From: Subject: =?Windows-1252?Q?news_@_nature.com=A0-=A0Don't_panic=2C_it_might_never_?= =?Windows-1252?Q?happen=A0-=A0A_mathematical_study_of_terrorist_attacks_n?= =?Windows-1252?Q?eed_not_leave_us_fearing_the_worst=2C_says_Philip_Ball.?= Date: Tue, 1 Mar 2005 19:07:05 +0100 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C51E91.DBB5E7B0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C51E91.DBB5E7B0 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.nature.com/news/2005/050214/full/050214-20.html =EF=BB=BF news @ = nature.com=C2=A0-=C2=A0Don't panic, it might never happen=C2=A0-=C2=A0A = mathematical study of terrorist attacks need not leave us fearing the = worst, says Philip Ball.
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Published online: 18 = February=20 2005; | doi:10.1038/news050214-20

muse@nature.com: Don't panic, = it might=20 never happen

Philip=20 Ball
3D""=20
A = mathematical=20 study of terrorist attacks need not leave us fearing the = worst, says=20 Philip Ball.
3D""=20
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Karl Marx believed that = history=20 unfolded according to an underlying=20 = law.

Statistically speaking, it = seems that=20 things can only get worse. A study of the statistics of = global=20 terrorism concludes that attacks will become more severe in = the=20 future, and that an attack that kills as many people as the=20 destruction of the World Trade Center on 11 September 2001 = is likely=20 within the next seven years1<= /A>.
It all sounds=20 very depressing and seems to imply, depending on your = viewpoint,=20 either that the 'war on terror' is essential or that it is = futile.=20 But can we really assert these things based on statistics=20 alone?

Computer scientists Aaron Clauset and Maxwell = Young of the=20 University of New Mexico, Albuquerque, have analysed the = data on=20 terrorist attacks compiled by the National Memorial = Institute for=20 the Prevention of Terrorism in Oklahoma City. They say the = numbers=20 follow a 'power-law' relationship.

A graph of = the number of=20 attacks n plotted against their severity x (in = terms=20 of injuries and/or fatalities) reveals that n is = roughly=20 proportional to x -1.85. Put simply, this = means=20 that the frequency of attacks decreases as their size = increases -=20 which is what you'd expect - but also that this relationship = holds=20 for events ranging from those that injured or killed just a = few=20 people to those that, like the Nairobi car bomb in August = 1998,=20 produced over 5000 casualties.

Startling = implications
This might=20 sound like no more than a formal way of presenting the = statistics,=20 but the power-law relationship has startling implications. = For=20 example, Clauset and Young say that the statistics suggest a = strong=20 probability of an attack as devastating as that on the World = Trade=20 Center within seven years.

And the power-law = relationship implies=20 that the biggest terrorist attacks are not 'outliers': = one-off=20 events somehow different from the all-too-familiar suicide = bombings=20 that kill or maim just a few people. Instead, it suggests = that they=20 are somehow driven by the same underlying = mechanism.
3D""=20 So far as there are laws = in=20 history, laws are worth nothing and = history is=20 worth nothing. 3D""=20

Friedrich=20 = Nietzsche
<= /TD>
3D""=20
3D""=20
Similar power-law relationships between size and = frequency=20 apply to other phenomena, such as earthquakes and = fluctuations in=20 economic markets. This indicates that even the biggest, most = infrequent earthquakes are created by the same processes = that=20 produce hordes of tiny ones, and that occasional market = crashes are=20 generated by the same internal dynamics of the marketplace = that=20 produce daily wobbles in stock prices. Analogously, Clauset = and=20 Young's study implies some kind of 'global dynamics' of = terrorism.=20

Moreover, a power-law suggests something about = that=20 mechanism. If every terrorist attack were instigated = independently=20 of every other, their size-frequency relationship should = obey the=20 'gaussian' statistics seen in coin-tossing experiments. In = gaussian=20 statistics, very big fluctuations are extremely rare - you = will=20 hardly ever observe ten heads and ninety tails when you toss = a coin=20 100 times. Processes governed by power-law statistics, in = contrast,=20 seem to be interdependent. This makes them far more prone to = big=20 events, which is why giant tsunamis and market crashes do = happen=20 within a typical lifetime. Does this mean that terrorist = attacks are=20 interdependent in the same way?
Universal = history

This touches on a deep, difficult and = long-standing=20 question that has divided historians for centuries: are = there=20 universal laws governing human history?
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Positivist philosopher = Auguste Comte=20 suggested that there are robust laws of social=20 = behaviour.

