The fall of empires as an exponential distribution

I was alerted to Samuel’s Arbesman’s new paper, The Life-Spans of Empires, by the fact that he pointed to his research on his weblog. Interestingly I’m not the only one who was interested, as after I pointed to it on my link round up a few people asked if they could get a copy of the paper (yes, I almost always send papers if I have access). Luckily it’s a nicely elegant piece of work, basically quantifying what we’ve already probably known qualitatively. There isn’t that great of a value-add to quantification as such, but with a mathematical understanding of a topic one can engage in an algebra of mental manipulations so as to construct models with which one can project other facts. Quantitative information is often an excellent way to generate “free information” from theoretical models. The figure above is the primary result of the paper. Basically Arbesman took a data set which was laying around which measured the lengths of various empires (N = 41), and showed that the rise and fall of these political entities tends to follow an exponential distribution: e−λt . …