My struggle with the many views on complexity continues. I have now managed to synthesize five “megaviews”.The taxonomy is certainly not definitive, but if anything it’s a step ahead compared to my 2008 book as well as to Seth Loyd’s old 32 different definitions…
Here are the five major meanings of “complexity” that you will find in any literature, whether scientific or fictional, and their respective overlaps. Even the colloquial use of the term is included here: when just anybody utters the word, one or more of these meanings is implied.
Nonlinear (or dynamical) meaning: The effects caused by mutual interactions between the components of a [nonlinear] dynamical system. These may include feedback, emerging behaviour, self-organization, unpredictability and non-deterministic chaos.
Computational (or static) meaning: The computability of a function or algorithm; the time and/or effort it takes to solve a problem. The intersection with nonlinear complexity occurs, in my opinion, via the concept of Kolmogorov entropy.
Epistemological meaning: This is originally due to Edgar Morin (and in lesser part to Isabelle Stangers and Ilya Prigogine) but is being refined. See. e.g., Minati, Pessa, Collective Beings, Springer, 2007. Sample issues: What does “system” mean? What does “component” mean? What does it mean that a component may belong to both complex and non-complex systems at the same time? How does the observer modify the object of her investigation?
Literary meaning: See e.g. Jorge Luis Borges or Carlo Emilio Gadda. Gadda, for example, published in 1946 a detective story (Quel pasticciaccio brutto de via Merulana) that does not come to an end: the mystery cannot be solved because reality is too complex. Detective Ciccio Ingravallo cannot reach the ultimate causes or motives of the murder, because causes not only produce effects but also are affected by these and influence each other. Gadda’s literary view overlaps with both the nonlinear meaning and the computational one (reality as a “ball of thread”), although this latter intersection is not represented in my graphic -the nonlinear intersection is prevalent anyway.
Hyperbolical (or fideistic) meaning: Most books, papers and writings of sort on complexity for management, organizational theory, psychology. This literature attempts to draw from both the epistemological and the nonlinear one, but in most cases doesn’t get much of either and usually degenerates in a banal anti-scientific approach. On a mission from God to liberate the world from determinism and reductionism, its authors believe that all is chaotic, no predictions whatsoever can be made and Nature escapes human insight entirely.