Friday, March 17, 2017

Complex Open Classrooms: Open and Closed

In this series of posts, I am arguing that classrooms are complex open systems, and that if we want to know how best to configure and engage a classroom, then we should work to the strengths and affordances of complex open systems rather than against them. As should become obvious, I do not think that most current educational efforts play well with complexity. Rather, I am convinced that too often we try to force classes to behave as closed systems. In other words, we try to move classes (indeed, entire schools and educational systems) from the complex domain to the simple domain, and we develop instructional, economic, political, and ethical structures to support and reinforce that simple domain. This is a problem for me, and I'm trying to think my way through it, but I am not at all suggesting that classes are currently structured as complex open systems, though some clearly are (#rhizo14/15 and DS106 come immediately to mind). My argument, I think, will run something like this: if classes are complex open systems, then we should try to play to the strengths of those systems rather than against them.

It helps me, then, to think through how complex open systems, or rhizomes, emerge, function, and die (they all do). So far my review of complex open systems says that they are multiplicities of actants animated by flows of energy and information. I want to start teasing out the implications of the dynamic relationships in this mix, and the first point for me is the fact that complex open systems are … well … open. That's a big deal, and openness points to a drastic difference between education as it usually is (more simple and closed) and education as it could be (more complex and open). But keep in mind that I'm creating a binary here with either/or extremes. In reality, most classes fall on a continuum somewhere between these two extremes of totally open and totally closed. Still, I'll start by considering the extremes:
  • A complex open system totally closed to its environment will die. Period.
  • A complex open system totally open to its environment will die. Period.
A system must be open to Light and Word from outside itself, but a system must also choose what and how much it feeds, processes, and feeds back. A complex open system, then, must learn to manage its exchanges with its environment given its resources and situation. It must maintain itself—it must find a stable state—in the zone between two phase transitions: one toward cold fixity and one toward hot dissolution. This is the right understanding. If a system, a class for instance, closes itself too much from flows of energy and information, then it risks sliding into the black hole of frozen syllabi. If it opens itself too much, then it risks sliding into the black hole of hot chaos. Either way, class is over.

Of course, there is still a fair amount of flexibility between these two extremes, and this flexibility defines the autonomy and the character of the complex open system, the class. We educators are all familiar with those classes that tend to be more closed than open. Closed classes have been typical of my educational experience, persisting even into my doctoral program when I expected classes to open up. Fortunately, many did; however, I still remember with disgust the linguistics professor who read to us from his textbook for an hour-and-a-half each class period, taking no questions and inviting no discussion—just one stream of information from one source in one direction. Deadly. I also remember with joy the classes with Isaac Bashevis Singer in which we read our stories and followed them wherever they might lead us, accompanied by a most experienced and gifted guide. I remember the #rhizo14/15 MOOCs which triggered rather open-ended discussions in response to Dave Cormier's weekly koan. I have to say up-front that I favor more open classes, but I know that some amount of closure is also necessary. Even in #rhizo14/15, we didn't talk about anything and everything, and we had some disagreements about what to include and exclude.

This managed permeability at the boundaries of a classroom, or a person, points to an inherent property of complex open systems: the juxtaposition of opposites. Closed and open are opposites. The one eliminates and excludes the other. Yet both are necessary for a complex open system to emerge and function. These juxtapositions and tensions (order/disorder, equilibrium/disequilibrium, life/death, hot/cold) exist throughout complex systems. The tensions cannot be resolved either way, or the system dies. Edgar Morin calls this tense juxtaposition a dialogic: a necessary, creative conversation between opposites with no hope of reconciliation or synthesis. It is not Hegel's thesis, antithesis, and synthesis dialectic. Indeed, reconciliation and synthesis is death. The conversation must continue for the system to continue. It's the hum that keeps the engines running. We'll see how this tension plays out again and again.

Morin notes first that the flows of energy and information through a system create a disequilibrium. The flow rattles the marbles in the bag and starts them spinning, and if the energy and information are flowing appropriately, then some magic happens: the system self-organizes. "This nourishing disequilibrium allows the system to maintain an apparent equilibrium, a state of stability and continuity" (On Complexity 11). In other words, for complex open systems, a dynamic equilibrium emerges from chaotic disequilibrium on one hand and fixed equilibrium on the other. It takes both. Rather, it takes the tension between the extremes, and how we negotiate the turbulence of this tension defines the integrity and autonomy of a system: a person or a class, for instance.

