In Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences (Dover Publications, 2006), the physicist Wolfgang Weidlich develops a model of some aspects of human communities; his model is developed bottom-up in a manner similar to the development of a model of an industrial process or of (allegedly) well-defined human activities. Weidlich is wise enough to qualify his efforts by acknowledging that there are aspects of human communities which can’t be modeled in a quantitative manner.
Weidlich engages in what I would consider traditional modeling, an activity running pretty much parallel to the modeling of an industrial process such as the mixing of gases or liquids or even the modeling of a more complex system where multiple processes are involved as well as human workers. It is also a form of modeling which assumes the whole is the sum of its parts, though undoubtedly many `emergent’ properties can arise in a complex, sophisticated model. Again, Weidlich freely admits and intelligently discusses some of the ways in which the whole is greater than and different from the sum of its parts, but this type of methodology tends to separate a complex entity into sorts of being which are hard to again see as one entity. Sometimes, this will be a matter of separating the local (such as the individuals) and the global (the communities). In fact, in some of the somewhat successful models of economies of or other aspects of complex human communities, the individual disappears. In other somewhat successful models, such as that of Weidlich, the individuals are summed up in an additive way that isn’t quite convincing.
I’m advocating the use of models in which the local and the global are somewhat separate but are part of one coherent model, as in a Riemannian manifold where the geometry in a small region of a point is Euclidean, that of a Euclidean plane tangent to the point, but the manifold has a global geometry which might be very complex and very much non-Euclidean. There is nothing in Weidlich’s model which can truly be labeled as `global’ and this is true also of other models I’ve discussed in recently published essays.
I’m not advocating a direct use of the differential geometrical techniques which have worked so well in science and engineering—most famously in the general theory of relativity. I’m advocating rather a step towards the realm of the most abstract form of created being, the truths which the Almighty manifested as the raw stuff of Creation. Since these realms of being have complicated relationships in themselves and with other realms, then we have to work in a manner largely empirical. learning about reality from reality, learning how to think by observing how the objects of our thought actually behave. Let me take a situation, that of the American people and the United States. In a recent essay, Do We Need Conflict to “Drive the Rise of Ultrasociality”?, I wrote:
A people can be nonviolent and well-meaning in the small but, in the large, as a people, can be murderous and thieving war-mongerers. In recent centuries, some of the most violent nations have been those with populations made up of individuals who are law-abiding and even somewhat gentle by historical standards: Germany in 1914-1945, Japan in the 1920s through the 1940s, Great Britain during the years of Empire and a bit beyond, the United States through much of its existence as loosely connected colonies up to now and still going strong though maybe about to run out of gas.
The global (national) properties of Americans in the form of the American people are much different from the local (personal) properties. This difference between, say, the individual and the community is perhaps necessary and likely to be a good thing in many cases, but not in this case. More importantly for now, we should recognize that a qualitative (think of traditional historical or political analysis) or quantitative model of a complex human community can’t be built up by simply summing up the behavior of the individual members of the community. On the other hand, models such as that of Turchin and colleagues (which I discussed in Mathematical Models of Human History: Are They Plausible? and Do We Need Conflict to “Drive the Rise of Ultrasociality”?q) succeed in exploring specific aspects of human communities by modeling those human communities as independent entities with no relationship to the individual members of those communities. In the end, much is missing. The model of Turchin as his colleagues can tell us Central Asian nomadic warriors had a great effect on the development of complex societies in the Fertile Crescent and then upon the expansion of such complexity into other regions. They don’t tell us, aren’t set up to tell us, what qualities separate the barbarians who destroy and leave from those who conquer and stay as successful rulers. There is much else they can’t tell about many important matters different from, perhaps at a finer-grain, than the geographical spread of civilizations and military technology.
Again: I’m advocating that we try to develop models of human being, individual and communal, by abstracting from the more sophisticated models of physical science such as that used in the general theory of relativity where local regions of space are Euclidean and larger regions are curved in non-Euclidean ways. There might be a model in the state-space (undefined as yet in any authoritative way) in which regions around a single state (of a single entity?) are Euclidean and larger regions might have a non-Euclidean geometry. As is true of the general theory of relativity, large might include larger mass as well as larger distance. Other possibilities will likely arise.