. . . we study the frequency and severity of terrorist attacks since 1968. We show that these events are uniformly characterized by the phenomenon of scale invariance, i.e., the frequency scales as an inverse power of the severity, . . .Clauset et al., 2007 (pdf)
As we enter this season of peace, I find myself reflecting on war. And scale invariance.
The work cited above is old, and has been digested for some time. To recap, the frequency of terrorist events varies inversely as the square of the severity (typically measured in casualties)--and this relationship is independent of time selected, targets, weapon type, or responsible group. Even massive attacks, such as the September 11 attacks do not represent outliers, but form part of the statistical continuum of "normal" terrorism.
I've extended this graph to include a few other events.
In this chart, D represents recent estimates of the deaths during the Dresden firebombing, N1 represents deaths from the nuclear bombing at Nagasaki, T represents deaths during one particular firebombing raid of Tokyo, H represents deaths from the nuclear attack of Hiroshima, and N represents deaths during the massacre of Nanking.
We commonly carry out similar analyses for the purposes of risk assessments for natural hazards such as earthquakes. If we know the recurrence interval for small events, we can estimate the recurrence interval of very large events, provided the size-frequency distribution is characterized by scale invariance. We can carry out a similar assessment here. Unfortunately, we don't really know the recurrence interval of an event like the September 11 attack--but let us assume here that September 11 represents the largest terror attack one would expect in any 25-year period.
If so, then the recurrence interval for a Dresden would be 2500 years; for Nagasaki, it would be about 7500 years; for Tokyo, about 10,000 years, Hiroshima 15,000 years; and Nanking, about 50,000 years. I note that all of these events happened in the last century.
It seems likely that these state-sponsored events happen on their own frequency curve, which goes to show that nobody can do terror like the modern State.