CCK11: Knowledge and Context

If you are like me, then you don't have too much trouble imagining cognition as a network phenomenon: all thoughts, visions, dreams, calculations are based on the spidery webs of firing neurons flashing in unique patterns like lightning through our brains. I can imagine, then, some peculiar and unique flash of lightning in my brain each time I think of, for instance, Connectivism. Each time that flash of lightning fires, my brain creates the concept Connectivism, and re-traces those routes along those particular neurons, across the various regions of my brain, traversing both hemispheres, so that I can think Connectivism. In this scenario, a particular flash of brain lightning equals a particular concept, and I can reinforce that concept by flashing it again and again in different contexts until I firmly etch the pathways into the circuitry of my brain. Nice image.

But wrong. If Sporns and his fellow researchers are correct, then this network of firing neurons is too regular and static. It appears that the brain is much more complex than that, and it is possible that any given idea such as Connectivism is not fixed to any specific network of firing neurons. Rather, the brain may use different neurons over different times to create the same pattern of meaning, depending on what else is already happening in the brain. It seems, then, that as we cannot find a specific chunk of knowledge in our brains, we also cannot find a specific network pattern of knowledge in our brains. The brain is far too dynamic for that. As Sporns points out, specific brain functions are not tied to specific brain regions, nor are specific regions tied solely to specific functions:

Different complex functions are accomplished by transient assemblies of network elements in varying conditions of input or task set. In other words, different processing demands and task domains are associated with the dynamic reconfiguration of functional or effective brain networks. The same set of network elements can participate in multiple cognitive functions by rapid reconfigurations of network links or functional connections. (182,183)

Sporns concludes that "functions do not reside in individual brain regions but are accomplished by network interactions that rapidly reconfigure, resulting in dynamic changes of neural context" (183). This suggests to me that any given bit of cognition depends very much on the interaction between the bit of cognition and the neural context within which it immediately finds itself seeking expression. Sporns says that "the functional contribution of a brain region is more clearly defined by the neural context within which it is embedded [and] this neural context is reconfigured as stimulus and task conditions vary, and it is ultimately constrained by the underlying structural network" (183,184).

So what is the takeaway lesson here? For me, it is this: the brain is a most complex orchestra of two parts—a right hemisphere jazz band and a left hemisphere classical orchestra, and each time it expresses the concept Connectivism, it chooses different instruments and different musical arrangements, depending on what the rest of the orchestra, and the conductor, and the audience are all doing. Sometimes, the concept Connectivism may find expression in my brain from the classical side, expressed mostly with woodwinds and a single flute. At other times, the concept may find expression from the jazz side, expressed through a wailing saxophone, a drum kit, and an electric fretless bass, with some contribution from the classical brass section. Either way, or in some other way, I can still recognize the musical motif: the idea Connectivism, but it is not the same network pattern expressed invariably each time. Each time it is expressed, Connectivism is something slightly different, even in my own mind.

This reminds me, of course, of Edgar Morin's view of complex thought, that "the intelligibility of the system has to be found, not only in the system itself, but also in its relationship with the environment, and that this relationship is not a simple dependence: it is constitutive of the system" (11). Sporns' research into neural networks reveals to me that complexity functions in the brain's production of a single thought which depends on the interaction of any defined unit with its enclosing unit and with all the other units that it encloses and that enclose it. A concept depends on the interaction of a given neuron with its brain region, that brain region with the other regions, all those regions with the brain, the brain with the rest of the body, the body with its enclosing groups, and so on.

Emergence in CCK11

Emergence is one of the key concepts in network theory that most attracts me to the conversation. In his article Emergent Biological Principles and the Computational Properties of the Universe, physicist Paul Davies defines emergence neatly as "the appearance of new properties that arise when a system exceeds a certain level of size or complexity, properties that are absent from the constituents of the system." Emergence, then, is an antidote to the reductionist idea that we can understand anything by reducing it to its basic parts and then thoroughly describing those parts and their interactions.

In Chapter 9 of his book Networks of the Brain, Sporns notes the strong impact of reductionist thinking in modern neuroscience and its ultimate shortcomings in accounting for mind:

There have been many false starts in the attempt to link brain and cognition. One such failure is neuroreductionism, a view that fully substitutes all mental phenomena by neural mechanisms, summarized in the catchphrase "You are nothing but a pack of neurons," or, put more eloquently, "'You', your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behavior of a vast assembly of nerve cells and their associated molecules" (Crick, 1994). The problematic nature of this statement lies not in the materialist stance that rightfully puts mental states on a physical basis but rather in the phrase "no more than," which implies that the elementary properties of cells and molecules can explain all there is to know about mind and cognition. Reductionism can be spectacularly successful when it traces complex phenomena to their root cause, and yet it consistently falls short as a theoretical framework for the operation of complex systems because it cannot explain their emergent and collective properties. (180)

Sporns' argument echoes arguments from Edgar Morin that I have noted in previous posts that reductionist science has been "spectacularly successful [in] tracing complex phenomena to their root cause," yet has consistently fallen "short as a theoretical framework for the operation of complex systems because it cannot explain their emergent and collective properties."

I think I detect a similar reductionism at work in most educational theories, which reduce knowledge and learning to the functions of a single mind. Even the social constructivists still limit knowledge created in a group to the knowing of a single mind. This concept of knowledge and learning can be spectacularly successful in helping us trace the complex phenomena of learning back to the behaviors of a single individual, but it fails to provide us with a theoretical framework to account for the ability of a network of strangers to so accurately guess the weight of an ox in a rural English fair, as James Surowiecki describes in his book The Wisdom of Crowds. How does the crowd know the weight of the ox when obviously so few of the individuals in the crowd had even the remotest notion of how much the animal weighed? What emergent properties were at work that produced knowledge that no one person had? For Sporns, this question might be phrased: what emergent properties are at work to produce mind when no one neuron has mind? Reductionism fails us just here. When we collect enough neurons in one place and interconnect them, then new structures and functions emerge—not out of nothing, but into something that wasn't there before. Likewise, when we collect enough students in one place and interconnect them, then do new structures and functions emerge?

I think Carl Bereiter is questioning this specific reductionist tendency in education when he says in the Preface to his book Education and Mind in the Knowledge Age (2002): "What is being challenged is the basic conception of the mind as a container of objects—beliefs, desires, conjectures, remembered events, and the like—which the mind works on in cognition" (1). If Bereiter is correct, then knowledge and learning cannot be reduced to a single mind containing a complicated collection of chunks of knowledge and other cognitive objects and upon which the individual mind operates to create its mental picture of the universe.

