If nothing is predictable, all is at the edge of chaos, and behaviors always emerge unexpectedly in Nature, it follows that no rigorous, methodical, controlled approach is possible. That is how the pop-complex enthusiast does reason (and often explicitly states, such as, e.g., in some essays on emerging behavior and Darwinian evolution).
In her mind, all we are left with are animistic beliefs or at most some organized religious scheme. In the [few] more sophisticated cases, the pop-complex zealot accepts at most the notion of numeric simulations: scientific investigation is reduced to studying the behaviour of complex adaptive systems.
[Nota bene: We are not talking about hard-science researchers here. We are referring to approaches in the popular literature about complexity, such as the one on complexity and management, complexity and human organizations, complexity and psychology, complexity and medicine, etc.].
Now, why is this happening? Because many people, including intellectually gifted people such as some of the pop-complex exponents, are afraid of mathematics. Math repelled many if not most of us in mid and high school. And those who did not venture into “hard” scientific studies afterwards have remained forever preys of such repulsion.
To these folks, mathematics is the hallucinating and monstrous sequence of untameable formulae that we remember from when we were fifteen: a deterministic mechanism (two of the most recurring, obsessive words in pop complexity) that needs to be followed pedantically in order to get to some predefined result.
The learned person knows that mathematics is quite another thing, and that our teen-age recollections aren’t but the exercises that we were given in order to make sure that we were learning the concepts and acquiring an inclination for precision. (Similarly, Latin literature is about reading Virgil, Ovid and Horatius, not inflecting nouns and conjugating verbs. However we need the latter in order to progress to reading).
Like music, mathematics is about creativity, abstraction and beauty, not merely exactitude. Vast parts of mathematics and formal logic aren’t exact at all, as they involve estimating, approximation and guessing. Math isn’t deterministic, either: one of its quintessential activities, giving proofs, is profoundly non deterministic.
The fortunate Italian reader who questions our words is welcome to reading Discorso sulla matematica by Gabriele Lolli (Bollati Boringhieri 2011), where the author equates the fundamental mathematical methods to the literary ones discussed by Italo Calvino in his Lezioni americane (1985-1988), namely
(A book for which we anxiously wish an English edition.)
If pop complexity authors really studied mathematics as opposed to just some of its grammar, they would learn how to position non-linear phenomena and complex approaches under the light they deserve, instead of drawing caricatures.