Another Analytic View About Quantifying Social Forces

Montroll [Proc. Nat. Acad. Sci. USA75(1978) 4633–4637] had considered a Verhulst evolution approach for introducing a notion he called "social force", to describe a jump in some economic output when a new technology or product outcompetes a previous one. In fact, Montroll's adaptation of Verhulst equation is more like an economic field description than a "social force". The empirical Verhulst logistic function and the Gompertz double exponential law are used here in order to present an alternative view, within a similar mechanistic physics framework as done in [Proc. Nat. Acad. Sci. USA75(1978) 4633–4637]. As an example, a "social force" modifying the rate in the number of temples constructed by a religious movement, the Antoinist community, between 1910 and 1940 in Belgium is found and quantified. Practically, two temple inauguration regimes are seen to exist over different time spans, separated by a gap attributed to a specific "constraint", a taxation system, but allowing for a different, smooth, evolution rather than a jump. The impulse force duration is also emphasized as being better taken into account within the Gompertz framework. Moreover, a "social force" can be as here, attributed to a change in the limited need for capacity of some population, coupled to some external field, in either Verhulst or Gompertz equation, rather than resulting from already acquired but competing goods as in [Proc. Nat. Acad. Sci. USA75(1978) 4633–4637].