Rhizomatic Thought, #etmooc

I came across a video and a couple of quotes today that illuminated and expanded for me some ideas I've been discussing in #etmooc about rhizomatic learning.

Brian Rose shared the NASA video Fiery Looping Rain on the Sun:



This kind of inspirational video leads to comments (270+ when I looked last, 4:00 pm EDT, Fri, Feb 22). For instance, Jeremy Ellwood quoted Neil Degrasse Tyson's view about feeling small in the light of such enormous power:

I look up at the night sky, and I know that, yes, we are part of this Universe, we are in this Universe, but perhaps more important than both of those facts is that the Universe is in us. When I reflect on that fact, I look up—many people feel small, because they’re small and the Universe is big, but I feel big, because my atoms came from those stars.

Then Brian Rose quoted Apollo 14 astronaut Edgar Mitchell, who spoke about looking back at the Earth from the Moon:

"You develop an instant global consciousness, people orientation, an intense dissatisfaction with the state of the world, and a compulsion to do something about it. From out there on the moon, international politics look so petty. You want to grab a politician by the scruff of the neck and drag him a quarter of a million miles out and say, ‘Look at that, you son of a bitch.”

These comments make explicit why I like the rhizome: it allows me to think over and beyond networks based on simple connectivity. The rhizome is networks+, connectivity on steroids.

More accurately, the rhizome is connectivity across multi-scale networks, across what Basarab Nicolescu calls different levels of reality. This connectivity—not just within a network but across sub-networks and super-networks—is important for my rhizomatic thinking as it helps me grasp and visualize the extent of rhizomatic structures, or assemblages to use Deleuze and Guattari's term (I suspect they wanted to avoid the more rigid, mechanistic overtones of the term structures). D&G speak of asignifying ruptures within a rhizome, in which our naming, labeling, and definition of a thing suffers a rupture, a line of flight, that unnames the thing as it moves from one scale of network to another scale, from one level of reality to another. Asignifying ruptures, deterritorialization, reterritorialization, and the logic of the included middle all seem abstract and obtuse concepts until you hear an Edgar Mitchell say it so plainly: "From out there on the moon, international politics look so petty." When you view the political arguments which seem so important here on Earth from a different level of reality, from the Moon, then you see that that the contradictions fade away, and the arguments become completely asignified, meaningless, void, not even a playground squabble. These concepts, then, help me understand one of the heuristics available to rhizomatic thinking: that whatever we are learning must be viewed from more than one level of reality, from more than one scale of the network. When we view things in this complex, rhizomatic manner, then contradictions often fade in lines of flight into the included middle.

Then, the comment by Neil Degrasse Tyson captures a second heuristic of rhizomatic thinking, what Edgar Morin calls the holographic principle. The patterns of the Universe echo in my cellular structures. We are composed of stardust, and we are the dust of the stars. I am not speaking poetically here, nor am I alluding to Joni Mitchell (though Woodstock remains one of my favorite songs, especially the version by Mathew's Southern Comfort). I am being literal. The patterns of energy and information exchange that work in the stars also work in me. The information in my DNA and cells come from the stars and feed back into it. I fancifully think that if the entire Universe were to blink out, leaving only me floating alone, then any reasonably intelligent, technologically adept species from another universe that found me could use the data in my cellular structures to pretty much recreate a universe that works more or less like this one (okay, that last part isn't literal, but it might be the start of a good science fiction story). This echoing of information throughout a network and across network scales echoes the fifth principle of the rhizome: decalcomania. As connectivism says, learning has much to do with embodying and recognizing patterns. Yes, "the Universe is big, but I feel big, because my atoms came from those stars."

Rhizomatic Growth in CCK12

In a response to my previous post, fellow CCK12 MOOCer and blogger, Matt Bury, describes a number of techniques that he uses to build communities of inquiry and practice in his classrooms, and it reminds me that formal theories—if we choose to call Connectivism a formal theory—grow in very informal, rhizomatic ways, spreading like oil—or as Deleuze and Guattari say of the rhizomatic growth of language: It evolves by subterranean stems and flows, along river valleys or train tracks; it spreads like a patch of oil. It is not proselytized as a monolithic system of thought. I think this is one of the appeals of rhizomatic thinking for me, and I suspect it may be for others as well.

