A fourth characteristic of complex systems, or rhizomes, is that actants interact dynamically. In his Prologue to his book Complexity and Postmodernism, Paul Cilliers says:
In a complex system, … the interaction among constituents of the system, and the interaction between the system and its environment, are of such a nature that the system as a whole cannot be fully understood simply by analysing its components. Moreover, these relationships are not fixed, but shift and change, often as a result of self-organisation. This can result in novel features, usually referred to in terms of emergent properties. (Prologue)Complex classrooms, then, have no fixed relationships among its actants or among other, external clusters of actants; rather, all actants can shift and change in their relationships with all the other actants. This, of course, upsets the traditional classroom which tries to control and fix the relationships among the actants: teachers and students, and peripherally, administrators, staff, parents, and others. In complex classrooms, interactions do change. Sometimes a student teaches while the teacher learns.
Dynamic interactions are not just a characteristic of complex systems; rather, they are constitutive of those systems. No dynamic interactions means no complex system. Cilliers says:
Complexity is the result of a rich interaction of simple elements that only respond to the limited information each of them are presented with. When we look at the behaviour of a complex system as a whole, our focus shifts from the individual element in the system to the complex structure of the system. The complexity emerges as a result of the patterns of interaction between the elements. (p. 5)The dynamic interactions begin with the infusion of Light and Word into the complex system. We can see the results of this infusion of energy in a pot of oatmeal, for instance: as we add heat to the pot, the oatmeal slowly begins to roil and turn the closer it gets to the boiling point, becoming animated. Similarly, as we turn up the flows of energy and information in a class of students, they become animated and begin to roil and turn, to interact dynamically with each other and with the information. This inflow of energy and information is a starting point. Consider our bag of inert marbles. Now imagine that they are animated by the flows of energy and information such that they are able to process that energy and information, store energy and information, and respond to each other and to their environment. This is the magic that happens in living systems, all of which are complex. As animated actants, the marbles can and must interact dynamically with each other and with their environment (remember that Deleuze and Guattari say that "any point of a rhizome can be connected to anything other, and must be" (7)), and dynamic interactions are not limited to simple physical jostling, things bumping into things like marbles in a bag, though jostling and bumping are certainly included. Rather, dynamic interactions are any perturbation of energy, matter, information, or organization, and usually all of them together, between any two actants. In other words, actants in a complex system are able to recognise and respond to perturbations of energy and information from within their system and without. They can feed, process, and feedback, rearranging themselves--self-eco-organizing--to meet the demands of their situations. This dynamic interactivity fundamentally defines the system at all scales: it defines communities, schools, classes, students, organs, tissues, and molecules--all the way down and all the way up.
And it defines a complex system both from inside and outside. Derrida writes convincingly to me that the inside and outside are not so distinct, and I keep his point carefully in mind. Still, distinguishing the inside (the individual, to use human terms) from the outside (society) is often useful. Indeed, it is necessary to distinguish any system from its surround. It's necessary for autonomy and identity. However, as Morin says, autonomy and identity are not a separation but a distinction:
The notion of human autonomy is complex because it depends on cultural and social conditions. To be ourselves, we need to learn a language, a culture, knowledge, and this culture itself needs to be varied enough to allow us a choice among the stock of existing ideas, and to think in an autonomous way. So this autonomy is nourished by dependence. We depend on an education, a language, a culture, a society, a brain, which is itself the product of genetic programming, and we depend also on our genes. (On Complexity 44)Autonomy, then, in terms of dependence—another of complexity's wonderful and productive contradictions. We work out our own lives, our own salvations, between the extremes of autonomy and dependence. We must have both, and our negotiations between these two extremes are another source of the dynamism inherent in any complex system.
In his book Complexity and Postmodernism, Cilliers anticipates Morin, saying of human social systems in particular:
Individuals are engaged in a constant exchange of information. Remember that a specific node in a neural network has limited significance, that it is the patterns of interconnections that encode information and generate meaning. Similarly, no human individual’s existence is meaningful in isolation: ‘the self does not amount to much’ (Lyotard 1984: 15). The individual is constituted by its relationships to others. (pp. 119-120)Lyotard's conclusion that the self does not amount to much immediately rearranges our traditional thinking about classrooms, certainly in the United States with its extreme focus on the individual student. I suspect that we have wasted incalculable time and energy by limiting student interactions with other students and by employing assessment regimes that focus on one student/one grade. We tend to strip away all the interactions that define a student and make a student an interesting, engaging person, in order to focus on one test score, one data stream, one set of perturbations. We end up removing most of what makes a student interesting and worthwhile to others and probably all of what makes a student valuable to themselves.