Edgar Morin explains quite nicely this paradoxical space in which complex open systems emerge and sustain themselves:
This guaranteed state, constant but fragile (the term we will use here is steady state), is somewhat paradoxical. The structures remain the same even though the constituents are changing. This is not only true for the whirlpool or the flame of a candle, but also of our organisms, where our molecules and cells are renewing themselves incessantly, while the whole remains apparently stable and stationary. In a way the system has to close itself off from the outside world to maintain its structures and its internal environment. If it did not, it would disintegrate. This closure is allowed by the very fact that the system is open. The problem becomes even more interesting when we suppose an indissoluble relationship between maintaining the structure and its changing constituents. Here we find a primary, central, obviously key problem of living beings. This problem is, however, ignored and obscured, not only by the old physics, but also by Western Cartesian metaphysics, for whom all living things are considered closed entities, not as systems that organize their closing (that is to say, their autonomy) in and by their opening. (11)
As Morin goes on to explain, we achieve identity, our distinction from the swelter and noise of the ecosystem, by judiciously closing ourselves off, but these closings are possible only because we are open in the first place. We are not either open or closed—we are both open and closed, and to emerge and sustain ourselves as complex open systems, we must engage both extremes, both open and closed, both order and chaos, both equilibrium and disequilibrium.

I have to emphasize that this is not an argument for some golden mean between two extremes. That is far too simple. Because we exist in a turbulent space, we must constantly modulate between too open and too closed, shifting this way or that based solely on the demands and configurations of the moment, constantly aware that too far either way can drop us into a deadly phase transition. We must be constantly aware, like a starling in a flock, defining our own space in a constantly shifting and morphing larger space. I really wish I could tell you exactly where in the flock you are supposed to be, but that depends on the dynamic, evolving interactions between you and the rest of the flock. And the wind, and predators, and temperature, and … well, you get the idea. You must maintain the integrity of your own space within the shifting parameters of the flock, and you must do it on the fly.

Again, Morin says it better:
The intelligibility of the system has to be found, not only in the system itself, but also in its relationship with the environment, and … this relationship is not a simple dependence: it is constitutive of the system. Reality is therefore as much in the connection (relationship) as in the distinction between the open system and its environment. [original bolded] This connection is absolutely crucial epistemologically, methodologically, theoretically, and empirically. Logically, the system cannot be understood except by including the environment. The environment is at the same time intimate and foreign: it is a part of the system while remaining exterior to it. (11)
To understand a class or a person, then, you must understand the ecosystem they are in—the myriad relationships within the class and outside the class. This is, of course, an impossible task, but we must do it anyway. So welcome to your complex open life. Welcome to complex open classes.

This paradoxical open/closed nature of complex open systems clarifies why boundaries and identities are always so problematic. Like cell membranes or our own skins, boundaries are permeable, both keeping us mostly contained while at the same time connecting us to our ecosystems and managing the exchanges of energy, matter, information, and organization. Boundaries both distinguish and connect, and as our connections shift and morph, the boundaries of necessity expand, contract, and reshape. Boundaries for complex open classes are always provisional because there are always interactions and exchanges among actants within the class itself, across classes, and with the ecosystems of school, community, state, etc. There must be. A class cannot be defined and understood simply as a group of 1 teacher and 30 students. A class is a buzzing hive of interactions among teachers, students, smartphones, weather conditions, moon phases, nutritional flows and levels, electricity grids, textbooks, tablets, computers, networks, neurons, blood pressures, viral and bacterial swarms, and infinitely more, all coping with different agenda and perturbations—some complementary and some conflicting.

This open/closed nature of complex systems has many implications that I hope to work through, but the insight for me today is that all complex open systems such as classes emerge, function, and evolve in the turbulence of a flock on the wing, and while a class can thrive in a stabilized dynamic, it cannot thrive in a fixed structure or no structure. Instructional ethics, then, must map to the malleable and semipermeable membranes of classes.

