Power laws are gathering quite some attention again, thanks to a few new papers (e.g., this one and this one) by Albert-László Barabási and his coworkers, published in Nature. Cosma Shalizi and others disagree: once again, just because some dataset on a log-log plot looks like you could easily fit a straight line to it, it is not safe to conclude that it is a power-law distribution.
One of the papers looks at the letter-writing habits of Darwin and Einstein, and concludes that the response times have a power-law distribution with an exponent of 3/2. The other “reports that the probability distribution of time intervals between consecutive emails sent by a single user and time delays fro eamil replies follow a power law”. Shalizi and Stouffer et al. claim that these are in fact lognormal distributions.
I am wondering if you could ever get a paper published in Nature that looks at some dataset, shows that it has normal or lognormal distribution, draws some overarching and universal conclusions from that, and… and that’s it.
Or, to translate it to the much more mundane language of geologists, that only applies to dirt, not to Einstein’s letters: there is no interesting story in showing that bed thicknesses or sedimentary body sizes have a lognormal distribution, but if it’s a power law, suddenly you can talk about the “scale-independent physics of turbidite deposition” and the importance of non-equilibrium thermodynamics in the geometries of deltas and everything else under the sun.
That’s why power laws are great.