I'm somewhat curious that the concept of emergence is not more prominent in our CCK11 conversations. I wonder why.

CCK11: Knowing and Points of View

In a previous post, I tried mapping my knowledge of Connectivism. I created a couple of static images that showed how I related to various other entities in the network of concepts, people, and experiences that make up my knowledge of Connectivism, but even as I posted these images, I complained that they were not quite dynamic enough.

My sister, introduced me to a new mapping tool called SpicyNodes that seems to do a better job of capturing at least some of the dynamism that I sense in knowledge networks, so I started again mapping what I know of Connectivism—in part to learn SpicyNodes and in part to learn Connectivism. This is my first attempt, but I share it with you because I think it works well enough.



Note that unlike my earlier static images, this SpicyNode allows for a shift in perspective as one traverses the network. This is important.

This SpicyNode, for instance, begins with the Connectivism node in the middle. Keep in mind that this was a rhetorical decision on my part. There is nothing inherent in the Connectivism node that makes it the starting node of this network, or even the key or central node. I just happened to start there. I could have started with one of the other nodes: me, Stephen Downes, George Siemens, but I didn't. Rather, I made a rhetorical, political, logical choice to start with the Connectivism node for this particular SpicyNodes text. I should not confuse my choice of order among the nodes with the natural order (if there is one) of the Universe. Even this small collection of nodes is a rhizomatic structure in the sense that Deleuze and Guattari suggest: it has no center, no president, no controlling concept, except the one that I (or you) give it. My choice is mine, and in this particular case, was likely influenced by the fact that I'm enrolled in the CCK11 MOOC: Connectivism and Connective Knowledge.

So I started with the Connectivism node, but in SpicyNodes, I can move to another node, and the network magically rearranges itself about the new center. This captures visually a delicious interaction between knowledge and point of view. Our knowing at any given time depends on our point of view at that time.

Click on Stephen Downes in the SpicyNode above, and see how the whole pattern of knowledge about Connectivism rearranges itself. Click on George. Click on the subnodes. The pattern shifts. There is no knowledge, then, of Connectivism—there is only a knowing of Conenctivism from a particular point of view.

This would seem to break us apart into isolated silos of knowing, but while isolation does occur (Us: the Wall should come down, and Them: the Wall should stay up), it is neither inevitable nor permanent. In his book On Complexity (2008), Edgar Morin says that we must engage other points of view through dialog, not with the aim of reconciling our points of view through some Hegelian dialectic, but with the aim of understanding, accommodating, and perhaps sharing our points of view through a Morinian dialogic. We must accept that knowledge cannot calcify into absolutes of inviolable patterns, tiny dialectics falling like mollusk shells to a sea floor; rather, knowing must remain a dynamic dialog with others, always conducted from the center of our own point of view but with conversations like cellular filaments arcing among all the different points of view to permit a shared conversation that mutually informs all points of view.

For me, at least, this captures the idea behind MOOC CCK11: a dynamic dialog, mostly in writing, that permits a shared conversation that informs all points of view without trying to make them all the same (a useless task anyway).

CCK11: ManyMe, or the Legend of Legion

Last night I posted some thoughts about the network nature of knowledge. While describing how my own understanding merges with understanding at a higher level, I used the metaphor of my voice joining a choir, and I said that "as my voice moves into a choir, my own unique tone and tenor becomes blended and a different voice emerges, a group voice." Even as I wrote those words last night, I was uncomfortable with my choice of the word tenor. It is not a wrong word or even an inappropriate word for the context, but it is not exactly the word that I was looking for, so I was uneasy with it. However, the evening was getting late, I was getting sleepy, so I moved on, ignoring the word.

Or so I thought.

I was awakened early this morning in a hotel room in Chicago by the word I was looking for: timbre (the quality given to a sound by its overtones, as (a): the resonance by which the ear recognizes and identifies a voiced speech sound (b): the quality of tone distinctive of a particular singing voice or musical instrument). This is the word I was looking for. It preserves the euphony that I was looking for—the consonance, assonance, and alliteration—and it has the more useful meaning of overtones, or echoes, that better captures the image I want of patterns echoing into other patterns.

We are all familiar with this kind of thing. We go to bed worrying with some issue only to awaken in the morning with the answer. Common enough. But here's the question relevant to my discussion of networks, especially neural networks: where did this answer come from? I was asleep, unconscious. Who figured this out? Who continued to look at tenor, recognized it as a near miss, looked for the alternative, and then woke me to give me the answer? uberMe? And who is this uberMe? The unconscious mind? That isn't a very enlightening answer.

Sporns makes an interesting observation at the beginning of Chapter 8 in his book Networks and the Brain (2011) when he details how the brain is not limited to merely processing the signals it receives through our sensory organs as we make our way through this world. Rather, the brain is extremely active, even when no sensory impressions are coming in, when the body is quiet, or unconscious as in sleep. Sporns says:

Until now, much of the interest in theoretical neuroscience has focused on stimulus-driven or task-related computation, and considerably less attention has been give to the brain as a dynamic, spontaneously active, and recurrently connected system. … Even cursory examination of structural brain connectivity reveals that the basic plan is incompatible with a model based on predominantly feedforward processing within a uniquely specified serial hieararchy. … The vast majority of the structural connections that are made and received among network elements cannot be definitively associated with either input or output. Rather, they connect nodes in complex and often recurrent patterns. … Even in regions of the brain such as primary visual cortex that are classified as "sensory," most synapses received by pyramidal neurons arrive from other cortical neurons and only a small percentage (5 percent to 20 percent) can be attributed to sensory input. (149, 150)

So much of the brain's activity, even vision, has little to do with sensory input or output; rather, it has to do with the brain's internal creative, organizing, sense-making functions (at least, that's how I'm interpreting Sporns' comments). And this activity is quite independent of my conscious mind, or awareness, which seems to be heavily dependent on the sensory side of the house.

Knowledge, then, even that knowledge easily identified with my own brain, is under the influence of forces and processes of which I have very limited control or conscious awareness. There is an uberMe, an unterMe, which is also at work, and apparently does not tire and require sleep as does the conscious littleMe does.

