Boundaries and the Included Middle

So Mending Wall does not present us with a binary choice between the discrete individualism of reductionism and classical logic on the one hand or the undifferentiated unity of holism and mysticism on the other. Rather, the poem presents a third way, a middle way, but not in the Aristotelean sense of a Golden Mean or in the Hegelian sense of a synthesis. This way is definitely not from Aristotle, but rather from quantum physics and chaos and complexity theory, ideas that were just emerging when Frost was writing. The poem embodies something that Basarab Nicolescu calls the included middle, a concept that I still have not mastered but that is becoming increasingly important to my understanding of boundaries.

I first encountered the term included middle in Nicolescu's book Manifesto of Transdisciplinarity (2002), a difficult book that I'm still not ready to discuss. According to Joseph E. Brenner in his essay The Logic of Transdisciplinarity (from Nicolescu's book Transdisciplinarity: Theory and Practice, 2008), "the logic of the included middle [was] developed by the Franc-Romanian philosopher Stèphane Lupasco (1900-1988) and extended by Nicolescu … [as a] needed replacement of the neoclassical logical framework that underlies current individual, social, and scientific paradigms" (155). As I understand it, the developments of quantum physics which sees light as both a particle and a wave at the same time establishes the need for a new logic to complement and transcend the old, classical logic, which Nicolescu (In Vitro and In Vivo Knowledge in Transdisciplinarity: Theory and Practice) says was "founded on three axioms:

1. The axiom of identity: A is A.
2. The axiom of noncontradiction: A is not non-A.
3. The axiom of the excluded middle: There exists no third term T ("T" from "third") which is at the same time A and non-A" (6).

According to this fundamental way of constructing Reality, light can either be a particle or a wave, but it can not be both at the same time. Quantum physics, however, said that light was both particle and wave and at the same time. Something had to give. Lupasco and Nicolescu decided that logic would give, and so they developed the logic of the included middle, and I think it is this included middle that Mending Wall captures for me.

The wall in the poem is, of course, the boundary between the narrator's farm and the neighbor's farm. It is also the boundary between the narrator's dislike of walls and the neighbor's like of them. According to the old logic then, traceable all the way back to Aristotle, the narrator's farm is the narrator's farm, it is not the neighbor's farm, and there is no middle ground that is both narrator's farm and neighbor's farm. This logic makes great sense at the level of common, everyday Reality. It puts everything in its place and keeps it there. Most of us act on this common, classical logic everyday.

But when we shift levels of Reality, then the limitations of this logic become obvious. Nicolescu says that natural science has discovered at least three different levels of Reality—"the macrophysical level, the microphysical level, and the cyber-space-time"—with a break in the laws and concepts applicable to each level. These levels exist simultaneously and through engagement with one another, and the contradictions at one level (A vs. non-A) become non-contradictory at another level. I do not have the skill with mathematics or formal logic to describe this for you, but I think the poem gives me a way of visualizing this concept. At the everyday scale, or Level B, of reality, the wall creates a boundary between the narrator's farm and the neighbor's farm such that each is itself and not the other and there is no middle zone that they both occupy. There is indeed a boundary between the two at Level B of Reality, and a person can step over that boundary. Or not. This defines our day-to-day existence at Level B. 

However, if I stand at the boundary and rise upward to the level of the macrophysical, to Level A, then the two farms become smaller and smaller until they become two dots and then one dot and then nothing. No boundary. Likewise, if I fall downward to the level of the microphysical, to Level C, then the two farms become larger and larger until they become molecules, atoms, and strings of vibrating energy. Again, no boundary, at least not between two farms. Thus, the contradiction at one level of reality is a non-contradiction at another level. It is not resolved, as it would be in a Hegelian dialectic, because the contradiction continues to exist on Level B at the same time that it does not exist at Levels A and C. There is no resolution, only a certain tension among the various points of view. The wall both is and is not at the same time. Turn your head one way, and it is. Turn your head the other way, and it is not. The wall is both actual and potential at the same time. Your knowledge of its state depends on your position relative to the wall.

Well, I think this is one way to think about the included middle. It's one way to think about boundaries.

Boundaries as Zones of Engagement

So in his poem Mending Wall, does Robert Frost really want to tear down our walls?

No, he doesn't. That is too naive a reading, and Frost is doing something far more interesting, I think. Frost is not locked into an either/or choice. As near as I can tell, Frost is defining boundaries neither as a line that separates nor as the point at which we all merge seamlessly into the Cosmos. Rather, Frost (if not the narrator) is defining boundary as a zone of engagement. For me, this is worth thinking about.

Note first that the wall is where the two farmers, the narrator and his neanderthal neighbor, meet and engage each other in "just another kind of out-door game, One on a side" (ll. 21,22). The wall/boundary does not separate the two men into discrete entities; neither does it merge them. Rather, the wall is the zone where each engages the other in a kind of game. Well, where else can we engage another except at the boundary and in some kind of game?