I must append something about the open education movement, which I support. What does open education have to do with complex open systems as I am exploring them here? I'll start with a definition of open education from the Open Education Consortium:
Open education encompasses resources, tools and practices that employ a framework of open sharing to improve educational access and effectiveness worldwide. …The idea of free and open sharing in education is not new. In fact, sharing is probably the most basic characteristic of education: education is sharing knowledge, insights and information with others, upon which new knowledge, skills, ideas and understanding can be built. … Open is key; open allows not just access, but the ability to modify and use materials, information and networks so education can be personalized to individual users or woven together in new ways for large and diverse audiences.
The focus here is on access and efficacy, or the "ability to modify and use materials, information and networks so education can be personalized … or woven together … for large and diverse audiences." In terms of how I have used open and closed in this post, the Open Education Consortium seems interested in encouraging two things: increasing the flows of useable information through classes and increasing the flows of students through those classes. This follows from the definition of education as "sharing knowledge, insights and information with others, upon which new knowledge, skills, ideas and understanding can be built." This is a solid definition of education as we traditionally understand it: a more knowledgeable teacher or school transferring knowledge and skill to less knowledgeable students. The Open Education Consortium seems to understand open in terms of connecting more students and more resources to more classes (I'm using classes here to encompass everything from one-on-one tutoring sessions and a single person with a book, through traditional lectures and demonstrations, to computer drills and 160,000 member MOOCs in traditional educational institutions and outside).

This OEC emphasis appears to restrict education to one flow of information in one direction: teacher > students and in one space/time. I am arguing against such a restriction. Perhaps it's the language they are using, but this language seems to be the norm, and it seems to work for a closed, simple classroom structure. I want to push back on that language.

Open for me recognizes all the flows of information and energy through a class: flows from a teacher, of course, but also flows from the students who bring a wealth of information often relevant to the discussion at hand. I also include flows from the ecosystem: news, gossip, Spotify, text messages, sunlight, cultural norms, diet, electricity, water, air, political, social, and religious systems, and of course, gravity. Here's the point: those flows are there regardless of how the class attempts to close itself to all flows except that flow from the teacher to the students and back to the teacher in a closed loop—in a closed, simple system in which the teacher feeds prepared information to the students who feed it back in tests to complete and end the cycle. This is a very closed, sterile approach to education that is far too close (pun intended) to equilibrium. (I'm using an extreme example here to emphasize my point, but most of us have been in classes that were uncomfortably close to this extreme.) Complexity emerges in the zone far from equilibrium, closer to chaos. Chaos, of course, is also deadly for a class, but as a complex open system, education needs the turbulence of chaos to animate learning.

Learning emerges in the zone far from equilibrium. Lev Vygotsky hinted back in the 1930s at this zone of proximal development where the learner moves beyond what she already knows into that near chaotic, turbulent realm beyond her mastery. That's where the learning is. That's where the wild things are. It helps, of course, if she has the benefit of a guide who is experienced with the territory and can help her map the chaos, but regardless, the learner must be willing to open herself to the uncharted and must be willing to push beyond that which she knows. This is risky, rocky terrain, but education must cultivate this turbulence, and too much simple, closed education does not. Rather, simple education is structured to reduce the turbulence.

Turbulence means failure, frequent failure, as learners explore new neural, physical pathways. Our current educational culture abhors failure and is geared toward removing and mitigating failure rather than embracing it as a prime educational strategy. Embracing failure in my writing classrooms has been one of the keys to improving writing. I'll give a concrete example: I give assignments that I know most students do not already know how to do, and I provide very little explanation up front. Rather, I encourage them to try and promise that we will fix any problems they encounter. Let's say I tell them that they must format their academic document according to MLA style 8 (a departmental requirement), give them the link to Purdue OWL, and start them writing. Most fail the assignment, so we explore the failures in class in groups. We correct all failures, and grades go up. (I don't like grades, but I must give them, and my students expect them, so I try to use grades as productively as possible. This means regrading and regrading all documents.) Students all fail at MLA in different ways, and the turbulence of the failure primes them to learn. They engage a new flow of information, and the turbulence knocks them over. Most of them do not like it at first, especially the A students, but then magic happens: they identify what they don't know in a rather narrow zone, and they have the chance to fix it, to learn it. They see that most everyone fails in some way with MLA, even their teacher, and they develop strategies for coping.

So my students are allowed to fail, and they are allowed to learn from their failures. I believe that they learn from failures quicker than anything else, but they must have the opportunity to learn. Failure can't be the end point; rather, learning must be built into failure. Given that the failures are usually particular to each student, then the learning must be particular to each student, and suddenly, almost unexpectedly, my class is student-centered. Of course, allowing for and addressing individual failure wanders off the traceable path of a rigid lesson plan in twenty or thirty or a thousand different directions, but that's where the learning is. It opens the class, and I cannot tell you how much I, the expert guide, have learned about MLA by watching my students fail at it.