Hmm … this requires more thought by all the Me's in me, but now I have to go to a conference session. Later.

CCK11: Complex Networks and Knowledge

I think that the concepts of complex networks that I've gleaned so far from Morin and Sporns and of decalcomania that I've taken from Deleuze and Guattari lay two cornerstones for my emerging view of knowledge and learning.

First, complex networks suggest that knowledge is not a single thing, or single think (sorry, I couldn't resist, and I may yet edit this awful wordplay); rather, knowledge is a network of patterns enclosed by larger patterns and enclosing smaller patterns. Any given knowledge pattern is constantly open to the dynamic interactions of all those other various patterns on their various levels. This reinforces Morin's admonition that we define any entity—a cell or a word, say—not from its boundaries inward, but from its center outward. Or better yet, we should define a cell from its center both inward and outward. The center of the cell is not an endpoint of definition; rather, it is the starting point of definition, and to understand the cell, we must move from that center both outward to larger patterns and inward to smaller patterns. The cell must be understood as itself and as a part of an enclosing ecosystem and as an ecosystem for other entities, all dynamically interacting with each other, affecting each other and being affected by each other. Any given knowledge is like this cell: recognizable and addressable as itself, and yet not completely understood without consideration of its constituent parts and its ecosystem and of the ways that it interacts with both those micro and macro scales.

Thus, my knowledge of Connectivism is in fact a pattern of neurons, but that is just a starting point. Moving inward, that pattern of neurons encloses various patterns in different regions of the brain. Each of those patterns encloses individual neurons and individual electro-chemical processes, which enclose individual cells and electrical charges, which enclose other things, and other things, and other things, all the way down to quarks and strings, and maybe beyond that if we ever develop instruments that can see that far in. Back to our starting point and moving outward, the pattern of neurons that is my knowledge of Connectivism is enclosed by my conversation in MOOC CCK11 (among numerous other conversations I'm having—for instance, this blog), which is enclosed by an ecosystem of larger thought about education, which is enclosed by a larger system, and then a larger system, and then the entire Universe, and maybe beyond that if we ever develop instruments that can see that far out. To understand completely my knowledge of Connectivism, then, I must understand everything else.

This, of course, is absurd silliness. It is also our hope for the future. There is no end to learning anything, so we should never be bored. However, in the everyday discourse of common day, we simply can't let a single cell or bit of knowledge bleed into everything else in the Universe, even though it is quite literally connected to everything else in the Universe. A cell or an idea must in some useful way be recognizable and describable and must have potency in and of itself. How do we get out of this predicament?

Perhaps Nicholas A. Christakis and James H. Fowler have an answer for us in their book Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives (2009). In describing how social networks work, they note that the influence of people extends out to about three degrees of separation. In other words, the patterns of our own lives influence our friends, our friends' friends, and our friends' friends' friends. After that, the potency of our patterns of behavior and belief fade and lose their efficacy. Perhaps some mechanism similar to this is at work among the various levels of patterns of any given entity. What do I mean?

Well, consider my knowledge of Connectivism as a single cell. My knowledge is still a recognizable entity with some potency within the context of this blog, though this blog also discusses other things. My knowledge is still recognizable and potent within the context of MOOC CCK11 and the larger discussion about Connectivism, but I think you an begin to see that my unique knowledge is beginning to fade in this larger conversation as it joins to and is overwhelmed by more voices and stronger voices. As my voice moves into a choir, my own unique tone and tenor becomes blended and a different voice emerges, a group voice. Connectivism means something different at this scale. Though my own meaning may still be recognizable, at two or three degrees removed from my single voice—my single understanding—the unique pattern of my knowledge begins to fade into the wider pattern of the general conversation about Connectivism. When we move up to a larger choir—the discussion of education in general—then my voice is quite lost, its identity and potency subsumed by and faded into the cacophony of voices. There are still a few voices potent and identifiable at this scale—Dewey, Piaget, Bloom, etc.—but most voices have long since drowned.

Thus, while I can trace the connections of my single knowledge about Connectivism to infinity and back (assuming I have the time, patience, focus, tools, and skill set), it makes great sense day-to-day to speak of my knowledge of Connectivism as a unique, identifiable entity with its own potency and contours and center. Being an English scholar, I think this entity is something of a convenient fiction, but it makes life much easier to manage.

I'll talk next post about decalcomania.

#CCK11: Mapping the Complexity of Knowledge

I spent some of the afternoon trying to create some images that captured my sense of how knowledge and, thus, learning are complex activities. I'd like to share them, though I'm already dissatisfied with them. Still …

I started trying to map my knowledge about Connectivism in Figure 1. Those of you in CCK11 will immediately recognize a heavy debt to Stephen Downes' illustration about the meaning of Paris.

Figure 1: My Concept of Connectivism

My understanding of Connectivism is represented by the six-pointed star in the middle of the image and is surrounded by people and resources that have contributed in some way to my understanding. My understanding is not one thing, even though the six-pointed star seems to suggest that it is. Rather, it is the dynamic pattern created by the retro-interactions of various people, some of whom know about Connectivism and some who don't, the CCK11 MOOC, readings, some of which are about Connectivism and some which are not, conversations, and my own critical analysis. No one of these things is sufficient to explain my concept of Connectivism; however, all of them are necessary.

It is easy for me to see in this image how just my understanding alone at this level is a complex activity: understanding is the emergence of an idea from the interplay of various patterns of meaning to create a new pattern which takes on intelligibility and a stable core even as it continues to develop and grow in meaning from the center out and even shifts its center from time to time as drastic new patterns occur. In other words, as I keep listening and talking, reading and writing, drawing and thinking, the six-sided star of my understanding of Connectivism defines itself from the core outward, gains its own identity and presence, and begins to interact with the other patterned elements in its field, affecting and being affected, or to use the term of Morin: retro-interactions.

Figure 2: Our Understandings of Connectivism

Complex, yes, but really only just the beginning. If I add the concepts of others—for instance, those of you in CCK11, represented by U1 and U2—then you can see how each of your understandings of Connectivism (represented by the four- and five-pointed stars) starts to interact with my own understanding, and the image becomes even more complex.