Of course, schools are not alone in reducing people to a small bag of convenient characteristics. All organizations tend to do the same: businesses, governments, churches, teams, and even families. And of course, engaging any person, or actant, in terms of all their dynamic relationships is impossible, as any dedicated ANT researcher knows. No one can know another that well--not even Rumi and his Beloved. We can't even know ourselves that well. Still, we must keep in mind that when we reduce any actant, any student, to one or two interactions, then we distort them, likely to the point that we lose what is most important about them. It's like dissecting a frog to learn how its liver works: we might learn something useful, but the frog is dead. We can focus our attention to analyze, but we must always remember to pull out to a larger view. Only from the higher view can we see the morphing patterns formed by dynamic relationships. As both Cilliers and Morin note, this runs counter to three hundred years of a highly successful Western science and technology which reduces reality to fundamental parts in order to analyze it. As Cilliers puts it:
The study of complex dynamic systems has uncovered a fundamental flaw in the analytical method. A complex system is not constituted merely by the sum of its components, but also by the intricate relationships between these components. In ‘cutting up’ a system, the analytical method destroys what it seeks to understand. (p. 2)This is not to deny the benefits of such analyses. Modern science and technology have demonstrated beyond question that analysis has its insights and can generate much actionable knowledge. Still, as Morin explains so well, this analysis blinds us to all outside our analyses. Cilliers also speaks of the problems with taking snapshots of complex systems to freeze the dynamic interactions so that we can study the moving parts:
Despite the fact that we cannot represent the essence of a complex system in determinate terms, we cannot resist, or perhaps even avoid, the construction of some kind of interpretation of the nature of the system at a given moment. These interpretations, however, are in principle limited. We are always constrained to taking snapshots of the system. ... The danger lies in falling under the spell of a specific picture and claiming a privileged position for it. Since it would not only deny the limitations of the specific angle, but also prevent further explorations [italics added by me], this spell must be broken by relentlessly showing the contradictions that result from fixing the boundaries from one perspective. Pointing out the contradictions that follow from such a closure is an activity that Derrida calls 'deconstruction'. (p. 80)A complex class is never in equilibrium. Rather, it is always mapping new knowledge and know-how, if only figuring out how to avoid doing the next assignment or how to cheat without getting caught. I can recall only one class in near equilibrium: I once visited a high school classroom to troubleshoot a network connection only to find a teacher lecturing conscientiously to about 10 students, all with their heads down, asleep at their desks. I watched in stunned amazement for a few moments before the teacher finally shrugged and said, "Well, they're all being quiet." The class had achieved a perfect equilibrium—at least until the bell rang.
And therein lies the problem with complete equilibrium: so long as we live within this complex world, equilibrium doesn't hold. On Earth and among living things, equilibrium is the exceptional state. We are all infused with too much energy and information from too many directions, and no classroom can filter all that energy and information to focus the class on one flow of information from one source in one direction: student to teacher. The attempt at such focus requires an excessive exercise of power, which itself becomes another flow of energy and information which can disrupt learning as quickly as anything else.
Indeed the very idea of learning is dynamic, far from equilibrium. Learning demands dynamic change—an expansion beyond that which we already know. Learners are expanding beyond their old knowledge, or at least reinforcing and strengthening their old knowledge. Learning means rearranging and strengthening one's internal state to adequately respond to and cope with outside streams of energy, matter, information, and organization. These streams are never totally under the control of any student, parent, teacher, curriculum, or school.
Not only are students in a classroom dynamic because of the inflows of energy and information and the constant reorganization of their own internal states, but also because students are actants in multiple clusters. A student has multiple acting roles (child, sibling, parent, spouse, lover, team member, friend/enemy, buyer/seller, acolyte, proselyte, nerd, peer leader/follower, and countless others) that make incessant, often conflicting demands on the student. Moreover, as Cilliers notes, these clusters are all dynamic and "interact with other clusters, both directly as well as through the individual members they share with each other" (p. 7). Student families are part of my classes, and my classes are part of those families, even in college. Usually the interpenetrations are subtle—a tension in the class that I cannot identify and usually gloss over—but sometimes the tension is insistent and disruptive. A few terms ago, the father of one of my students was killed in the line of duty as a police officer. This was a community event that the class could not gloss over and had to deal with. Cilliers says:
Clusters should not be interpreted in a spatial sense, or seen as fixed, hermetically sealed entities. They can grow or shrink, be subdivided or absorbed, flourish or decay. The clusters are dynamic and interact with other clusters, both directly as well as through the individual members they share with each other. (p. 7)Clusters, in other words, are rhizomes, and all the points (or actants) in a rhizome interact with all others. My students' social, home, and work lives are in my classes everyday, whether I acknowledge them or not, deal with them or not. They are ready and potent streams of energy and information that the class can harness and co-opt for its own learning purposes.
