From: Subject: Economist.com Date: Thu, 21 Jul 2005 12:56:18 -0500 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C58DF3.95FE2F80" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C58DF3.95FE2F80 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.economist.com/printedition/PrinterFriendly.cfm?Story_ID=4197737 Economist.com 3D""=20
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Modelling conflict

Rules of=20 engagement
Jul 21st 2005
From The Economist print=20 edition


Scientists find surprising regularities in war and=20 terrorism

ON JULY = 19th,=20 IraqBodyCount, a group of academics who are attempting to monitor the = casualties=20 of the conflict in that country, published a report suggesting that = almost=20 25,000 civilians have been killed in it so far. In other words, 34 a = day. But=20 that is an average. On some days the total is lower, and on some=20 higher=97occasionally much higher.

It is this = variation=20 around the mean that interests Neil Johnson of the University of Oxford = and=20 Michael Spagat of Royal Holloway College, London. They think it is = possible to=20 trace and model the development of wars from the patterns of casualties = they=20 throw up. In particular, by analysing IraqBodyCount's data and comparing = them=20 with equivalent numbers from the conflict in Colombia, they have = concluded that,=20 from very different beginnings, these conflicts are evolving into = something=20 rather similar to one another.

The = groundwork for this=20 sort of study was laid by Lewis Fry Richardson, a British physicist, = with a=20 paper on the mathematics of war that was published in 1948. Using data = from=20 conflicts that took place between 1820 and 1945, Fry Richardson made a = graph=20 displaying the number of wars that had death tolls in various ranges. = The=20 outcome was startling: rather than varying wildly or chaotically, the=20 probability of individual wars having particular numbers of casualties = followed=20 a mathematical relationship known as a power law.

Power-law = relationships=20 crop up in many fields of science and are often a characteristic of = complex and=20 highly interacting systems (which war certainly is). Earthquake = frequencies and=20 stockmarket fluctuations are both described by power laws, for example. = Power=20 laws also have properties that make them different from statistical=20 distributions such as the normal curve (or bell curve, as it is = familiarly=20 known). Unlike a bell curve, a power-law distribution has only one tail = and no=20 peak. Small tremors occur frequently, but over a few decades enormously = large=20 earthquakes will also occur with reasonable frequency. As will deadly = wars and=20 attacks.

In May, = Aaron Clauset=20 and Maxwell Young, of the University of New Mexico, modified Fry = Richardson's=20 method to look at terrorist attacks. Instead of total casualties in a = conflict,=20 they plotted the deaths from individual incidents. Again, they got a = power law.=20 Actually, they got two. Power-law relationships are characterised by a = number=20 called an index. For each ten-fold increase in the death toll, the = probability=20 of such an event occurring decreases by a factor of ten raised to the = power of=20 this index, which is how the distributions get their name. Terrorist = attacks=20 within G7 countries could be distinguished from = those=20 inside non-G7 countries by their different = indices. G7 countries were more likely to suffer large attacks. = Indeed, in=20 an article published earlier this year by Britain's Institute of = Physics, Mr=20 Clauset and Mr Maxwell said that =93if we assume that the scaling = relationship and=20 the frequency of events do not change in the future, we can expect to = see=20 another attack at least as severe as September 11th within the next = seven=20 years.=94

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Dr Johnson = and Dr Spagat=20 took the method a couple of steps further. They extended Mr Clauset's = and Mr=20 Maxwell's idea of looking at the sizes of individual incidents within a = campaign=20 to other sorts of conflict, and also looked at how those conflicts have = changed=20 over time. As they report in a paper published recently in arXiv, = an=20 online archive, they found, yet again, that the data follow power laws. = And for=20 both of the wars they studied, the indices of those power laws have been = approaching the value Mr Clauset and Mr Maxwell found for non-G7 terrorism, though from different directions. In = other words,=20 for the war in Iraq, the data indicate a transition from an index = characteristic=20 of more lethal, conventional war between armies to one closer to = terrorism. No=20 real surprise there, perhaps, though it is interesting to see = perceptions on the=20 ground reflected in the maths. For the Colombian conflict, though, the = data show=20 the opposite, a transition from a war characterised by smaller, less = cohesive=20 forces to a more unified rebel front=97something that ought to worry = Colombia's=20 government.

Dr Johnson = and Dr Spagat=20 put forward as an explanation a mathematical model they have developed. = It=20 consists of a group of self-contained =93attack units=94, each of a = particular=20 strength. Such units can join together or fragment into smaller pieces. = Over=20 time, an equilibrium of joining and breaking is reached, but where that=20 equilibrium lies depends on the strength of any central organisation. = The model=20 explains the power-law behaviour seen in both conventional wars and = terrorist=20 attacks. Different rates of fragmentation lead to different = indices=97conventional=20 war is fought with robust armies that are unlikely to fragment, while = terrorists=20 are more likely to have shifting alliances.

Dr Spagat = points out=20 that, if their model is correct, it makes casualty data useful in a = situation=20 where intelligence about the enemy is hard to come by=97as seems to be = the case in=20 Iraq at the moment. For instance, it should be possible to distinguish = an=20 insurgency with a rigid command structure from a group of smaller, = randomly=20 linked units. Learning about the distribution of earthquakes may not = prevent the=20 Big One, but for war and terrorism, power-law statistics may teach = governments=20 something about how to defeat the enemy, and make war less = deadly.


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Copyright =A9 2005 The Economist Newspaper = and The=20 Economist Group. All rights reserved.
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