Peter Turchin likes to cast himself as a bit of a rebel "against the establishment", despite the fact that he's one of the most prominent academics in that esta

Peter Turchin likes to cast himself as a bit of a rebel "against the establishment", despite the fact that he's one of the most prominent academics in that establishment. What you are understanding from that statement is, unsurprisingly, very uncontroversial. To understand what Turchin is actually saying though, it's worth framing the underlying paper: Turchin is a big advocate of something he calls cliodynamics, which is essentially psychohistory. One of the fundamental assumptions underlying it is that all of human history obeys uniformitarian rules and thus figuring out those rules is simply a matter of having enough data. So, he's spent the past while gathering a dataset and in this paper does PCA against it to find the variables that are most correlated with his measure of social complexity. Where most people would find issue is with the underlying assumptions there. A lot of people don't agree that human history obeys uniformitarian rules and if they do, they don't necessarily agree with lumping different societies together in a PCA.