Complex systems must be dynamic in order to self-organize, or said another way, classes must be dynamic in order to learn. Cilliers says, "A complex system, such as a living organism or a growing economy, has to develop its structure and be able to adapt that structure in order to cope with changes in the environment" (p. 11). Later in his book, Cilliers elaborates: "The capacity for self-organisation is a property of complex systems which enables them to develop or change internal structure spontaneously and adaptively in order to cope with, or manipulate, their environment" (p. 89).
Dynamic interaction, then, has direct consequences for learning: all complex systems can adapt and learn, a characteristic for a future post in this series, but students can learn and adapt only because they are dynamic systems. Cilliers explores this dynamism in terms of Derrida's concepts of trace and différance. A trace is an interaction among actants in a system—for instance, neurons in a brain or students in a classroom—a pathway that is more or less dynamic. The more dynamic an interaction is, the more the pathway is walked, then the stronger the trace and the more weight it carries within the system. In human terms, weighted traces are, for example, the strongly held beliefs, deep friendships, rituals and habits, frequently travelled highways, voting preferences, buying patterns, and so on that give shape and meaning to our lives. We are born with the potential for these traces, but not the traces themselves. We develop those, we learn them. They are the dynamic structures that become provisionally different from the other possible but latent traces and pathways that we could have developed. These two concepts, traces and différance, help both Derrida and Cilliers illuminate the dynamics among actants within a system and among systems. Cilliers says, "Both concepts, trace and différance, are employed to say something about the inner workings of language, or rather—since language becomes the model of any system of interacting signs—of all complex systems" (pp. 44, 45). Cilliers summarizes the impact of trace and différance within complex neural networks this way:
If an ensemble of neurons … generates a pattern of activity, traces of the activity reverberate through the network. When there are loops in the network, these traces are reflected back after a certain propagation delay (deferral), and alter (make different) the activity that produced them in the first place. Since complex systems always contain loops and feedback, delayed self-altering will be one of the network's characteristics. This characteristic has much in common with the notion of différance—a concept that indicates difference and deference, that is suspended between the passive and active modes, and that has both spatial and temporal components. (p. 46)I can easily imagine a classroom as a complex neural network optimally functioning far from equilibrium, dynamically tracing pathways among multiple actants—humans of all sorts, tools, spaces and times, processes, other systems—individual learners autonomously distinguishing themselves through dependent connections, spinning out traces to be explored and mapped. And here I find myself back with Deleuze and Guattari's concept of the rhizome, especially its fifth characteristic: cartography, or mapping as distinguished from tracing (they are not using the term trace in the same sense as Derrida—rather, they are talking about mapping one's own pathways rather than tracing the pathways of someone else). The traditional, autocratic, simple classroom attempts to create only one, static, sanctioned trace or pathway: from teacher to student. Traces among students are discouraged and the one path between teacher and student is not dynamic: it flows only one way. Students are supposed to copy or trace (in D&G's sense) the path provided by the teacher. They are not encouraged to map new pathways or traces (in Derrida's sense) for themselves. I'm encouraged by new learning methods that embrace and cultivate both the dynamism of the trace between teacher and student and the multiple traces among students and their communities. Students bring their knowledge and their multiple connections to class anyway, so why not recognize those traces and work with them? Co-opt the energy and information before it runs over you.
I should pause here to note that I am not opposed to tracing (D&G) existing traces (Derrida). While the aim of education for me is to enable learners to map (D&G) their own traces (Derrida), copying existing pathways provided by mentors and teachers, learning existing knowledge, is just as important as being able to create new knowledge. Indeed, from the learner's point of view, tracing existing knowledge and mapping new knowledge are much the same thing. Learning existing knowledge means that the knowledge is still new to the learner. Learning is always mapping the new rather than tracing the old.
And tracing the old has at least two benefits. First, learners can be guided and supported by mentors and teachers who have already walked the path and understand its affordances and dangers. This kind of support can be invaluable for both timid and reckless learners—one afraid to step onto the path and the other heedlessly running down the path.
The second benefit is even more powerful and brings me to another characteristic of complex classes: they must have a memory system. Memory is another example of the dialogical nature of complexity: complex systems are capable of both dynamic interactions and stable memories. Both are critical for the identity and persistence of the system, and they are opposites. They are not reconciled or synthesized. Rather, complex systems such as humans and classrooms are suspended in the tension between these two opposites, sometimes intent on forming new models of reality, sometimes intent on strengthening old models. Learners must be able to form new models of their realities, and they must be able to conserve their old models. Humans are limited both by what we know and by what we don't know. Humans are empowered both by what we know and by what we don't know. These contradictory statements are all true. We need both dynamic change and stubborn stability. We are all liberals and conservatives.
But more about memory later in another post. To my mind, dynamic interactions are first—but that may just be my progressive, liberal bias. For me, all the actants in a complex classroom connect and interact in shifting patterns. They must. Any instructional ethics must map and remap this swelter of connectivity and interactivity.
