I recently came across Kurt A. Richardson's 2001 article On the Status of Natural Boundaries: A Complex Systems Perspective which helps me clarify my thinking on this issue. Richardson uses complexity theory to guide him through the dilemma of reductionism on one hand, in which boundaries are clear, discrete, and persistent, and holism on the other hand, in which boundaries disappear altogether as everything merges into the Universe or God.
Richardson begins by making a very useful distinction between complex and complicated systems. He states that he is concerned with complex systems, which he defines neatly:
A complex system is comprised of a large number of non-linearly interacting non-decomposable elements. The interactivity must be such that the system cannot be reducible to two or more distinct systems, and must be sufficient (where the determination of sufficient is problematic) to allow the system to display the behaviours characteristic of such systems. (p. 230)He then clarifies the difference between these complex systems and the often similar looking complicated systems:
The principle difference between a complicated system and a complex system is not the presence of large numbers of entities and nonlinear interactions. The key difference is the nature of the overall connectivity, particularly the existence of feedback mechanisms. Despite the existence [of] nonlinearity complicated systems do not self-organise into new structures. They do not display a wide range of qualitatively different behaviours. The extent and nature of the nonlinear interactivity is what differentiates between a complicated and complex system. The division between these two categories at a compositional level is very blurred however. It is problematic to know from compositional information whether a system is complicated or complex without having information about its behaviour. Complicated and complex systems, then, can only safely be differentiated from each other by observing their respective behaviours.A complicated system, then, is like a modern jet fighter: large numbers of entities with a myriad of interactions, including some nonlinear interactions, among its parts; however, the jet fighter is incapable of evolving, or self-organizing into new structures.
This distinction between complicated and complex systems helps me to understand the traditional classroom and the value of cMOOCs. A traditional school is a complicated system composed of large numbers of entities and interactions. Some classes are complicated systems, say those with students exceeding Dunbar's Number, but most are simple systems composed of a fixed number of entities (1 teacher and 25 students) and a few, mostly linear interactions: curriculum + instruction —> student learning. In such simple/complicated systems, boundaries are fixed, clear, and enforced. The subsystems (teacher, students, curriculum, lessons, texts, etc) are rigidly differentiated and the interactions among them are stable, predictable, and enforceable. The boundaries are in place and real, and any blurring of a boundary is considered a failure by purists or as a daring experiment in free learning by rebels. Either way, the reality of the boundary is reinforced. Violating a boundary confirms the boundary just as much as enforcing the boundary.
cMOOCs, unlike traditional classrooms and xMOOCs, are intentionally complex systems. cMOOCs and xMOOCs are differentiated by their respective behaviors. Like xMOOCs and some traditional classes, cMOOCs have large numbers of entities with a myriad of interactions, but unlike those complicated systems, cMOOCs can and do self-organize into different and new structures. They evolve through nonlinear interactions, feedback loops, non-local causalities, dialogic tensions, and a range of other behaviors characteristic of complex systems, and new structures of people and ideas emerge that could not have been anticipated by the designers of the MOOC. These complex interactions unfold across blog posts, tweets, Youtube videos, Flickr posts, and coffee cups, and new patterns of people and ideas emerge out of the interactions. Boundaries in cMOOCs, as in other complex systems, are different than the boundaries in simple and complicated systems.
Complex systems, then, are difficult to evaluate. Simple/complicated systems, with their fixed entities and interactions, have a strict linear progression which leads to a predictable, and usually measurable, outcome (if a teacher does A + B + C, then the student must learn D, which we can measure on a test and repeat A + B + C until the student learns D). However, as Richardson points out, complex systems "display many possible qualitatively different behavioural regimes (the nature and variety of which evolve), as well as exhibiting emergence, i.e. the emergence of macroscopic system structures and behaviours that are not at all obvious from their microscopic make-up … The order parameters that best describe the current behaviour of a complex system are not fixed, they evolve qualitatively as well as quantitatively." Factor in the butterfly effect (systemic sensitivity to initial conditions), and it's easy to see how difficult it becomes to predict the outcomes of any given cMOOC. This inability to predict outcomes changes the nature of evaluation. If we do not have a fixed, predictable outcome, then how do we measure the efficacy of the instruction?
Well, I seem to be slipping away from my original point about boundaries, but only a bit. A fixed, predictable outcome is a kind of boundary. It is an endpoint, a destination. In a traditional class or xMOOC, that boundary is discrete. A cMOOC does not have an endpoint or destination. Rather, it is more like another complex system, thunderstorms. Like thunderstorms, cMOOCs build in intensity, form their new structures (not random, but not totally predictable either), expend their energy, and subside, though they can continue to echo long after the thunder has stopped. So here's Richardson's main point about the distinction between complicated and complex systems: "the boundaries describing subsystems in a complicated system are prescribed and fixed whereas the boundaries delimiting subsystems in a complex system are emergent and temporary."
Anyone who has been in a cMOOC can see this fluidity of boundary, for instance, in deciding who is a student in the MOOC and who isn't. If you define student as someone who is actively participating in the MOOC, then that shifts wildly from week to week as people engage, disengage, get distracted, re-engage. And who's the teacher? That can be slippery as well. You can easily measure and quantify enrollment in a traditional class. Measuring a cMOOC is more like measuring a thunderstorm. Just when is a cloud part of the thunderstorm, and when isn't it? That can be hard to quantify or even qualify. The boundary keeps shifting as the thunderstorm, or cMOOC, evolves in its phase space. Come to think of it, developing procedures for defining the phase space of a cMOOC might be a fine start to evaluating them, but it's beyond my abilities.
So what does Richardson say about boundaries in complex systems? In short: "The only real absolute boundaries in a complex system are those that define the basic constituents and their interrelationships. All other boundaries are emergent and temporary. In order to relate these arguments to the real world it is assumed in addition that the universe is a complex system, i.e. the one and only well-defined system." He's having his cake and eating it, too, which is entirely permissible. The only complex system with absolute boundaries is the Universe itself. All other boundaries—in other words, everything else that we know about, including superstrings—are emergent and temporary. Now, curiously enough, this includes both traditional classrooms and xMOOCs as well as cMOOCs; the difference is that cMOOCs recognize and encourage emergent and temporary boundaries and structures, while xMOOCs and traditional classrooms pretend that their boundaries and structures are permanent and in some way blessed or sanctioned.
Okay, then, let's assume for the sake of argument that boundaries really are emergent and temporary. Does that mean that anything goes, that we can create boundaries where we wish as we wish, as the constructivists would have?
Richardson says no. He insists that we do not need to resort either to a constructivism that insists that "all boundaries are created in our minds and as such do not correlate with objective reality at all" or to a naive realism that insists that our ideas "perfectly map to their espoused objects." We can map reality, and those maps are based on the interactions of two complex systems, which implies a complex interaction: natural reality and conceptual reality. As Richardson says of the relationship between the natural and conceptual:
Rather than having a fixed relationship with natural boundaries, or having no relationship at all, conceptual boundaries do have a complex and changing relationship to reality. Sometimes this link might be so tenuous as to be unusable. Sometimes this link is so strong as to give us the impression that we might actually have absolute Truth to hand.As Richardson says, "In the field of complexity there is evidence that, though there may be no real boundaries, there are resilient and relatively stable emergent structures." Mapping the world, then in the sense of Deleuze and Guattari's cartography, is problematic, but it is not impossible. Boundaries both conceptual and natural make that mapping possible, even necessary. They also make it temporary and emergent.
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