The monolithic system of thought, of course, has a most useful function. For a time, sometimes for a long time, it steadies our thoughts and allows us to measure progress and change. We can define goals and even appear to meet them. Yet, if Deleuze and Guattari are correct, then this measurement and movement is always something of a fiction—a useful fiction often, but a fiction—and eventually it becomes a fascist kernel that becomes more interested in preserving its own identity and establishing its own hegemony than in being useful. Even this open-ended, freely evolving Connectivist community may eventually write its own creed and bless those who are inside that creed and castigate those who are outside.

But never fear. If Deleuze and Guattari are correct, then the rhizome will simply move on, flowing around and beyond the little fascist knots that calcify from time to time. This movement in rhizomatic structures comes most explicitly, and sometimes forcefully, through asignifying ruptures, the fourth characteristic of the rhizome.

#change11 The Nothing Rhizome Pt 2

Yesterday, I started addressing a question from Sui Fai John Mak about why I would call the rhizome nothing, and I found myself wandering through the first three of the six characteristics of the rhizome that Deleuze and Guattari list in their book A Thousand Plateaus (1987):

1. Connectivity (an obvious connection to Connectivism)
2. Heterogeneity
3. Multiplicity

Today, I want to continue the conversation by working through the final three characteristics:

1. Asignifying ruptures
2. Cartography
3. Decalcomania

I suppose that asignifying ruptures most clearly capture Deleuze and Guattari's push back against power, especially the power we humans exercise through signifying, through naming things. They say that asignifying ruptures work "against the oversignifying breaks separating structures or cutting across a single structure" (9). We humans are excellent at breaking up reality into manageable pieces by analyzing and segmenting and naming and numbering and quantifying, and these are all useful mental processes that help us build airplanes, buildings, institutions, societies, and so on, but they are also fictions and power structures from which the rhizome flees through deterreritorialization and reterreritorialization. Or as Robert Frost says much more plainly: something there is that doesn't love a wall. Any slice of reality contains within it both the classifications we humans create to manage that reality and the lines of flight that undermine those classifications. As D&G say: "Every rhizome contains lines of segmentarity according to which it is stratified, territorialized, organized, signified, attributed, etc., as well as lines of deterritorialization down which it constantly flees. There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome" (9). APPLICATION: Traditional education exerts much energy in classifying, stratifying, organizing, and naming students, teachers, subjects, disciplines, classes, tests, theories, etc. John is an A student, Mary is a C student, and Bubba is an F student. Manuel is a rising senior, and Jinchaun is a freshman. George is a Professor, and Dave is an Assistant Professor, and Stephen is a Dean. I teach essay writing: descriptive, persuasive, argumentative (sometimes the same as persuasive, sometimes listed separately. I don't know why), comparison (or comparison/contrast), expository, formal, informal, research, literary, cause/effect, and more. You can google essay forms or essay types and find oodles of classifications, all more or less arbitrary and, as near as I can tell from 30 years experience in teaching writing, all more or less useless. I've never found an essay that I really liked—say, something by Annie Dillard—that fit any of these groups very well. Rhizomatic education, then, recognizes that reality leaks out in lines of flight from our attempts to peg it, to name it, to pin it, wriggling on the wall, and tries to accomodate those lines of flight. The Change 11 MOOC just suffered a couple of asignifying ruptures with Nancy White's social artists and Dave Cormier's rhizomes and nomads, but unlike a traditional class, we MOOCers work with those lines of flight, riding along with them, ignoring them, or refuting them, as we are so inclined, but not knocked over by them. Indeed, we set up the MOOC to encourage just such ruptures. Rhizomatic learning does not deny the virtues of our analytical mind, but it recognizes that reality ain't really like that and can squirt out of our categories at the weirdest times.