= Immanuel Kant, writing in his = essay Idea=20 of a Universal History from a Cosmopolitan Point of View = (1784),=20 proposed that "Individual men, and even whole nations, = little think,=20 while they are pursuing their own purposes...that they are = advancing=20 unconsciously under the guidance of a purpose of nature = which is=20 unknown to them."

The idea that there are = robust laws of=20 social behaviour analogous to the laws of physics - laws = which are=20 beyond our power to change - is what underlay the = 'positivist'=20 philosophy of Auguste Comte in the 1830s. It moved Leo = Tolstoy to=20 ask: "What is the force that moves nations?" A belief in the = 'law-like' unfolding of history and economics also provided = the=20 foundation of Karl Marx's theories, and it continues to = inform the=20 thinking of Marxist historians today.
In contrast, = what one=20 might call the 'Great Man' view of history, championed by = Thomas=20 Carlyle in the nineteenth century, holds that this sort of=20 positivism is a chimera and that history is instead a much = more=20 contingent affair whose course is determined by the rise of = powerful=20 figures such as Napoleon and Hitler. Friedrich Nietzsche had = a=20 strong sympathy for this position: "So far as there are laws = in=20 history," he said, "laws are worth nothing and history is = worth=20 nothing."

So does global terrorism operate in a way that = individual=20 states or initiatives cannot hope to control, or can a = concerted=20 effort to eliminate it reshape the power-law statistics of=20 attacks?

Deadly quarrels
British = physicist Lewis=20 Fry Richardson made a similar study between the 1920s to the = 1950s.=20 He collected data on "deadly quarrels": fatal conflicts = ranging from=20 small local skirmishes to world wars. He found that their=20 size-frequency distribution also followed a power law. =
When=20 Richardson published his findings in 1960, they seemed to = convey a=20 very gloomy message: wars were apparently getting bigger, = and the=20 two biggest events had occurred only 25 years apart in the = very=20 recent past. It looked as though the world was headed for = another,=20 even more deadly war. But in reality, changes in global = politics=20 altered the very nature of wars. They did not by any means = go away,=20 but they are now fought for different reasons and in = different=20 ways.

Clauset and Young are careful to point out that = their own=20 doom-laden forecasts assume that the power-law relationship = for=20 terrorism, based on 36 years of data, will continue to hold = in the=20 coming decades.

ADVERTISMENT
Although=20 it may be tempting for people to read the predictions as a = form of=20 statistically driven determinism, we must remember that = statistics=20 do not themselves have any motive agency in the real world. = For=20 example, when eighteenth-century statisticians discovered = that the=20 annual frequency of crimes obeyed gaussian statistics, some=20 interpreted this as evidence for a kind of 'social force' = that=20 compelled some people to commit crimes.
It is sadly = possible, of=20 course, that Clauset and Young's predictions will come to = pass. But=20 it is worth bearing in mind that several apparent power-law=20 statistics in social phenomena have turned out, on closer=20 inspection, to have natural cut-off points that preclude = very large=20 events2<= /A>.=20 And whatever the case, we should be wary of predictions = based purely=20 on statistics. History teaches us that it is possible, = sometimes, to=20 change the rules that generate them.
3D""=20 3D""=20 T= op
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References
  1. Clauset A. & Young M. = Preprint=20 http://xxx.arxiv.org/abs/physics/0502014=20 (2005).=20
  2. Amaral L. A. N., Scala A., = Barth=C3=A9l=C3=A9my M.=20 & Stanley H. E. Proc. Natl Acad. Sci. USA = ,=20 97. 11149 - 11152 (2000). | Article | PubMed | ChemPort |
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