What immediately impresses me is that none of us can have exactly the same knowledge of Connectivism. We all come at the concept from different angles and with different concepts, different neural pathways, different understandings of teaching and learning, different emotional fields, different connections to others and to other resources. This seems so obvious as almost to be not worth saying, yet our educational system is predicated on all students learning the same things, at the same time, through the same lessons, and monitored by the same tests. This assumption of standardization is simply wrong. Consider U2's understanding of Connectivism in Figure 3.

Figure 3: U2's Understanding of Connectivism 

It looks nothing like my own understanding. Indeed, there is only an overlap where U2 and I share somewhat similar patterns and some common resources, but both U2 and I have lots of patterns, people, and resources that contribute to our understandings that don't directly contribute to each other. U2 and I cannot possibly have the same understanding.

How can we communicate, then? Well, as near as I can see, communication lies on the borders between the miraculous and the impossible, and the best that U2 and I can manage is a functionally similar understanding. We cannot share an exact understanding. There is no chunk of knowledge that we can both swallow mentally and then say, "Yup, you've got it! Exactly!" The best we can do is to continue in dialogue (in all its various manifestations) until we both create functionally similar patterns of knowledge that allow us to say, "Yeah, that's pretty much what I mean."

Then as if this wasn't complex enough, I'm reminded what Sporns says about the various layers of networks: "Networks span multiple spatial scales, from the microscale of individual cells and synapses to the macroscale of cognitive systems and embodied organisms. … In multiscale systems, levels do not operate in isolation—instead, patterns at each level critically depend on processes unfolding on both lower and higher levels" (2). Thus, within my own mind, a similar complex network of patterns is churning and emerging, and this level affects the churning and emergence of knowledge at the wider level of the MOOC, and in turn, the MOOC level is affected by the wider discussions of education, chaos, complexity, and so forth. These wider discussion are themselves part of a larger ecosystem of discussion about society, politics, and economics, which are themselves elements within language and thought throughout the Ages. And on, and on. Worlds within worlds, patterns within patterns, all self-similar at each scale. All dynamic within their own scales and adding to the dynamism of all the enclosed and enclosing scales.

Finally, if I really wanted to capture a sense of this complexity, then I would have made a movie that captured all these patterns at all the various levels growing, fading, clarifying, and fragmenting as they interacted with elements in their own scale and with the other scales. I don't know if I have the technical talent to create that movie, but I definitely don't have the time just now. Maybe later. It'll be impressive, I think.

CCK11, Connectivism, and Quantitative Analysis

In my previous post, I walked a long way around to finally say that one of the main reasons I like Connectivism is because it seems to be a vibrant conversation within the context of a much larger conversation about complex network structures. If Morin and Sporns are correct, then science in general is moving away from the closed-system, reductionist science of the past to an open-system, complex science of the future. From my point of view, the people engaged in the conversation heating up about Connectivism are moving in a direction that is complementary to this larger shift. I want to be part of that shift.

However, Sporns' book has opened my eyes to what I suspect may be a gap in the Connectivism community: quantitative research. In the Introduction to his book Networks of the Brain (2011), Sporns points out that "connectivity comes in many forms—for example, molecular interactions, metabolic pathways, synaptic connections, semantic associations, ecological food webs, social networks, web hyperlinks, or citation patterns" (1), and I assume that we can include students and teachers in traditional classrooms, MOOCs, and PLNs. He points out, however, that all these different kinds of connectivity require hard scrutiny from the perspective of network science. He says: "In all cases, the quantitative analysis of connectivity requires sophisticated mathematical and statistical techniques" (1).

Perhaps I have overlooked this pocket of discussion, but I think Connectivism lacks a strong, quantitative voice. I know that I don't have that voice, but I think all our conversations could be a bit more grounded if they were informed from time to time with precise observations and quantifiable measurements. Now, I'm an English teacher, so I am not suggesting that quantitative analysis is the only answer, but it is certainly part of the answer.

What might we investigate quantitatively? Sporns suggest several lines of research for neuroscience that might be enlightening for those of us in education in general and composition in particular. For instance, he notes that "nervous systems are composed of vast numbers of neural elements that are interconnected … [thus, we can] probe for architectural principles that shape brain anatomy" (3). Similarly, MOOCs are composed of vast numbers of people and resources that are interconnected by computer networks; thus we can probe for architectural principles that shape a MOOC's anatomy. The writing specialist might phrase it this way: MOOCs are composed of vast numbers of documents from blog posts, to essays, to Elluminate sessions, to tweets that are propagated and interconnected by computer networks; thus, we can probe for architectural principles that shape the written and recorded conversation.

This last question, of course, is of real interest to me, and I am confident that I could tie any findings back into the scholarly conversation about writing, but I am not confident that I have the "sophisticated mathematical and statistical techniques" to generate those findings. Still, this MOOC is sitting here with all these linked documents. It's a shame to see it go to waste. Anybody with sufficient quantitative skills (and I don't even know enough to know what those are) want to join me in this research? Or is this research already underway? Anyone?



PS: The ink was not dry on this post when I happened on a post by Sui Fai John Mak about quantitative research into Connectivism and MOOCs. He references some studies by Dave Cormier, Rita Kop,  and others, which shows that this conversation has been heating up. So it was there all along, and I just didn't hear it until I started thinking about it. Seems that's the way my brain works.

Formalism in CCK11

Our CCK11 Elluminate conversation today, 2011 Feb 09, featured guest speaker Neil Selwyn, who said several times that he thought we might lose something valuable if we indeed ever managed to rid our educational selves of formal institutions and practices. I imagine that he meant such things such as universities, school boards, curricula, programs of study, grading scales, and college deans. I think I have a faint appreciation for his point, but first I want to quibble with his use of the term formal.

To my mind, Mr. Selwyn was contrasting the wide open, free, self-directed, personalized, sometimes chaotic connect-and-collaborate informal structures of networks with the closed, restrictive, other-director, depersonalized, usually well-defined command-and-control formal structures of hierarchies. Popular usage of formal suggests that hierarchical structures are formal while network structures are informal, but I disagree. I take formal to mean any structure that is capable of generating a recognizable form on the basis of some regular procedures. If this is so, then a flock of birds is a formal structure: it is recognizable as a structure (a flock) and it is formed on the basis of a few, regular procedures. A fractal image is just as formal as, say, a triangle. A swirling eddy of water is just as formal as, and much more common than, a perfectly executed circle. Some forms are rigid and geometric, while others are flexible and fractal, but all are forms and, in that sense, formal.