In her 2010 book Vibrant Matter: A Political Ecology of Things, Jane Bennett says that "human decency and a decent politics are fostered if we tune in to the strange logic of turbulence." I think she is right. I think a decent education will follow if we tune in to the strange logic of turbulence.

Thursday, March 9, 2017

Complex Open Classes: Light and Word

I started my unpacking of complex open systems with the notion that they are multiplicities, but not a multiplicity like a bag of differently-colored and differently-sized marbles unified only by virtue of being in my bag. If the bag breaks and the marbles bounce away across an expansive concrete floor, then we would hardly think of the marbles as a unified system anymore. I think I have tended to view my students this way sometimes: just a random collection of differently-colored, differently-sized people wrapped up in the bag of my Composition 1101, Section 99 class. Of course, seeing them this way is unfortunate for them and for me, but it seems to be an expedient reduction to help me through the busy trivia of my day. It's a way of disengaging from the multiplicity of the class, the swarm, to get other things done.

When I'm rested and mindful again, then I know that the students are not a grab-bag collection of random, inert things to be acted upon. Rather, they are a swarm of living, striving beings (actants), all animated by flows of energy, matter, information, and organization. Regardless of the scale at which I consider them, they are animated and sustained by the Light and the Word.

Energy, matter, information, and organization are hard-nosed scientific concepts that I borrow from Edgar Morin's discussion of complexity in his book On Complexity, and I will use those terms in various configurations throughout this exploration, but I like the poetic imagery of the Light and the Word. These are old images that have crossed the millennia to reach us and that along the way have taken on much social, political, philosophical, and religious baggage, but that's because they can do the heavy lifting. They are deep images that echo from the Beginning: "Let there be light" or "Big Bang". I also like that they echo my conservative Christian background. There is something pleasantly perverse about using the Light and the Word to account for a worldview and ethics that fundamentalists will see as do-your-own-thing, anything goes, and relativistic. They are wrong, of course. Complex open systems and the complexity ethics that attend them are anything but anything goes, but more on that later.

As a complex open system, then, my writing class cannot exist without a sufficient flow of Light and Word, energy and information. A writing class needs flows of energy and information to animate the multiple actants—students, teachers, texts, computers—into a functioning system. Everything needs those flows. This current post, for instance, needs flows from electrical systems, computer hardware and software, a millennia-long conversation about ethics, ontology, and epistemology, the organizational structures of the English language and Google Blogger, and of course, you the reader and me the writer with our own inherent flows of energy and information. Without all this throughput and more, this current text could not come to life and emerge into the wider world. Nothing comes to life without similar flows of Light and Word.

This is, as far as I know, a universal principle. In his 1968 book Energy Flow in Biology: Biological Organization as a Problem in Thermal Physics, Harold J. Morowitz notes two important ideas about complex, open, self-organizing entities: "that energy flow alone can give rise to order in a system" and "that energy flow is necessary to maintain order once it has been achieved" (26). Morowitz convinces me that complex, open systems (including my writing classes) emerge, express, and maintain their lives as flows of energy and information—flows of Light and the Word. Morowitz doesn't deal specifically with information, and I confess that I do not know which came first: the Light or the Word. From this great distance of 14 billion years, the existing evidence can seem tenuous and ambiguous, the ancient texts obscure; still, I am convinced that all the activities of life need flows of both Light and Word.

The flows are always from a hotter source to a colder sink, and they must be just right: too little, and a complex open system freezes into stasis; too much, and a system explodes into fiery chaos. As Morowitz says it:
At very low flows the system approaches equilibrium with the thermal sink; at very high flows the system approaches equilibrium with what must effectively be a very hot source. Order generally means that the system has a character different than equilibrium systems. At both extremes of flow, this condition fails to obtain. Sustained order must therefore be a property of systems of intermediate flow rate. (42, 43)
Both extremes mean death. Life happens in the sustained tension and turbulence between too cold and too hot. Learning happens in this same temperate zone. Of course, too little and too much, too cold and too hot, are not fixed values but depend mostly on the situation at hand, and all systems have some room to move. Complex open systems—we humans, for instance—have real choices to make about which flows of Light and Word to engage and how much, but we have no choice about engaging. We must engage the Light and the Word, or we die. So we must engage, and we must make choices, or have those choices made for us. This is the agonistics of the rhizome, and I think the ethics should be obvious, but I will draw out those implications later. Still, the hard fact is that no classroom can exist without appropriate flows of Light and Word: energy/matter and information/organization. Period.