These first four characteristics, I think, explain why lots of people are so confused when they first join a MOOC: a MOOC is an explicitly and intentionally rhizomatic structure:

1. Connection: any MOOCer can connect to any other or to anyone else not in the MOOC. We don't simply connect to the teachers: Professors Cormier, Downes, and Siemens. We connect more to each other, and for me that has been Jeffrey, Glen, Bonnie, Sui Fai John, Jenny, and others, none of whom are willing or able to tell me what I should be learning or if I have learned it. This is great unless you are thoroughly conditioned to having someone tell you what the learning is all about. Well, rest yourself. You can decide what to learn and what to ignore. Trust yourself.
2. Heterogeneity: We MOOCers are not the same. We are not homogenized. While we all share an interest in higher education and how it might be changing, that common interest is too vague to provide much guidance in where we are supposed to be going and how we are supposed to get there. We came in on different paths, and we are almost certainly passing through this MOOC on different paths. Cool—unless, of course, you are worried about falling behind. Well, rest yourself. You can't fall behind, as you are likely the only one of 2,000 scholars going your way.
3. Multiplicity: We MOOCers are each the convergence of different life trajectories that we bring to the mix of all the other life trajectories in the MOOC. We focus on a few of those trajectories to gain some sense of what we are trying to do here, but the open structure of the MOOC allows all those trajectories to emerge in the mix. It can be overwhelming if we try to cover it all. Well, rest yourself. You can't cover it all.
4. Asignifying ruptures: We MOOCers know that the conversation can take some abrupt, even startling, turns and flights into ideas and concepts that we never anticipated, or even knew about. This can be exciting and challenging or terrifying and frustrating, as not everyone likes snowboarding over a ledge without knowing where the trail's going, or if there even is a trail. Well, rest yourself. You don't have to follow every trail—in fact, you can't—and next week, we'll be back on a trail that works for you.

MOOCs just don't have any of the traditional structures and signposts that people expect when they sign-up for a course. A MOOC isn't a course—it isn't a thing as we usually define things. Rather, a MOOC is an assemblage, a multiplicity. We are legion, and that can be tough to deal with.

But after thoroughly confusing our sense of reality, Deleuze and Guattari give us a couple of strategies for dealing with rhizomes such as a MOOC, and it is just here that I want to note a slight disagreement with, or rather an amendment to, something that Dave Cormier said to George Siemens in his Change 11 presentation. When they were discussing the rhizome as a metaphor and George was pushing for clarification on how rhizomatic learning handled knowledge, Dave said that rhizomatic learning did not address epistemology, or something to that effect—sorry, I'm too lazy to find it in the recording just now. While rhizomatic learning certainly has no systematic epistemology, I still think it has something to say about ways of knowing.

The first strategy for knowing in a rhizomatic structure is cartography, or mapping. Mapping is a process of constantly monitoring and testing reality, assessing the feedback, and adjusting the map. Mapping assumes that reality is shifting; therefore, knowledge must shift, if it is to remain useful for engaging reality. Most of us don't like shifting knowledge—we want the correct answer, the eternal answer. We want what Deleuze and Guattari call tracings, or "an overcoding structure or supporting axis, something that comes ready-made" (12). The Truth. Mappings are different. 

What distinguishes the map from the tracing is that it is entirely oriented toward an experimentation in contact with the real. … It is itself a part of the rhizome. The map is open and connectable in all of its dimensions; it is detachable, reversible, susceptible to constant modification. It can be torn, reversed, adapted to any kind of mounting, reworked by an individual, group, or social formation. It can be drawn on a wall, conceived of as a work of art, constructed as a political action or as a meditation. … A map has multiple entryways, as opposed to the tracing, which always comes back "to the same." The map has to do with performance, whereas the tracing always involves an alleged "competence." (12, 13)

 APPLICATION: Traditional learning proceeds by fixed curricula and lesson plans about authoritative knowledge with regular measures to determine how competently a student has traced the lines of the lesson. Knowledge in traditional education is a tracing of what is already known. Rhizomatic learning is a mapping, an engagement with reality, a fixing of points of reference, measurements and tests, assessment of feedback, and then an adjustment of the points of reference or creation of new points, with no hope of ever fixing the points of reference, and with total recognition that the very act of mapping itself is part of the reality under examination. This totally collapses the Cartesian dualism that underlies our modern scientific point of view that posits an object for us subjects to trace, or know. Rhizomatic learning says this is not the way to engage reality. It certainly isn't the way to engage a MOOC. When entering a MOOC we must anchor to some point (almost any will do initially: a person, a blog, a presentation, a bit of reading) from which to establish a vantage point. That anchor and vantage point may work for the entire MOOC, or we may switch, but we need that first anchor. What we cannot do is look for some syllabus through which we can trace a course of learning. It ain't there. We must map the MOOC: fix a vantage point, fix other points from there, check distances from where we are to someplace else we might want to be, look for the steps to get to the new place, and strike out, asking others along the way, confident that our goal will shift. That's how you learn in a MOOC.

