Scale, by Geoffrey West, is a thought provoking book about coarse grained quantitative network theories which concern the entire human species and its interaction with the environment. Although verbose — as I think the intended audience is upper high school and entry-level college — it is clear in its depictions and explanations. This book is an important summary of really profound work and research performed at the Santa Fe Institute. And it is a great introduction to understanding power laws and scaling in biology and network topologies.
Category: power law
Do there exist studies on the distribution of the lengths of kingdoms and dynasties — distinct political entities — since the 3rd millennium B.C.E.? It seems likely that someone has already studied this topic, but I can not find any papers online. To explain, I have included a file, here, containing the beginning and end dates of about 700 distinct social groups since the dawn of recorded history. It was complied from various Wikipedia pages. I do not doubt that the data is not very reliable, however, graphing the histogram of these lengths, see Figure 1, would provide at least a rough idea of their distribution.
It does seem that a nice distribution curve exists which models the data. The distribution seems to take the shape of a power law at first glance. Doing some work in R, I found that a power law with one set of parameters fits the tail nicely but fails to fit the first half; and vice versa, a power law with a different set of parameters fits the majority but not the tail. My hypothesis is that a power law with alpha equal to 3 may be the best fit. This is a prediction based on the lectures of Geoffrey West, in which he explains that most biological systems exhibit power law distributions with alpha in the 2.5-3.0 range. However, as seen in Figure 2, this does not seem to be the correct range for alpha if a power law is the best fit for this preliminary data.