You're correct in attacking the math the authors use. It's clear they are bending the math to fit the phenomena. However, that doesn't invalidate the hypothesis

You're correct in attacking the math the authors use. It's clear they are bending the math to fit the phenomena. However, that doesn't invalidate the hypothesis. This paper appears heavily influenced by Nassim Nicholas Taleb: systematic failure, bounded vs unbounded variance, (more data) => (more noise) => (more spurious relationships), natural vs artificial systems, and even the reference to the heuristics of ancient cultures. It looks like the authors were trying to apply math to observed phenomena. They may not have the right math to make it work-so they fudged it a bit. Nassim talks about similar phenomena here: http://arxiv.org/a/taleb_n_1.html http://arxiv.org/a/taleb_n_1.html