The second strategy for knowing in a rhizomatic structure is decalcomania, or pressing patterns. Most of us know decalcomania as the process where children put paint on their hands and press the paint onto paper, leaving blue, purple, yellow, and red handprints. Deleuze and Guattari suggest that patterns emerge in the rhizome through a pressing, not a transfer but more an echo. They are careful to say that it is not mimicry, which is tracing. Rather it is a blossoming of a sympathetic, self-similar, fractal pattern. Almost the same, but not quite. APPLICATION: In traditional learning, knowledge is transferred in little nuggets called facts from the teacher's brain to the student's brain; or in progressive classes, the teacher enables students to create their own little nuggets. In rhizomatic learning, the brain is  an amazingly sensitive organ for echoing the patterns that it recognizes in its environment, for feeding those patterns back into its environment, and then taking in the new patterns. Deleuze and Guattari say:

Thought is not arborescent, and the brain is not a rooted or ramified matter. What are wrongly called "dendrites" do not assure the connection of neurons in a continuous fabric. The discontinuity between cells, the role of the axons, the functioning of the synapses, the existence of synaptic microfissures, the leap each message makes across these fissures, make the brain a multiplicity immersed in its plane of consistency or neuroglia, a whole uncertain, probabilistic system. … Many people have a tree growing in their heads, but the brain itself is much more a grass than a tree. (15)

The grass of the brain is very sensitive to the moving of wind and rain, echoing the pattern of each, but there is no transfer of pattern. The wind does not transfer its pattern to the grass. In a MOOC, we echo the knowledge (a blog, a presentation, a tweet) that we press against. That echo is never exact, never the thing itself transferred from another mind to our mind. Rather, it is a sympathetic reterritorialization, more or less similar, of a pattern that we perceived. Our minds then operate on that newly emerged pattern, that knowledge, reworking it to fit into the knowledge and patterns already in our minds, looking for consistency and resonance however we define those qualities (rationally, emotionally, aesthetically, etc.), and then feed those patterns back into the ecosystem, deterritorialized and reterritorialized, where they are taken up, or not, and reworked, and fed back into the system, over and over and over. This describes the messy process of learning in a MOOC, and for me, it describes it better than does behaviorism and constructivism do, though they have insights as well.

Well, I've gone a long way around to tell Sui Fai John Mak why I think a rhizome is nothing. I hope the answer works for him, but at any rate, I hope he understands now why I like rhizomatic learning. As a metaphor, a way of mapping but NOT precisely tracing, the rhizome helps me understand learning in a MOOC much better than most any other theory or metaphor that I know. And with people such as Dave Cormier and Bonnie Stewart, the metaphor is just getting richer.

#change11 Defining the Rhizome

I just watched the Ed Tech Weekly interview with Dave Cormier about rhizomatic learning, and by the end of the hour, I found myself chafed by the attempt to encourage Cormier to define the concept. The interviewers Jeff Lebow and Jennifer Maddrell seem very pleasant, engaged educators who really wanted to understand Cormier's point, and I do not even slightly suspect them of badgering Cormier; rather, I think the very nature of academic language itself forces us to seek definitions first and then talk later. All of the participants wanted to distinguish rhizomatic learning as a particular learning theory or process or way of knowing (it can be all of those) that is distinct from, say, the positivist way of knowing or the constructivist way of learning. The hope, I think, is that the concept of rhizomatic learning can lead to specific teaching and learning behaviors that will improve education. I think there are a few problems with this attempt to wrangle the rhizome into something it isn't.

