Measures of complexity: a nonexhaustive list

Abstract

The world has grown more complex recently, and the number of ways of measuring complexity has grown even faster. This multiplication of measures has been taken by some to indicate confusion in the field of complex systems. In fact, the many measures of complexity represent variations on a few underlying themes. This column presents an (incomplete) categorization and tabulation of measures of complexity. An historical analog to the problem of measuring complexity is the problem of describing electromagnetism before Maxwell’s equations. In the case of electromagnetism, quantities such as electric and magnetic forces that arose in different experimental contexts were originally regarded as fundamentally different. Eventually it became clear that electricity and magnetism were in fact closely related aspects of the same fundamental quantity, the electromagnetic field. Similarly, contemporary researchers in architecture, biology, computer science, dynamical systems, engineering, finance, game theory, etc., have defined different measures of complexity for each field. Because these researchers were asking the same questions about the complexity of their different subjects of research, however, their answers have much in common. Three questions that are frequently posed when attempting to quantify the complexity of the thing (house, bacterium, problem, process, investment scheme) under study are 1) How hard is it to describe? 2) How hard is it to create? 3) What is its degree of organization? I use these questions to group measures of complexity. Measures within a group are typically closely related quantities.