Periodization of History: A theoretic-mathematical analysis

Author: Grinin, Leonid
Almanac: History & Mathematics: Analyzing and Modeling Global Development

Is it possible to apply mathematical analysis to prove a theory that is intended to account for historical processes? Is it possible to develop mathematical models for such a complex subject as historical processes? If we begin to an­swer these two questions starting from the latter, the answer might be an un­equivocal yes, it is quite possible, at least for those aspects of the historical re­search that relies on quantifiable data. What is more, such models are desir­able, as they may reveal some otherwise concealed characteristics of the sub­ject matter. A scholar might discover that she or he had always been thinking mathematically, even though they considered themselves to apply a pure hu­manistic approach to their research.

The answer to the former question is somehow more complicated. When we speak about some global general theories any figures, cycles, diagrams and coefficients cannot prove too much by themselves. Especially, if the respective analysis includes ancient periods for which all the figures are likely to be much too approximate and unreliable. Thus, for general theories covering im­mense distances in time and space, the main proves are a good empirical basis, logics, internal consistency and productivity of theoretical constructions; that is, a theory's ability to explain the facts better than the other theories do. On the other hand, any theory is better when it is supported by more arguments. Mathematical proofs can be rather convincing (when they are relevant, of course); and when a scholar can support her or his conclusions not only with logic and empirical data but also with equations that formalize the detected regularities, for then the value of the respective ideas grow in a rather sub­stantial way. This is especially relevant with respect to those aspects that are more liable to mathematical analysis, for example, those connected with de­mography.