We need the Light and the Word, then, to animate a system, and this, of course, involves us with entropy, or the amount of disorder within a system. We redirect flows of energy and information through a system such as a class in order to reduce the amount of disorder, or entropy, in the system. It takes a fair amount of energy and information to organize a class into a functioning system (think just of the transportation systems needed to make it happen), and there is always the first law of thermodynamics to deal with: the preservation of energy. In short, the amount of organization and complexity created in one place is always equal to the amount of disorganization created elsewhere. For instance, using a traditional print textbook requires a destruction of trees and a manufacturing plant somewhere. When we choose to direct our own, personal energies toward a given class, then we are not directing our energies elsewhere: we aren't writing our dissertation, playing with our families, working on our next presentation or novel. We must feed a class, and that always means taking from something else. To me, the ethics here are also obvious, but more on that later.

Note that energy and information flows come from outside the system proper. This may seem obvious, but it is not trivial. This relationship changes everything, and I will explore these changes in the next few posts, but for now, we should note that Light and Word come from beyond us and through us. We humans begin as fertilized eggs with a mix of DNA coming from two parents, and then we are nursed and fed Light and Word in a womb for nine months, before living for a number of years with caretakers who are responsible for feeding us energy/matter and information/organization. We eventually assume primary responsibility for our feedings: we feed, process, and feedback, feed, process, and feedback in constant cycles as Light and Word flow through us. As Edgar Morin notes in On Complexity, this means that we never achieve equilibrium, or not until we die. He says:
A closed system, like a rock or a table, is in a state of equilibrium. In other words, matter and energy exchanges with the exterior are nonexistent. The constancy of the flame of a candle, the constancy of the internal environment of a cell or an organism are not at all linked to such an equilibrium. There is, on the contrary, disequilibrium in the energetic flux that feeds them, and without this flux, there is an organization deregulation that quickly leads to decline. (10, 11)
As Mark Taylor says in his book The Moment of Complexity (2001), we live in a state far from equilibrium, and we are always in danger of slipping too close to the cold or the heat, toward fixed order or chaos.

I must say something about what I mean by Light and Word, or energy/matter and information/organization. I'll start with energy. I am not enough of a scientist to give a very precise definition of energy, so I'm comfortable using the definition from Wikipedia: "In physics, energy is the property that must be transferred to an object in order to perform work on – or to heat – the object, and can be converted in form, but not created or destroyed." It's that primordial force released at the Beginning, and that has expressed itself in many different forms as the Universe has self-organized over the past 14 billion years, or so, eventually becoming one of my writing classes (all in all, that seems a disproportionate effort for one writing class, but I'll take it as a blessing). I use the word Light to express this vitality, this ability to organize oneself and to perturb and to respond to perturbations.

This ability to self-organize and to perturb and to respond to perturbations segues directly into my understanding of information and reveals how entangled energy and information are for me. I'm open to the idea that Light and Word are different terms for the same thing, but that isn't a question I want to engage in this conversation. Rather, I'm comfortable saying that information is any perturbation that makes a difference. Mark Taylor quotes Gregory Bateson as defining information as "a difference that makes a difference" (105). That captures the gist of it for me this morning. All complex open systems can organize themselves in such ways as to sense perturbations, differences in their environments, and respond to those perturbations in ways that are meaningful to the system—respond if only barely enough to survive the perturbation. This information processing can be quite basic and fundamental as when early particles first sensed wrinkles in space/time and began to aggregate, self-organize, into galaxies under the constant and persistent instruction of gravity, as thorough and patient a teacher as I've ever met. I confess that I do not know how quarks sense things such as gravity waves, but my confusion is evidence that they can. Otherwise, I wouldn't exist and neither would you. So for me, classroom discussion, coo-chats with my four-month-old granddaughter, and this very blog post all share the same fundamental communication mechanisms as those processes that created the Universe. I like that.

Complexity ethics, then, must map well to the flows of Light and Word that sustain complex open systems and to the dynamic relationships between any system at any scale and the ecosystem that animates it. That's a tall order for classroom ethics, but it grounds the ethics, driving the pylons deep. So far, I like where this is going for me. We'll see.

