Chaos and Complexity Theories

Chaos and complexity theories, along with fractal geometry, form what came to be called the “new sciences” during the latter part of the 20th century. These sciences, developed in recognition of relativity, quantum theory, and evolution, are based on a general acceptance that “nature”—our environment, planet, universe, and cosmos—is fractaled and turbulent. Here life and death, creativity and stagnation, imbalance and balance dance together in what one observer called an “orderly disorder.” This entry describes the origins of the concepts of chaos and complexity and their application in qualitative research methods today. Furthermore, the entry encourages readers to look at new possibilities in qualitative research, possibilities inherent in the procedure of layering that bring forth the depth and creation of new meaning.

Traditional research methods, quantitative or qualitative, assume a stable and steady universe, as Isaac Newton and others posited. To use Newton's own phrasing, “Nature is pleased with simplicity” and “is conformable to Herself.” Adopting this meta-physical assumption, quantitative researchers developed the concepts of norming and the bell curve. Norming, however, assumes a stable and steady population; it does not work on a population undergoing transformative change. To hearken back to Francis Bacon and his (then) new science, a “new method must be found.” Qualitative research, when it has an emphasis on triangulation, also assumes a steadiness for its tripartite viewing. In fact, the notion of research itself focuses on searching for that which is believed (indeed assumed) to be true, good, useful, and valid. There is a sense of definitiveness to (traditional) research, often stated in an authoritative way as in the phrase “research says.”

Complexity theorists proceed from recognition and acceptance of the indefinite and probabilistic; they realize that nature is complex, not simple (albeit encompassing and using simples). Whatever conformity nature displays is dynamic; that is, our planet, universe, cosmos, and selves all maintain an order even as they undergo constant change. Emergence, self-organization, self-similarity, patterns, and relationships all become important concepts in this new orderly disorder. Observing the universe, we now realize that the night skies are filled not only with twinkling stars but also with “dark energy,” pulsars, exploding galaxies, and “black holes” that devour all they ensnare. Amid all of this disorder, creativity abounds; order still exists, but now our concept is not of a simple stable order but rather is one of a complex order—complex enough to merit the term disorder.

The mathematics used to show patterns of bringing forth the order in this disorder is that of nonlinear equations. Known but neglected during much of the 20th century, these equations gained significance during the latter part of that century with the advent of powerful supercomputers, able to iterate first hundreds and then thousands of times per minute. These equations are nonlinear in that they do not develop straight lines on a graph or even smoothly curved ones. Rather, how they proceed is unpredictable, known only after the fact (i.e., a posteriori). In a nonlinear x/y functional [Page 75]relationship, the xs are not prechosen (except for the beginning or “seed” x) but rather evolve from the y (as a function of x) being inserted back into the equation as a new x. Such recursive development can be deterministic as one looks back interpretively, but to predict with any accuracy from Situation 1 to Situation 4 is at best probabilistic—due to intervening Situations 2 and 3—with the attempt of probabilistic predictions for Situation 8 or 9 being near to impossible. This recursive patterning, often labeled “deterministic but not predictable,” accounts for weather predictions being given only in short-term probabilistic frames. In a metaphoric sense, to see Situation 2 emerging from Situation 1 and leading on, and indeed influencing (but not determining) Situation 3, brings forth the need for inquiry-oriented research to be interpretive, open-ended, probabilistic, historically situated, and culturally contextual.

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