Telescopes and Microscopes

Abstract

This is a classic work for several reasons. First is its scholarship. It appears that the author read “everything”! He traces the evolution of feedback thought through such disparate disciplines as economics, cybernetics, political science, psychology, sociology, and management. As he goes, he translates with humility the original authors’ concepts, examples, and drawings into a modern, common one: the causal loop diagram. This permits us readers to share a common denominator for understanding and comparing.

Appendix – Differential Equations and Causal Loop Diagrams

Let me add, as a final note, that feedback loops can be represented mathematically as systems of differential equations or difference equations. And they are represented those ways in the text. For the reader not comfortable with those representations, there are ample verbal explanations and also many diagrams of what the equations symbolize. And many of the diagrams are from the original sources, giving us a view of the variety of representations of what might seem like a simple notion.

Here is an example, from population dynamics. Assume that we are interested in the growth of nationalism in a society (Richardson, pp. 222–227). There are two rate of interest to us: the rate of assimilation (e.g., nationalism) and the rate of mobilization (literacy, political awareness, and urbanization). The total population has two components: the assimilated (nationalized) and the differentiated (not or not yet assimilated). Then these equations capture the dynamics:

The equivalent causal loop diagram drawn by Richardson to help us visualize this system of differential equations is:

In the end, in order to understand dynamic feedback we only have to be able to trace through the loop diagram. There is no closed-form formula for a loop. It is a collection of equations. Differential equations are statements about rates, usually with respect to time. The reason that visual aids are needed is that it is difficult to make inferences from the list of equations: you trace the connections in your mind, so might as well draw them on paper!