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VoiceOfRa comments on No peace in our time? - Less Wrong Discussion
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What does "turning point" mean in the context of a power law distribution?
The simplest power law , a*x^k has two parameters which govern the overall location and the fatness of tails, I think. You could expect a change in either or both. So you could fit a time-series model in which a and k can change each year by an amount drawn from a distribution, and then see whether the data supports a large net change since 1945? This is what I take Stuart as suggesting.
The problem is that you can't estimate 'k' well enough, at least that's what Taleb argues at various places.
The available data must support some range of ks, some precision, and if allowing any shift of k over time indicates that k has fallen a lot lately, that's pretty bad for their theory. If they say you should ignore the data, then they're doing theology.
The point is range of ks is quite large. That's what Taleb's work as a professor of Risk Engineering is about.
If the range of ks is large then the posterior probability of a shift (or to put it another way, the estimated probability that pre-WWII ks differ from post-WWII ks) will be appropriately small and Taleb will have demonstrated what he wants to demonstrate without so much rhetoric and an analysis that largely misses the point.