That being said, hierarchies are different from networks, or rhizomes (to use my favorite term). Hierarchies are closed, rigid, and authoritative. Networks are open, flexible, and collaborative. Hierarchies are imposed on reality. Networks emerge from reality. I greatly prefer networks over hierarchies, and I suspect that many in CCK11 share this preference and predisposition.

Still, I think that Mr. Selwyn has a point. Hierarchies have built much of human culture for the past few millennia, and perhaps we dismiss them at our peril. It's at least an idea worth contemplating for a few minutes. Of course, in the past, we hardly had any options. If we wanted to build large organizations (churches, states, businesses, universities), then we almost had to resort to hierarchical structures, bureaucracies and such. We did not have the technology to enable one hundred thousand people to spontaneously gather and coordinate their behavior for some effort or play. We needed churches and states for that, so we built them—some big ones, too. In some ways, then, hierarchies have been one of the crowning achievements of humanity. I just happen to believe that they've been rendered somewhat irrelevant by networks, but perhaps not totally irrelevant.

The question, then, is what do hierarchies do well that we should keep them, at least in special cases?

Clay Shirkey posted an essay entitled Ontology Is Overrated that addresses this very issue, I think. What he calls ontological classification is very much like what I refer to by the word hierarchy. They both impose a prescribed order on reality rather than allowing an order to emerge from reality (this is reminiscent of Deleuze and Guattari's distinction between tracing reality and mapping reality). Shirkey makes a strong case that the new technology allows for humanity to largely abandon ontological classification schemes for more flexible tagging schemes for tracking and finding information. However, he notes, classification and hierarchy still have some strengths. Hierarchical classification works best when the domain being organized has:

1. Small corpus
2. Formal categories
3. Stable entities
4. Restricted entities
5. Clear edges

This is all the domain-specific stuff that you would like to be true if you're trying to classify cleanly. The periodic table of the elements has all of these things -- there are only a hundred or so elements; the categories are simple and derivable; protons don't change because of political circumstances; only elements can be classified, not molecules; there are no blended elements; and so on. The more of those characteristics that are true, the better a fit ontology is likely to be.

Shirkey adds that this scheme also benefits from being used with certain types of people, those who are:

1. Expert catalogers
2. Authoritative source of judgment
3. Coordinated users
4. Expert users

If the educational objective fits the above characteristics for both content and students, then traditional hierarchical structures may provide the student and teacher real benefits over a network structure. Thus, the first introduction to a new programming language might benefit from a more formal approach, in the sense that Selwyn was using the term. However, becoming a really good programmer means that eventually we leave the formal behind and move toward the more informal.

Even as I write this, something in me rebels. I'll have to think some more.

Decalcomania and CCK11

In his blog connectiv: On Connectivism and Learning, Jaap distinguishes between training and learning when we train ourselves to play a piece of music. I think he is capturing the distinction I am trying to explore between tracing and mapping, competence and performance, and working and playing. Jaap's training, then, is tracing and working toward competence, and learning is mapping and playing toward performance. Music provides a wonderful metaphor: to play well enough to bring joy and satisfaction (and perhaps a paycheck) to both herself and her audience, a musician must have competence with music and instrument (which requires ten thousand hours of work), but she must also transcend mere competence into performance in order to play the music on her instrument and to expand and express as an artist. Training/tracing and learning/mapping are not opposing activities, but different ends on a sliding scale of activities, and both are connectivist in nature.

I understand both training and learning as Connectivist through Deleuze and Guattari's concept of decalcomania, one of the six characteristics of rhizomatic structures that they explore in their book A Thousand Plateaus (1988). Decalcomania is the artistic process of transferring an image or pattern from one structure to another, usually by pressing the two structures together. According to ARTTalk, "technical explanations of decalcomania describe the method as geometric shapes--irregular, broken or fractured (rather than smooth and even). The two images created by pressing one area of liquid with a top sheet of paper display a form of 'self-similarity,' appearing similar in scale and magnitude - very nearly exact duplicates. In early production, this meant that the creation of two images was made with each attempt. Infinitely fine detail is immediately apparent yet, when magnified, yields startling accents." The capitalismandschizophrenia.org website defines Deleuze-Guattarian decalcomania as a method of "forming through continuous negotiation with its context, constantly adapting by experimentation, thus performing a non-symmetrical active resistance against rigid organization and restriction."

A class about fractals at Yale University notes that decalcomania can form dendritic fractals, as in the picture below:

To my mind, decalcomania is a process for transferring a pattern from one thing to another, and it describes quite accurately how we create meaning in our minds. In decalcomania, a surface with a potent image or medium is pressed against another surface. After the two surfaces are separated, self-similar images reside on both surfaces. The images can diverge more and more as the two surfaces vary in material, texture, porosity, density, color, and so forth. The images can diverge again given the viscosity and consistency of the intermediary medium being pressed between the two structures, and the images can diverge even more if the pressing is inexact or uneven and smears. Decalcomania, I think, provides a nice metaphor for understanding learning and training: the process of impressing patterns between student and class, person and world, guitarist and guitar, artist and canvas.

But first, let me correct a part of my definition. In decalcomania, pattern is NOT transferred from one thing to another. Transfer is an habitual manner of speaking that obscures a deeper insight. Only in it's most basic and popular form of decals, where an image is removed from a special paper and applied whole and unaltered to a new surface, does decalcomania reduce to mere pattern transfer. Unfortunately, this is the dominant metaphor for traditional learning and all training: a knowledge pattern is transferred whole and unaltered from a source into a new brain which then has that new knowledge pattern. This is fundamentally wrong and leads to all sorts of counter-productive pedagogical strategies and theories.

Rather, decalcomania awakens patterns in both structures. When an artist presses some medium—paint, for instance—between two surfaces—say, cloth and paper—then the act of pressing and releasing the paint creates a pattern on both the cloth and the paper. The two patterns very well may be self-similar, but they are highly unlikely to be exact duplicates. Even in industrial processes which impress images on some surface (on a Coke bottle, for instance), "infinitely fine detail is immediately apparent yet, when magnified, yields startling accents," or variations.