Wednesday, March 1, 2017

Complex Open Education: Multiplicities

So does complexity theory provide us with a way of thinking about ethical behavior in education? I think so, but first I have to clarify for myself how I am framing education. I've been trying to do this for several years now, and I just haven't found the mechanism to do so. I think I may have it together enough to do so now.

I start with an understanding of education as a complex open system, or in Deleuzional terms: a rhizome. I've been trying to figure out what this means, and I have not been able to rely solely on Deleuze and Guattari. They are not the only ones to think about complex open systems, and they are not the clearest, though they are often among the most evocative for me. Still, my thinking has been enabled and enriched by reading many others, and I make free use of them when I need to. For me, the rhizome is but one good effort by a couple of pretty clever fellows to express the shift of thinking from a reductionist mode in the simple/complicated domains to a complex mode in the complex/chaotic domains. This shift is quite evident in modern science since the early 20th century, but not so much in education, where we've spent the past two hundred years trying to render classrooms as simple spaces with clear, fixed goals and activities. To my mind, classes function in the complex domain and are most properly and effectively addressed as complex open systems, or rhizomes.

Can I give a traditional definition of a complex open class, from the outside, and will it help? Yes and no, but I'll do it anyway, because as Deleuze and Guattari so wryly noted: "We get the distinct feeling that we will convince no one unless we enumerate certain approximate characteristics of the rhizome" (ATP, 7). Still, I will enumerate from the outside but only on the condition that I unpack from the inside. So my definition: a class is a complex open system made up of many actants that are animated and sustained by flows of energy and information that fuel self-eco-organizing, nonlinear interactions among the actants and enable the system to function with some coherence and continuity within the context of other complex open systems. Ethics emerge from the self-eco-organizing behaviors of complex open systems, such as classes.

So there's the nugget of a definition. I will try to unpack this idea of education as a complex open system over the next few posts.

First, let's start with the obvious: complex open systems are composed of many elements, nodes, or actants. I will use the term actant from actor network theory to emphasize the heterogeneity of classrooms, which include not only human teachers and students, but also texts, administrative and pedagogical processes, physical spaces with a myriad of actants (I'm old enough to remember the smells of chalk and, later, dry eraser, neither of which often reinforced the instructor's point despite what they wrote on the board—those smells took me away), conversations, passions, boredom, electricity, water, inspiration, and a million other non-human actors usually not included in discussions of instructional design.

Deleuze and Guattari open their description of rhizomes with the principles of connection and heterogeneity, saying: "any point of a rhizome can be connected to anything other, and must be" (ATP 7). So they, too, are starting with the idea that a rhizome is made up of many elements. Likewise, in his 1998 book Complexity and Postmodernism, Paul Cilliers begins his list of 10 characteristics of complex open systems by noting that they are composed of many nodes, or actants. A class is composed of more actants than anyone can expect to track or manage, but one should be aware of as many actants as possible without being distracted. This points to a dialogical tension inherent in all complex systems that becomes increasingly obvious as we unpack them.

Education at any scale, then, is a multiplicity. A class—my English 1101 Composition I class, for instance—is a multiplicity, not a unity; therefore, we should speak of the class as some students, not the class, preferring the indefinite article over the definite, as D&G suggest (ATP, p. 9). The indefinite article some preserves the presence and connectivity of all the other students and actants spread like grass around the world. Of course, we often speak of the class, but it is for convenience, to over-signify and define from outside some students into a unity. It is a kind of shorthand that has, unfortunately, become the only reality for many of us. We believe that the educational world is made up only of discrete actants: classes, students, teachers, schools. Our manner of speaking has obscured the heterogenous interconnectivity of the rhizomatic class, and we speak so regularly of the class that we come to believe in it as a closed system: a discrete, unified entity with its independent beginning and end, its unique rules and syllabus. Despite all our efforts, rules, and instructional designs, however, the class is not a closed system. It is a rhizome, a complex open system, an assemblage of many actants.

