rare events

(in reply to this blog post)

According to this chart we should  expect a 9/11 every 50 years, a mega-9/11 (where 30,000 people die in a terrorist attack) once every 500 years, a mega-mega-9/11 (where 300,000 people die in a terrorist attack) once every 5000 years, and so on. (Watch out for that terrorist asteroid in 6567, it's a doozy!)
The interesting thing about this from a mathematical perspective is that there is no "average number of deaths from a terrorist per year." If you average over a short period of time, you get a small number of deaths per year; over a longer time you get a larger number per year, and this continues without limit, because the rare mega-mega-mega-event dominates the entire time interval. If you've ever heard of the "length of the coastline" problem, this is a similar issue-- the length of a coastline depends on the length of your ruler.
This also means that, in the long run, there is no price high enough to insure against this kind of disaster. No matter how much the insurance company charges, eventually there will be a big enough disaster to make the company unable to pay out. Tropical rainfall and earthquakes have shown a similar fit.
This is also the root of the trouble in the St. Petersburg paradox.