Another analytic view about quantifying social forces

TL;DR

This paper offers an alternative physics-inspired approach to quantifying social forces using logistic and Gompertz models, analyzing temple construction as a case study to reveal different regimes and external influences.

Contribution

It introduces a novel application of logistic and Gompertz functions to quantify social forces, moving beyond Montroll's original concept and emphasizing the role of external constraints and population capacity.

Findings

Identified two distinct temple inauguration regimes in Belgium (1910-1940).

Quantified social force as a change in construction rate influenced by external constraints.

Emphasized the importance of impulse force duration within the Gompertz framework.

Abstract

Montroll 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 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/capacity of some population, coupled to some external field, in either Verhulst or Gompertz equation, rather than resulting from already existing but competing goods as imagined by Montroll.