Decalcomania, then, helps me explain my interaction in MOOC CCK11. I have pressed some media between myself and MOOC CCK11—different media: Elluminate sessions, discussions, back channel chats, blog posts, essays, Facebook comments, Youtube videos, etc.—and each pressing has awakened in my mind new patterns or reinforced or changed old patterns. Each pressing has also awakened different patterns in MOOC CCK11. Both I and MOOC CCK11 are different because of the impressions each has made on the other. (Of course, CCK11 is bigger than I am, so the impression I make is smaller on it than the impression it makes on me; however, think of the impressions made by Downes and Siemens to see more clearly how the act of impressing works both ways, changing both the individual and the group.)

This process can be explored more. For instance, I am certain that my learning is slightly different, perhaps radically different, from the learning of others in MOOC CCK11, even when we consider the same media. In strictly physical terms, no two brains are structured alike; therefore, a pressing between my brain and MOOC CCK11 through the medium of a given Elluminate session will create a necessarily different pattern of knowledge amongst my neurons than amongst, say, Stephen Downes' neurons. The surfaces of his brain and of my brain are perhaps similar but still different, even in physical detail and certainly in knowledge detail. I may not even map what I learn in the session in the same area of the brain as he does. I certainly won't map it with the same arrangement of neurons. It takes multiple pressings through different media for the two of us even to begin to approximate consistent knowledge patterns in both our brains and in our interactions. (It's the whole process of getting to know each other.)

This process of decalcomania seems to describe many of the classes I've taken and taught. It also explains to me why the industrial method of education as described by Sir Ken Robinson has become so ineffective. If you haven't seen him speak on this issue, then watch Sir Ken explain why we need a radical shift from the industrial paradigm of education:

Performance vs Competence in CCK11

Mapping and tracing are both efforts by people to orient themselves within a given structure, say a class or a conversation. Whereas tracing attempts to assign an order to the structure, mapping seeks to uncover the order in the structure. In terms of MOOC CCK11, tracing attempts to impose an order on the class (roles, meeting times, duration, interactions, etc) and on the content (beginning, middle, end, etc), and when a tracing does not find the expected points, it becomes disoriented. Mapping, on the other hand, does not impose an order, but remains open to the possibility to any order or to no order at all (though the human mind is quite adept at imposing or creating order even in the absence of any apparent order). Tracing is an attempt to wrangle reality into sense, while mapping is an attempt to uncover the sense in reality.

This last distinction points to another reason why I am attracted to the conversation about Connectivism. Connectivism is still in the mapping phase of theory construction. It seems to me that most theories begin with a mapping phase that seeks to uncover the sense in reality. Moreover, this attempt to map some slice of reality is usually in reaction against some other theory that has calcified into dogma and seeks only to trace reality, or to wrangle reality into the sense of the theory. Mapping is often prompted when a Galileo at last notes enough points in reality that don't fit in the old theory without excessive wrangling and so begins to look at reality in a fresh way. To my mind, Connectivism is looking at reality in a fresh way. If eventually Connectivism becomes accepted theory, then it will likely go the way of most theories and itself become dogma, a tracing rather than a mapping (not a static map, but a dynamic tracing—a verb rather than a noun), a routine rather than a ritual. But that hasn't happened yet, so until it does, I will enjoy the ride.

It helps, then, to sharpen our distinction between mapping and tracing. Deleuze and Guattari note that "the map has to do with performance, whereas the tracing always involves an alleged 'competence'" (12,13). I find this so insightful and quite germane to education with its practice of assessment and grading. It reminds me of a story I once read about an education professor who visited a kindergarten class and asked the five-year-olds which of them could sing, dance, and draw. At each question, all the children enthusiastically raised their hands, certain that they could sing, dance, and draw. The professor then returned to his college classroom and asked the same questions. Of his adult students, only a few could sing, a different few could dance, and yet another two or three could draw. He concluded that the main function of modern education was to teach people what they couldn't do.

I appreciate the professor's point, but I think that Deleuze and Guattari can give us a more precise way of explaining what happens to students between kindergarten and graduate school. If we assume a sliding scale between performance and competence, then kindergarteners are focused almost totally on the performance end of the scale in total disregard of how well they sing, dance, or draw, while grad students are focused almost totally on the competence end paralyzed by assessments of how well they sing, dance, or draw. Kindergarteners are concerned only with exploring and mapping an activity through their performance, while grad students are concerned only with competently tracing a sanctioned activity.

In this MOOC, Downes and Siemens are refusing to grade the performances of most students, and this disregard for the traditional markers of competency confuse some of us. How do we know if we are doing it right, dancing right, learning what we are supposed to be learning? Most of us have lost the questions on the performance end of the scale that drive open-ended, free form inquiry, mapping, and play (though I suspect the members of this MOOC are perhaps more open to performance than most students; otherwise, they wouldn't be in this MOOC). I think that a big part of the lesson in MOOC CCK11 is to reawaken those questions of performance and play within the MOOC's members.

One might accuse me of totally favoring performance over competency, but I do not. However, I do have a profound distrust of the merely competent, which in my experience, informs too much of traditional education and all of the back-to-basics movement. I insist that education should be large enough for both performance and competence, and that the best education happens in the interplay between the two. For example, mastery of the guitar is a fine educational process that necessitates a nuanced balance between performance (play) and competency (work). A guitarist must work the guitar to attain competency with it, and this can require ten thousand hours of practice, hitting the same notes over and over, going through the same fingering patterns, reading the same musical scores. But the guitarist must also play the guitar to attain more than competency with it, and this builds upon the ten thousand hours and sustains the guitarist's drive to put in the ten thousand hours. Performance first informs competence, and then it transcends competence, but mere competence is never enough to make a guitarist. This is perhaps easy to see in a jazz guitarist who can improvise whoever he wants, but even a classical guitarist who is tightly constrained by working a musical score (competency) must also play that musical score (performance).

Associating performance with play and competence with work makes sense for most educators, I think, and it makes sense to me that traditional education has focused too much on the work of competency and not enough on the play of performance. Education has sadly overlooked the ludic element in our pedagogical mix, and MOOC CCK11 is a nice corrective to that pattern.

Mapping Knowledge in CCK11

I want to talk more about what I find engaging about this MOOC: CCK11, even at the risk of sounding as if I'm sucking up, but it seems to me that a number of people have recognized that learning the MOOC way is in fact the main content/task of the course. As Tracy Parrish said in one of her early posts about CCK11: "It's amazing (and slightly sneaky) that what I'm learning about is how I'm learning about it." So I want to clarify for myself what is working for me. I may eventually get around to what isn't working. We'll see.