First, the rhizome is a metaphor, not a theory or a procedure based on a theory. When speaking of rhizomatics in the interview, Jeff Lebow says, "I think the metaphor is helpful." To my mind, this is spot on. A metaphor is a help in understanding something else, it is not the something else itself. Rhizomatic learning speaks of a more or less helpful way of looking at and thinking about learning. It is not a prescription for learning — it is at best a somewhat helpful description of how learning happens. Through the metaphor of the rhizome as first explored so nicely by Deleuze and Guattari in their book A Thousand Plateaus (1987) educators can look afresh at learning and see things that they had not seen before. At least, this has been the case for me.

For instance, the metaphor of the rhizome is a fine antidote to our tendency toward reductionism. This reductionism lies in the background of the interviewers' attempts to define rhizomatic learning, I think. Like most of us, they want a handy nugget that says, "Oh, yes, that is rhizomatic learning."  The metaphor of the rhizome, however, helps us to see that reductionism is always a fiction. No thing can ever actually be reduced to a discrete thing, or not in reality. We can think of ourselves as discrete and alone in the Universe, a train of thought that usually leads to all sorts of misery and suffering, but none of us are discrete, however convenient or persuasive the reductionist fiction might be.

I am not saying that we should avoid reductionist thinking. That is silly. As Morin has shown, science has scored huge successes through reducing an aspect of reality to a single point, studying it in great detail, and discovering things about this reduced entity that it could hardly have discovered in any other way. Reductionism has great focus and, thus, great power. Rhizomatic thinking, on the other hand, encourages us to replace the discrete thing into its ecosystem, to recontextualize it, and to integrate what we learned through our extreme focus into our knowledge of the whole. In short, we can learn a great deal by studying a single tree, but what we learn only makes sense in the context of a forest. We must see both forest and tree. The rhizome metaphor helps us to do that.

The second thing that bothers me is that a definition of rhizomatic learning reduces the rhizome to the status of one thing among other things: rhizomatic learning as opposed to constructivist or behaviorist learning. Here's the thing: the rhizome is not a thing, it is nothing. This is partly what makes the rhizome so difficult to discuss within a language made of nouns and verbs, or things doing things. This is partly why D&G are so difficult to read: they are trying to map a structure through a language primarily adapted to mapping different kinds of structures. Modern academic language is a fine tool for mapping linear, hierarchical, positivistic structures. Mapping the rhizome with this tool is a bit like building an igloo with hammers and screwdrivers. It can be done, I suppose, but … In their discussion of the rhizome, Deleuze and Guattari are not trying to focus our attention on the rhizome so much as they are trying to get us to relax our focus, our critical intellect, to capture the arcs, the asignifying ruptures, the starts and fits and interconnectedness of things. From this point of view, then, things are the precipitate of experience (to use Randall Collins' term) at the intersection of multiple arcs of existence at any given time. Think of a plate of spaghetti. Keith Hamon is one noodle strand intertwined and thoroughly embedded in the mass of noodles, and my sense of myself or your sense of me as a discrete entity totally depends upon where along the noodle strand you or I happen to be focusing and what other noodles intersect me there.

Reductionism wants to disentangle the single noodle of my life, stretch it out on an examination tray, name and number the parts, establish the tidy sequences of cause and effect, and finally declare that it understands me. And here's the thing: it will understand a great deal about me that could not have been understood so easily while I was tangled up in the plate of spaghetti. But it will also lose a great deal, if not most, of the contours, the arcs, the twists and turns, the connections and intersections, the forces and counterforces that truly make my life interesting to me, if not to others. Stretched out on the examination table, washed clean of sauce, separated from all the other noodles, and allowed to harden, the noodle of my life will be reduced to the bare facts. Boring. Reductionism reveals nicely what about me is like other spaghetti noodles, but it hardly captures the unique contours that make me interesting, or me.

Rhizomatic thinking, then, is a useful strategy for looking at learning in a different way. It includes positivist thought and reductionist thought and all the other systems of thought, but at the same time that the rhizome provides a rich context for those systems of thought, it is also shifting, deterritorializing and reterreitorializing, and thereby undermining the very systems of thought that it incubated. Our job is to build these structures within the rhizome because they are useful, while remaining very aware that their usefulness has a shelf life. The danger is when we become attached to a system, an ideology, and refuse to acknowledge that it no longer helps.