In her book Vibrant Matter (2010), Jane Bennett borrows the term assemblage from Deleuze and Guattari to begin her exploration of vibrant matter, vital materiality, and she explains assemblage this way:
Assemblages are ad hoc groupings of diverse elements, of vibrant materials of all sorts. Assemblages are living, throbbing confederations that are able to function despite the persistent presence of energies that confound them from within [and from without, I would add]. … Each member and proto-member of the assemblage has a certain vital force, but there is also an effectivity proper to the grouping as such: an agency of the assemblage. And precisely because each member-actant maintains an energetic pulse slightly “off” from that of the assemblage, an assemblage is never a stolid block but an open-ended collective, a “non-totalizable sum.” (pp. 23-24)
For me, an assemblage, or multiplicity, is something like a piano. We speak of the piano, as if all of the parts have somehow vanished, fallen into a black whole, a unity, but they haven't. They are still there. We even speak of one note—say, B-flat—as if the other notes are not there. This is a convenience, of course, and often a necessity, but when we speak of one thing, all the other things are still there, still implicated, still pressing. If we play the B-flat, striking one key to awaken one string into vibration (see how we are already a multiplicity?), the other strings begin to vibrate as well. They form the hum, the noise, supporting the dominant, but not discrete, B-flat. The wood vibrates, the air, our bodies. All these actants form the character of the instrument. No actant alone can make that particular B-flat, or that piano, or that piano player. We say, "Hear the B-flat?" as if it is one thing, but it is not. It is a multiplicity, an assemblage, a rhizome. It cannot be otherwise, despite what we say.

When we speak of education, we always speak of a multiplicity, even when we speak about the individual learner or individualized instruction. These terms are handy, even helpful sometimes, but ultimately they obscure the multiplicity, the noise out of which all knowledge and skill emerges. The interconnectivity of multiple actants is at the heart of the connectivism of Siemens and Downes, at the heart of the community as curriculum of Dave Cormier. It is the heart of education. I begin, then, with multiplicity.

But, some may complain, what's the big deal? Well, I don't think I can overstate the importance of the multiplicity. Still, let me be clear that I am not replacing the individual with the multiplicity. All actants are both ocean and wave. Also, I do not seek some balance between them, some happy mean. Rather, I'm looking for an appropriate tension between the individual and the multiplicity, a dialogic as Edgar Morin uses the term. These are irreconcilable views of actants, but the tension between them is where all the creativity of life emerges. That's what I seek.

Still, I am aware that for the past 300 years Western culture has overwhelmingly privileged the individual in politics, business, religion, and yes, education. As Iain McGilchrist amply demonstrates in his book The Master and the Emissary (2012), the individual (roughly, the left brain) has taken precedence over the multiplicity (roughly, the right brain), and society has suffered because of it. I accept the gist of McGilchrist's argument, especially as supported by Edgar Morin's exploration of reductionist science in his book On Complexity. We have lost the multiple, and its loss has damaged us. As Serres notes in his book Genesis (1995), multiplicities, swarms, frighten us:
We are fascinated by the unit; only a unity seems rational to us. We scorn the senses, because their information reaches us in bursts. We scorn the groupings of the world, and we scorn those of our bodies. For us they seem to enjoy a bit of the status of Being only when they are subsumed beneath a unity. Disaggregation and aggregation, as such, and without contradiction, are repugnant to us. Multiplicity, according to Leibniz, is only a semi-being. A cartload of bricks isn't a house. Unity dazzles on at least two counts: by its sum and by its division. That herd must be singular in its totality and it must also be made up of a given number of sheep or buffalo. We want a principle, a system, an integration, and we want elements, atoms, numbers. We want them, and we make them. A single God, and identifiable individuals. The aggre­gate as such is not a well-formed object; it seems irrational to us. The arithmetic of whole numbers remains a secret foundation of our understanding; we're all Pythagorians. We think only in monadologies. (2, 3)
I'm trying to learn how to think with multiplicities. I do not find it easy, and I may never totally get there, in part because I am fairly adept at writing in unities. Most of the time, my posts, my paragraphs, my sentences are unified. My thoughts are unified. I whip the multiple into unity before thinking. I may have to switch to poetry. I'll see.

For me, the first implication of multiplicity is that knowledge and agency are distributed, network functions. Actually, everything is distributed across a multiplicity—my own identity, for instance—but I focus here on knowledge and agency because they are so core to education: I know how to do something and I am able to do it. We are accustomed to thinking of knowledge and agency as powers belonging to individuals. This is not so. For instance, I could say that I have the agency to play soccer. This sounds like my ability to do something, my individual agency, but even a casual exploration reveals the distributed, network nature of that agency. My playing soccer is the interaction of many of the subsystems of my body: respiration, digestion, cognition, reflexive, musculature, skeletal, and so on. My agency is not housed in any one of these subsystems, but emerges from the interactions of all of them. My agency is distributed across all those subsystems, and I cannot reduce my agency to any one of them. My soccer-playing agency does not reside in my feet.

