Though my inclination is to be skeptical, I have not even read the whole Nature piece, let alone the footnoted article. It struck me as interesting, however, that it was left to a commenter on the Nature article to mention Kondratieff cycles, which are posited 50-year swings in economic activity. Apparently the author of the piece didn't think the parallel was worth noting. And indeed, there are significant differences between (postulated) economic cycles and (postulated) political cycles. The former are somewhat less obviously and directly linked to or entangled with individual agency. (Not everyone will think that a valid point, of course.)
The notion of cycles of unrest/stability is not new; I believe that, w/r/t the U.S., Huntington's American Politics: The Promise of Disharmony made this kind of argument. Schlesinger's The Cycles of American History did too, though, I would guess, in a somewhat different way.
But, to quote the Nature piece:
What is new about cliodynamics isn't the search for patterns, Turchin explains. Historians have done valuable work correlating phenomena such as political instability with political, economic and demographic variables. What is different is the scale — Turchin and his colleagues are systematically collecting historical data that span centuries or even millennia — and the mathematical analysis of how the variables interact.Especially since I'm not going to understand the details of the mathematical analysis, who am I to say he (or they) shouldn't do this? Let a hundred flowers bloom, and it'll all come out in the wash. Or something like that.