So I recently finished Taleb's book The Black Swan, which is basically about the gross misuse of Gaussian distributions to predict a lot of (important) things that do not, in fact, behave on anything like a Gaussian curve. It's good stuff, an easy read (unlike myself, he has an editor that doesn't mind "cahatty"), and it resonates. A lot of it is obviously right and a lot of the criticism I've read of it hinges on the fact that it can't supply a replacement for the Guassian. As though being wrong but having something to do was better than acknowledging rates of error. I hear the cry, "But we have to do SOMETHING," often enough at work that I can commiserate. Of course we have to do something. We have to acknowledge and measure rates of error rather than assume they follow a curve that WE KNOW THEY DON'T.
Anyway, there's an underlying idea in there that runs even deeper than Taleb hints at. The idea that things "average out". Wedging data into Gaussian curve is one way of assuming this, but apparently in the field of anthropology it's been happening (and is being addressed) as well.
I recently ran into an old friend who I haven't seen for some 30 years. He's an anthropologist (or at least he lectures on it). We chatted and of course I overshared and even got grabby about his area of expertise. He was researching "agency" in anthropology and so I asked for some papers so I could understand what it was about.
Now, keep in mind that I have very little background study in anthropology, so my cursory analysis is probably way off (I certainly had trouble with many "terms of art" in the papers I read and occasionally made the almost certainly wrong assumption that they meant something like the plain English they seemed to. This doesn't work in any other field, so I don't know what I was thinking). Anyway, agency is the idea that a culture does not follow a trajectory that is defined by a vector for progress or even maintenance. That is, if cultures develop to "improve", we expect to see universal adoption of "better" tools when they arrive. We don't actually see that. While there is an eventual adoption of many, there is also a lot of clinging to inferior tools (I recently fought the emacs versus vi fight at work and had to deal with a whippersnapper who was hot on some new GUI thing, so I know how this works) for apragmatic reasons.
So the theory of agency says that you have to treat a culture as an aggregate of free-willed individuals who do not necessarily make pragmatic choices on average. They preserve suboptimal methods and tools for personal or political reasons. They like the texture of coarser corn meal because it's what they ate when they were kids. The process of chipping stone tools remains a skill that is revered and that reverence is sustained by them long after iron tools are available. And so on. Individual agency, then, impacts cultural development.
So here's the synthesis.
Gaussian curve users have as their core assumption that things average out. Yes there are outlying data points, but in general they cancel out and are rare and so things tend towards the mean. It turns out that's just not true about almost everything. It's true about average height. It's not true about average salaries.
Old school (non-agency thinking) anthropoligists seem to similarly assume that the actions of individuals average out culturally. That the whims of agency are outliers on a curve of change that is essentially pragmatic.
For data like salaries (or stock fluctuation, or coastline length, or deaths in warfare, or whatever), the curve is essentially fractal. That is, the variation at a fine scale is self-affine (self-similar if you must, but actually self-affine) with the variation at larger scales. The bottom 50% of salaries follow a curve that looks remarkably similar to the top 1%, shifted down.
And so it seems that anthropology is starting to discover that agency is self-affine with culture. That cultures reflect not the mean of all individual free-willed choice, but rather the whole spectrum of preference. The vagaries of personal preference and memory and politics and love are in fact reflected in the gross details of culture rather than submerged in a torrent of dissimilar data. On reflection this even seems obvious -- what can a culture BE except a novel expression of the finer details of its members? If it were some grey mean of behaviour, the similarity between cultures would surely be much greater than it is.
I'll close by again acknowledging that I may have found this correlation by virtue of failing to understand either idea sufficiently. But the concept of self-affine behaviour over differences in scale seems a natural result of the mathematics of non-Gaussian variation and certainly the impositions of free will cannot be considered Gaussian as they lack natural limits. They are necessarily, as per Taleb, from Extremistan.
How about that, huh? Gauss, fractals, and anthropology, and I didn't once mention memes (oops). Next time.