This makes me think of the night sky. We humans look at the panoply of stars, and we select a few with which to structure constellations, pictures and stories. Because from our vantage point the stars seem to shift so slowly — in our lifetimes hardly at all — then we are seduced into thinking that our pictures and stories are eternal. Modern astro-physics has taught us better. The rhizome of the universe is shifting at incredible speeds constantly, and eventually our treasured stories and pictures will no longer map well to reality. The stars will have moved. The challenge of the rhizome is to look afresh at those stars and to create new stories and new pictures. That's what the rhizome does.

The Hierarchy of Neural Complexity

Sporns says that "brain connectivity is organized on a hierarchy of scales from local circuits of neurons to modules of functional brain systems" (258). His use of the word hierarchy presents me with some problems as I have for the last few years contrasted hierarchical structures with network structures. In general, I have assumed that hierarchies were rigid, closed, traced, arboreal structures (to use terms from Deleuze and Guattari) while networks were flexible, scaleable, open, mapped, rhizomatic structures. Hierarchies admit only sanctioned, homogenous nodes within its structure and then fix them into a well-defined place with well-defined relationships to all other nodes; whereas,  networks admit heterogenous nodes within its open structure and allow nodes to develop relationships with any or all other nodes for any reason. For me, then, hierarchies and networks are not the same, and I cringe just a bit each time Sporns uses the term hierarchy to describe an aspect of neural networking.

But I think I have a resolution to my concern. I don't think Sporns is using hierarchy as I do; rather, he is describing various physical and functional layers of the brain and how they interact. As he says: "A recurrent theme in studies of collective behavior in complex networks, from epidemic to brain models, is its dependence on the network's multiscale architecture, its nested levels of clustered communities" (261). He is not so much describing a pyramidal structure as an onion structure. He's talking about layers enclosing layers enclosing layers and so on. This might be a mere quibble over visual metaphors but for his concepts of heterogenous coupling and multiscale dynamics, and some others like them. These principles prevent Sporns' neural hierarchies from calcifying into rigid hierarchies, as I have used the term. Indeed, heterogenous coupling in neurophysiology reminds me much of Deleuze and Guattari's first principle of the rhizome given in the first chapter of their book A Thousand Plateaus (1988): "any point of a rhizome can be connected to anything other, and must be. This is very different from the tree or root, which plots a point, fixes an order" (7). I think Deleuze and Guattari would be most comfortable with Sporns' concept of heterogenous coupling as very rhizomatic.

Sporns also talks about the brain's metastability, or tendency toward chaotic itinerancy:

the itinerant or roaming motion of the trajectory of a high-dimensional system among varieties of ordered states. Chaotic itineracy is found in a number of physical systems that are globally coupled, that are far from equilibrium, or that engage in turbulent flow. … It has also been observed in brain recordings … and neural network models … Over time, systems exhibiting chaotic itineracy alternate between ordered low-dimensional motion within a dynamically unstable "attractor ruin" and high-dimensional chaotic transitions. System variables are coherently coupled, their dynamics slow down during ordered motion, and they transiently lose coherence as the system trajectory rapidly moves between attractor ruins. (263, 264)

This chaotic itinerancy of neural networks with their roaming motions and trajectories and their constant transitions between coherent couplings and incoherent chaos is strongly reminiscent of another characteristic of rhizomes: the principle of asignifying rupture. Deleuze and Guattari say of asignifying ruptures:

Every rhizome contains lines of segmentarity according to which it is stratified, territorialized, organized, signified, attributed, etc., as well as lines of deterritorialization down which it constantly flees. There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome.

Rhizomatic structures, then, deterritorialize and reterritorialize only to deterritorialize again. If I understand what Sporns is saying, then it seems that neural networks have a chaotic itinerancy that is at least a Rorschach of asignifying ruptures. Perhaps, Deleuze and Guattari's asignifying ruptures have deterritorialized and reterritorialized as chaotic itinerancy.

