making definitions of complexity clear

This post continues my discussion about (1) the need for researchers to be clear about the definition of complexity they use and (2) to make sure that they test or demonstrate that the system they are studying actually meets the criteria of their definition.

As I have said in previous postings, I am not advocating a strict realist definition of complexity, such that the definitions researchers use and then test have to reveal the fundamental reality of the object they are studying as complex. One can use complexity as a metaphor (as in the case of postmodern complexity), as a proactive concept (as in the case of the leadership literature) or as a empirically useful way of describing something (as in the case of the natural and artificial sciences). What I am saying, however, is that one's definition should be rigorously applied.

My second and related point is that we need rigor in our definitions to bring together the otherwise disparate areas of study in complexity science. Synthesis in complexity science will not come through the construction of a singular definition. Instead, synthesis will come from researchers empirically, proactively, or metaphorically demonstrating that the definitions they use form a gestalt--a whole that is greater than its parts. And, it should be clear to readers and fellow researchers how the components of one's definition go together.

As a final point, researchers need to be careful that they do not move in and out of empirical to proactive to metaphor in their definitions. To me, this type of intellectual slippage is one of the major ways that scholars in the social sciences and humanities get into trouble with their usage of complexity science.

For example, a scholar will empirically demonstrate how a particular system of study is self-organizing. With this success, the scholar will proceed to make a whole bunch of additional definitional assumptions that the proof of self-organization means the system is also agent-based, network-like in structure, and nonlinear (one of the most misused mathematical terms by social scientists and humanities scholars). The term nonlinear, for example, is almost always used in a metaphorical way by social scientists and humanities scholars, to suggest that a social system is messy, not easily managed or controlled or not easily understood via statistical method. In actuality, nonlinear means that the system or, more specifically, the equation or equations used to understand a system are such that their output is not directly proportional to their input. In other words, when the term 'nonlinear' is used in a realist sense, it means that the system being studied and the factors of which it is comprised cannot be written as a linear combination. Furthermore, as a system, these equations are therefore usually impossible to solve, except through computational methods that provide proximate solutions; and the problems are often unstable, that is chaotic, operating near chaos, etc. So, if the researcher has empirically demonstrated that a system is self-organizing but uses the term nonlinear in a metaphorical manner (which may be close to its correct usage but not quite), then the researcher is really causing definitional confusion through a lack of rigor and clarity. For such a researcher to proceed to response to critics (who are rightfully confused) by arguing that the lack of clarity in his or her work is a function of studying complexity--when it is really a failure in the usage of some of the components in her or his definition--is to perpetuate rather than solve the problem they are working so hard to address.

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