I have sensed some uneasiness within the MOOC with the refusal by Siemens and Downes to behave like traditional teachers. Many of the group want these teachers to tell us what to learn and how to learn it and to verify that we have, in fact, learned it. On their side, Siemens and Downes are always pushing us to become independent learners, to grab the mic in the Elluminate sessions. (ASIDE to S & D: the group's reluctance to take the mic may merely indicate that those who wish to talk are already doing so within the chat area and feel no real need to speak aloud on the mic. Those who are lurking don't want to talk in either space.) At any rate, Siemens' and Downes' refusal to act as traditional teachers makes sense to me especially in light of the concept of rhizomatic structures as outlined in Delueze and Guattari's A Thousand Plateaus (1987).

I see this MOOC as a rhizomatic structure (something like a network structure and my preferred term), and one of the characteristics of such structures, according to D and G, is mapping, or cartography, as differentiated from tracing. Unlike tracing, mapping "is entirely oriented toward an experimentation in contact with the real. The map does not reproduce an unconscious closed in upon itself; it constructs the unconscious. It fosters connections between fields" (12). As Chuen-Ferng Koh says in Internet: Towards a Holistic Ontology: “Rhizomatic links … are formed through mapping—or active construction based on flexible and functional experimentation, requiring and capitalizing on feedback. The map is not … a blueprint whose workability has to be taken on faith; the map is never fixed, but a changing flux of adaptation and negotiation.” Tracing begins with a conception that is not necessarily part of a structure such as a class and appliqués (formerly not a verb) that conception to the structure (a class, for instance). Mapping begins with a structure (such as a class), and through a process of flexible and functional experimentation and response to feedback, builds an image that becomes a living part of the class, shifting and growing as the class shifts and grows and as the attention of the map-maker becomes sharper, better informed, more capable.

Deleuze and Guattari use a quote from Carlos Casteneda's Don Juan to illustrate the difference between tracing and mapping. When the Yaqui shaman Don Juan teaches Carlos how to map a garden for cultivating his psychedelic herbs, he says: "Go first to your old plant and watch carefully the watercourse made by the rain. By now the rain must have carried the seeds far away. Watch the crevices made by the runoff, and from them determine the direction of the flow. Then find the plant that is growing at the farthest point from your plant. All the devil's weed plants that are growing in between are yours. Later … you can extend the size of your territory by following the watercourse from each point along the way" (The Teachings of Don Juan, 88). See? The shaman doesn't say trace out a space 100 feet by 100 feet, clear the soil, and trace rows in the dirt to plant your seeds. That's starting with a blueprint of a garden, fixing the garden before it ever grows. Rather, the shaman advises that Carlos start with one plant, an anchor, a point to which he can connect, and then map the various pathways from that point, constantly checking, marking, mapping until he discovers how large his garden is and what shape it has taken.

Tracy Parrish is making maps of this MOOC here and displaying other maps of other network structures here. This map making is an essential part of participating in a MOOC, and it is fundamentally distinguished from making a tracing, or a blueprint, of a class. Traditional education assumes a blueprint, and most us, particularly those of us who were the best students, have become quite adept at following the blueprint. I think Siemens and Downes are suggesting that we quit following blueprints and learn to map knowledge. More on this later.

Eating the CCK11 MOOC

My current MOOC, CCK11, is reminding me again why I have been so attracted to Connectivism — not because it is a fine theory of learning and knowledge, but because it is a fine conversation.

I have read some educationists who argue that Connectivism is not a new theory or not even a theory at all, and I am not informed enough about the various educational theories to weigh in on the debate, but what I can say with great authority is that Connectivism has provided me with a wonderfully rich and ample conversational space. I think I value conversation over theory anyway. Conversations tend to be more open systems; whereas, theories are too often closed systems. Of course, conversations with fundamentalists tend to be closed and some theories are quite open to complexity and chaos, but in my way of thinking, conversations are more open than theories.

I teach writing, and I write. Connectivism has created a conversation that has allowed me to explore with some very interesting people how writing to learn engages me with my world. Connectivism has set a fine table with lots of dishes, and I intend to feed here for as long as the feast lasts, or until I am satiated.

The feast metaphor suggests to me that learning in the Connectivist sense is much like eating. Learning is ingestion. Let's see where this goes.

If Paul Davies (The Cosmic Blueprint, 2004) and Edgar Morin (On Complexity, 2008) are correct, then the emergence and maintenance of life depends on the exchange of energy between an open, physical entity and its ecosystem. As Morin says, this exchange involves "not only energy and matter, but also organizational and informational resources" (10). A consequence of this notion of an open system is "that the intelligibility of the system has to be found, not only in the system itself, but also in its relationship with the environment, and that 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. This connection is absolutely crucial epistemologically, methodologically, theoretically, and empirically" (11).

This connection between the open system (I, for instance, am an open system) and the environment is not a pipe, though that could be a useful metaphor. Rather, the connection is an engagement and an exchange. The connection is me eating my world and, in turn, being eaten by my world. My world and I exchange energy, matter, organizational patterns, and information. When that exchange stops, when I become a closed system, I die. For me to live means in a myriad of physical and mental ways for me to continuously eat at the table of life. When I quit eating, I die.

If either I or my Universe become closed systems, we both die. Fortunately, the Universe is an open system continuously engaging and exchanging energy, matter, pattern, and information among its various parts. Some physicists even postulate that this Universe may be exchanging energy, matter, pattern, and information with other Universes, perhaps through black holes, but that takes me far from any kind of expertise that I may have. I'm better to stick with the MOOC.

What makes this Connectivism MOOC such a rich conversational space is that it is still an open system. Its theory, if it has one, has not closed in on itself, petrified, and become pathological. Perhaps this is because it is still relatively new. Perhaps it is the nature of the theory itself. Whatever the cause, I find that my exchange with Connectivism gives me intellectual life.

Rather, it gives me the potential for life. It gives me an ecosystem that can sustain life, that can sustain an intellectual conversation, that open exchange of energy and information. To thrive in this space, I must myself remain an open system within an open ecosystem. If either I or Connectivism ever find the Truth, the Absolute Right Answer — thus becoming a closed, complete, static system with no possibility for more or new energy or information — then I die, or Connectivism dies, or we both do.