Seems possible. Anyway, chaotic itinerancy seems to fit nicely with D&G's whole idea about nomadology and motion in reality. Anyone know for sure?

Trends in Education: Multiplicity

A second key trend in education can be described by the third and fourth characteristics of rhizomatic structures as discussed by Deleuze and Guattari in their book A Thousand Plateaus:

• multiplicity
• asignifying ruptures

In this post I will use the single term multiplicity to speak of both characteristics, except when I want to speak of asignifying ruptures by themselves. 

Multiplicity is a complex concept that we might approach first from the ideas of connectivity and heterogeneity. Every point in a rhizome can and must connect to everything else; thus, we cannot understand any single point, except in a most abstract and academic way, without considering and accounting for all its connections. This brings us directly to holistic, environmental, systemic, relativistic, organic, fractal, chaotic thinking, and is in direct tension with the kind of rigidly reasonable individualism that has dominated much of Western thought and almost all of American thought for the past two centuries. In terms of multiplicity, then, any thing is best thought of as an assemblage of multiple assemblages—both near and far, now and then and yet to be, in and out, up and down—themselves assemblages of multiple assemblages. Thus, at whatever level or scale we consider any thing, we see assemblages of assemblages within assemblages, all interconnected in a fluidly orderly fashion, like a beautiful fractal image.

Orderly brings us to a key second feature of multiplicity: any multiplicity is self-organized. This is self-evident from a modern scientific point of view. If we consider the Universe—the uber-Rhizome—we see that most everything in it has self-organized. The initial spray of light coalesced into hydrogen and other atomic structures, which then organized into stars, then into planets, then into … well, us and eventually into this class at edfutures.com. We ourselves start with a couple of cells and then self-organize into an infant within another rhizomatic structure, or multiplicity, that we call mother. A star has its own light and gravity and self-organization, but that light and gravity extends throughout the universe, and to understand that star, we must consider both its own light, gravity, and self-organization and its relation to all the other lights, gravities, and organization. Any rhizomatic structure, then, contains all the facts and all the mystery possible, and to understand it, we can neither limit ourselves just to the facts or just to the mystery, but must consider the star in all its multiplicities. Clearly, we'll never completely understand any single star, or any single flower or person, and I take great comfort and joy in that. The Universe and everything in it is an infinite multiplicity.

A third point, also self-evident, is that rhizomatic structures are dynamic. They don't self-organize into static entities. They morph, they shift, they merge and sheer, they reorganize. They are susceptible to asignifying ruptures, those exchanges with and sheers into other rhizomatic structures that can so rearrange the rhizome that it appears to lose its significance and signification for us. It becomes asignified, no longer matching the language we've used to signify it. We try to capture rhizomes in language, establishing signs that point this way and that, walling in this space or that, but then the rhizomes shift and the signs point the wrong way. As Robert Frost so plainly says: something there is that doesn't love a wall.

And signification brings us to the final point for this post: our languages for signifying a rhizomatic structure are themselves multiplicities, giving us multiple ways to speak of and to signify any thing, each language with its own value and utility and each language interacting with and engaging the thing differently than another language will. We can start measuring anywhere in the rhizome, on any scale, using any language. Any measure will be more or less useful than others, more or less skillful, more or less salient, more or less common. No measure will be absolutely right or wrong.

To my mind, a multiplicity is easily envisioned in Blaise Agüera y Arcas' wonderful demonstration of Microsoft's new Photosynth technology. Basically, Photosynth is provides the technology to collect images, say of the Eiffel Tower, from around the Net, aggregate those images, and produce one, far more complete, multi-dimensional image that is far richer and more informative than any single image. Thus, the multiplicity produces an image that far exceeds the sum of all the parts.



So what is the point for education? That no student, no teacher, no subject is reducible to a single term. All statements about any student are provisional. "This is John, an exemplary A student, and this is Mary, a problematic F student" are both provisional, and do not say all that can be said or measured about either John or Mary or about ourselves for measuring and saying such things. That to teach any thing, we must define that thing, but our definitions are always provisional, always subject to change, usually sooner rather than later. That crowd sourcing in the style of Photosynth will produce a far richer image of reality than any single teacher or textbook can produce.