But you might complain that this is a trick, that in fact, all those organs and systems are individual me, but this is not the correct understanding. For instance, take away any one of those systems, and see what happens to my agency to play soccer. It is seriously impaired, if not eliminated altogether. I need a network to play.

Of course, the distribution of my agency extends far beyond the confines of my skin. I also need other players with their own internal agency to play with and against. I need a ball, a pitch, a referee. Without the multiplicity, I have no agency. This is not a trick. Jane Bennet explains distributed agency quite well when she says that "bodies [all actants, not merely the human] enhance their power in or as a heterogeneous assemblage. What this suggests for the concept of agency is that the efficacy or effectivity to which that term has traditionally referred becomes distributed across an ontologically heterogeneous field, rather than being a capacity localized in a human body or in a collective produced (only) by human efforts" (22).

Like agency, knowledge is a distributed, network function, an emergent property of multiplicity. We need a network to know, but this is not how we usually think of knowledge. Traditionally we think of knowledge as nugget of something that can be transferred like a token from a teacher's mind to a student's mind, but there ain't no token, and there ain't no transfer. Something else is going on.

Based on his work in building artificial intelligence systems before he became a philosopher, Paul Cilliers explores the distributed nature of knowledge in Complexity and Postmodernism, where he notes that modelling a complex open system requires a modelling apparatus that is as complex as the system being modelled. This is very different from our usual approach to modelling which typically reduces the size and scope of the thing being modelled to make it more handy. Unfortunately, it always eliminates details of the original, and in complex open systems, all details are critical, and the loss of any detail distorts the system itself. Think of it this way: if you want to model a building as a closed system of static planes, lines, volumes, spaces, and other geometric elements, then you can do that rather easily in a computer or with pen and paper, as those tools can work in the simple/complicated domains to capture and represent closed systems.

If on the other hand you want to model a building as a complex open system emerging from ten thousand years of architectural design, building techniques, the technical and economic streams of building materials, the social, political, and economic streams of real estate, the lives and inputs of builders and laborers, owners and occupiers, the interactions over the 100 year lifetime of the building with wind, rain, weather, gravity, temperature … well, if you want to understand that, then you will need more than pen and paper or even a supercomputer. You will need a human mind. Or something better. You will need a complex, sensitive fabric at least as complex as the complex open system being modelled. The human mind is the most complex, sensitive fabric that we know of, and it is capable of modelling in distributed representations (distributed in space/time) an amazing amount of this incredibly complex open universe that we inhabit.

But those representations are not little chunks, or little signs. Cilliers explains that "in most semiotic systems the sign acquires meaning by referring to something—it represents the referent" (81). So we typically set up a one-to-one correspondence between the sign house located at sectors 57 and 92 in our brains and an actual house, or class of things out in the real world. When we need to think house, our brain navigates to 57 x 92 and finds house, like a dictionary definition. It doesn't work this way. The sign house is never localized in our brains as a unique thing, nugget, or token. Rather, house is distributed across our brains in a familiar pattern of firing neurons. And as neuroscientist Olaf Sporns notes in his book Networks of the Brain (2010), the brain builds the pattern house on the fly, using what neurons are available at the moment, which helps me understand why memories and ideas can seem different from recall to recall, like fractals: similar enough to be usable, but different enough to be noticeable.

Meaning, or knowledge, then cannot be localized to a single neuron or even cluster of neurons. Meaning is distributed across a pattern of neurons on an as-need basis. And I will insist that just like agency, meaning extends beyond our brains to include our entire bodies, our histories, and our communities. It takes time and a whole community to learn. It takes a very complex fabric to represent reality, or as much of it as we are capable of representing (I do not think our minds, as richly complex as they are, are complex enough to represent all of reality. Something always exceeds our reach, but I can't prove that). Agency and knowledge are always the results of multiplicities, never of individuals. This is the proper understanding.

Educational ethics, then, must map the multiplicity of all actants. This is an impossible task, but nonetheless necessary. Welcome to the rhizome.