I have great faith that God has so ordered the Universe that the Absolute Right Answer does not exist, except in the most mundane and boring of spaces, those closed systems where the light is harsh, the conversation has died, and there's no more food. Thus far, the Universe has afforded me easy exit from such spaces. Connectivism has been one of those exits. Hallelujah.

Complex or Complicated?

I read an excellent post by Lindsay Jordan related to #CCK11, the MOOC that I'm currently engaging. Following a comment by George Siemens, Lindsay makes a fine distinction between complexity and complicated: an airplane is complicated; the weather is complex.

I think I would rather say, however, that an airplane is complicated and creating the airplane is complex — not because the original statement is incorrect, but because it might give the wrong impression that complexity is of natural origins while complicated is of human origins. Rather, an airplane is complicated because it is a mostly static collection and arrangement of parts; whereas, creating the airplane is complex because it is mostly a dynamic interplay of people, ideas, materials, and processes. A specific airplane is a machine, complicated perhaps, but not growing. Creating airplanes is a living process, complex and growing.

As Edgar Morin points out so eloquently in his book On Complexity, we make a huge mistake when we try to reduce the complex to the merely complicated, or worse yet, to the simple. Actually, complicated and simple differ only in degree, whereas complex differs in kind from both. In one sense, both simple and complicated refer to a collection of fewer or greater elements in a particular, static arrangement. Complex refers to a collection of elements in an "infinite play of inter-retroactions" (Morin, 6).

Static entities, such as machines whether complicated or simple, are knowable, and once known, they remain known. Complex entities are not knowable in this manner. Rather, we engage complexities through what Morin calls a dialogic principle: we must constantly dialogue with the complex, for it is constantly shifting, growing, becoming. The complex is always in the middle, passing from this state to that. It is never static, thus never known definitively. Only through our interactions and our various connectivities can we know the complex, and we must constantly fire along these connections to activate feedback loops that inform, shape, and tweak our knowing of the complex entity.

From my experience, this distinction in knowing between the merely complicated and the truly complex makes a useful distinction between training to master a complicated concept or skill and teaching to master a complex discipline. Both training and teaching are exceedingly useful, and each is pre-eminent in its own right; however, they should not be confused with one another. When we are learning the one and only right answer, then we are involved in training. When we are learning to probe open-ended questions with open-ended answers, then we are involved in teaching. Sometimes the same class can be a mix of training and teaching, but we teachers should know when we are doing the one or the other.

And as George Siemens has pointed out elsewhere, we should always keep in mind that the right answer is especially short-lived these days, as the half-life of knowledge is continuing to shrink. Less and less of reality is static (or changing so slowly that it is practically static), thus less and less of our knowledge can be static. Rather, we must be constantly updating what we know so that it matches well with what is.

Digesting #CCK11 - Riffing off the eating meme

You have to start somewhere — the middle seems best.

Actually, it seems the only place to start with a MOOC. I am again taking a massive open online course, a MOOC, with George Siemens and Stephen Downes, and again, people are struggling to orient themselves to this kind of learning. I am becoming convinced that the best learning to emerge from these MOOCs is learning to deal with the MOOC itself, regardless of the content about which the MOOC is organized.

Engaging a MOOC shifts a participant immediately and radically away from the command-and-control structures of traditional education and into the connect-and-collaborate structures of rhizomatic learning spaces. This can be extremely disorienting the first time, a fact that both George and Stephen seem to recognize and are attempting to address with videos posted to the Home Page of CCK11. Their sometime collaborator Dave Cormier has also posted some videos to YouTube talking about how to orient oneself to a MOOC. I'll repost one of those videos here:

For me, the key idea is to approach a MOOC from your own position. This is radically different from the way we approach most college classes, which come to us whole and contained. When we engage a traditional college class, we enter an existing structure with fixed content, fixed authorities, fixed space, place, and times, fixed goals, fixed paths to those goals, and fixed assessments to determine how far along the path we managed to travel within the prescribed time. Good students are often those who have learned to quickly identify the fixed markers, determine the right answers, and give them to the teacher. We can succeed (make an A) in a traditional class without being very self-aware. Just jump through the hoops and move on.

MOOCs do not function this way. Very little is fixed, other than the general topic, and I have noticed that wandering from the topic is hardly ever discouraged in a MOOC. If a sub-group in a MOOC taps into a rich vein of discussion, then they are free to follow it wherever. This lack of fixed reference points is disorienting, especially to good students who have mastered the traditional classroom. We cannot succeed in a MOOC without being extremely self-aware. We must know who we are, what we are about, and what engages us. To use a spatial metaphor, we must know where we are so that we can begin to orient ourselves toward this massive new structure that has many destinations and few signs.

But it is more complicated than that. We must accept that our very presence and engagement itself changes the MOOC. The fact that I am in the MOOC (or you) makes the MOOC different. This is another radical difference between MOOCs and traditional classes. Most of us can remember countless college classes that were mostly oblivious to whether we ourselves were in attendance or not, a member of the class or not. In a MOOC, it always matters who is in and who isn't. In a MOOC, membership is everything.

To use an astronomical metaphor, a MOOC is like a solar system, each member of the system exerting its own more or less powerful gravitational pull on all the other members. Some of us may be Jupiters, some of us Mercurys, some of us just lurking asteroids, and I suppose George and Stephen are the Sun, but whenever any new element is added, then the entire system must shift to accommodate. And we are all constantly adding new elements in the form of blog posts, videos, comments, Elluminate sessions, and so  forth, so that our solar system is becoming increasingly crowded, rich, varied, and diverse — larger than any of us can contain, and with more texture than any of us can cover.

This is why Dave suggests that we first pick a few points in the system to anchor ourselves. The Home Page of the website is a good anchor. The Elluminate sessions are good anchors. The Daily Digest is an anchor. And most importantly, our own professional interests are good anchors.

Then from those anchors we scan and connect to other points that catch our interest, that resonate with energy that we can recognize and follow. We begin to create our own gravity with our posts, comments, videos, lists, SL groups, Tweets, etc. We find that we cluster, that we fall into synchronized orbits with similar objects that attract us. We pull other objects into our orbits. We make many connections, follow some and abandon others. We begin to focus, plowing an orbit through this system, an integral part of the whole while still following our own path.

It's this interplay between our own path and the paths of all the others that makes for a harmonious solar system and that makes for a harmonious MOOC.

You have to stop somewhere — the middle seems best.