of history that derives from faith in such Natural law.

Posted by Orrin Judd at February 19, 2005 8:40 AM

Does bin-Laden have children or is he perhaps Mule from Asimov's "Foundation" series?

Posted by: Pat H at February 18, 2005 3:24 PM

This is like the old joke 'Why does the actuary bring a bomb with him when he goes on a plane? Because the chance of there being two bombs on a plane is significantly smaller than the chance of only one.'

You can play games with numbers and practically justify anything.

Posted by: Bart at February 18, 2005 6:41 PM

Pat H: bin-Laden is man of his religion, has many wives lots of children.

Natural Laws. Bah. Kant's far wiser contemporary got it right:

The History of The Decline and Fall of the Roman Empire by Edward Gibbon: Book I; Chapter III, Part II

Titus Antoninus Pius . . . diffused order and tranquillity over the greatest part of the earth. His reign is marked by the rare advantage of furnishing very few materials for history; which is, indeed, little more than the register of the crimes, follies, and misfortunes of mankind.

Posted by: Robert Schwartz at February 19, 2005 1:25 AM