On Boxing Day (December 26) 2004, a tsunami resulting from a 9.0+ magnitude earthquake killed about 250,000 people around the Indian Ocean. This was one of the deadliest natural disasters in recorded history. The Indian Ocean tsunami illustrated a major theme on this blog: the importance of catastrophes in human history, and in the history of life and the universe.

Earthquakes are one example of a phenomenon following a power law statistical distribution. The frequency of earthquakes drops off as an exponential function of their magnitude, so that on a logarithmic scale, the magnitude-frequency relationship looks linear. This is known as the Gutenberg-Ritter relation. (The deviation from linearity in the upper left part of the chart below may reflect measurement error, with a lot of tiny earthquakes not being detected.)

Power law distributions are found in many other contexts, for example, in the frequency of wars versus their magnitude (as measured by the number of war deaths). A power law distribution is very different from the more familiar bell-curve Gaussian normal distribution: extreme “black swan” events that are astronomically unlikely under a normal distribution may happen at appreciable frequency under a power law distribution. Depending on the exponent, a power law distribution may not have a well-defined variance, or even a well-defined mean.

For a technical discussion of why small scale processes sometimes aggregate to generate normally distributed outcomes, and other times aggregate to produce power law distributions, here’s an article on The common patterns of nature. A take home lesson – not always covered in introductory treatments of statistics and probability theory – is that catastrophes and extreme outcomes can be an expectable part of the natural order.

Steven Pinker and Nichlas Nassim Taleb have squabbled about the implications of all this for the probability of a peaceful future. Here’s a level-headed review. Several recent books carry this argument further. In Only the Dead: The Persistence of War in the Modern Age, Bear Braumoeller makes the case there is no good reason to think that war is in decline. Rather “international orders” – whether the nineteenth century Concert of Europe, or the post World War II liberal order – have often made for peace among participants *and* conflicts with non-participants. On the other side, in The Stupidity of War: American Foreign Policy and the Case for Complacency, John Mueller makes the case that the likelihood of war was and is greatly exaggerated, both during and after the Cold War, and argues for the virtues of complacency and appeasement. Of course this year’s Russian invasion of Ukraine forces us to revise our estimate of the probability of major war upward, but it doesn’t prove Pinker wrong: a snow storm in April doesn’t prove that March isn’t a wintrier month.

And here are a couple of blog posts from me about why the bloody early twentieth century was maybe more than just a run of bad luck.