This zone of engagement has some specific features. First, it has thickness. It is not a thin line that sharply demarcates one farm from the other; rather, it is a zone. And this thickness does not suggest impermeability, but permeability as the narrator's farm gradually yields to the neighbor's farm. Indeed, where "He is all pine and I am apple orchard," we might easily see some pine cones dropped on this side and a few apples scattered on that side, and of course, the grass, as a rhizome, has a sneaking habit of spreading over, around, and through the wall to join this side with that. Boundaries are zones, membranes, and they filter—they don't seal. Clearly at some point far enough on either side of the wall is all one farm or the other, but at the boundary, there is slippage, seepage, and oozing. And the wall/boundary is a matter of scale. We know from the benefits of modern science that if we drill down to the molecular level deep within the stone that we will reach a scale where it is impossible to tell any longer whether we are on this side or that. The farms have merged. Or we can scale up to the view of satellites, and again we lose the boundary as both farms merge into the surround.

The wall in the poem is the zone of tension between the narrator and the neighbor. It's where all the exciting stuff happens. It's where all the compromises are made. All far enough on this side, of course, is narrator, and all far enough on that side is neighbor, but here at the wall, it isn't quite narrator or neighbor. It is the included middle: the unresolvable tension of the dialogic engagement. It's where all the games of life happen, the good and the bad, the enjoyable and the miserable. Frost has captured in a quite simple image and event a very rich vision of complexity, I think, but I suspect no one will be convinced if I do not provide details. Tomorrow.

Defining Boundaries

In a few weeks, I will deliver a presentation about boundaries to the Southern Humanities Conference convening this year in Savannah, GA. The conference topic, Boundaries: Real and Imagined, was chosen at last year's conference, and I have come to think about boundaries often this year as I have read deeper into complexity theory. It seems to me now that boundaries are much more than the lines (real or imagined) that separate things (real or imagined).

As I've thought about boundaries, I've come to realize that I have most often used the term to signify a line which divides one space, entity, or idea from other spaces, entities, and ideas, separating and distinguishing among them. I also use boundary to talk about the line that marks the outer limits or extension of a space, entity, or idea. (You can see these usages in my blog posts as early as 2007, 2008, and 2009 and then later in 2011 and 2012). All the stuff within the boundary belongs to and is identifiable as that space or entity. All the stuff outside the boundary belongs to some other space or entity. Boundaries, according to my old usage, are the boxes that hold and define a thing—inside the boundary is the thing, outside the boundary is everything else. This view, of course, involves me in the issues with definition that I've been struggling with in this blog, and to my mind, boundary—as I've been using it—is an aspect of our reductionist and essentialist habits of mind, especially mine.

Humph! And all this time I've been imagining myself a post-structuralist. Oh, well. Let's see if we can weed this bit of neo-fascism out of my heart. Or, more likely, weave it into my heart with a slightly different thread. Given the rhizomatic nature of thoughts, I have no hope of weeding any idea from my head or heart.

I think my usage of boundary began to trouble me as long ago as 2010 when I started referencing Robert Frost's poem Mending Wall as I struggled to understand Deleuze and Guattari's concept of asignifying ruptures and the rhizome. As I understand it, asignifying ruptures are those flights of deterritorializations and reterritorializations of entities that unhinge our neat little definitions of reality, which has a nasty habit of regularly escaping the little boxes (significations) that we try to put it into. As Frost famously says in his poem, "Something there is that doesn't love a wall." That something is Reality, or the Rhizome. It doesn't like being boxed in, and I was delighted to find in Frost an early proponent of post-structuralism.

Or so I thought. I was forgetting the other repeated mantra in that poem: "Good fences make good neighbors." Hmm … something else there is, then, that does love a wall. But I argued with myself, clearly the poem, if not Frost himself, favors breaking down the walls that separate us, doesn't it? Near the end of the poem, after the narrator has stated his case against walls, he paints an uncomplimentary picture of his neighbor and his neighbor's point of view:

    … I see him there
Bringing a stone grasped firmly by the top
In each hand, like an old-stone savage armed.
Not of woods only and the shade of trees.
He will not go behind his father's saying,
And he likes having thought of it so well
He says again, "Good fences make good neighbors."

Isn't Frost suggesting that people who like clear, firm boundaries are stone-age simpletons who can't understand the value of tearing down the Walls, a firm value in this post-structural age and which I believe is the only point of agreement one can find between Pink Floyd and Ronald Reagan? Perhaps Forst is not so facile. I'll think about this more tomorrow.

Rewiring the Classroom

In the last 5 chapters of his book The Art of Changing the Brain, Zull suggests the practical implications of neuroscience for the classroom, beginning with the use of sensory experience:

• SENSE LUSCIOUS: Using the power of the sensory brain to help people learn – The brain is wired for sensory experience, and while sight is the most powerful of the senses for most people, sensory experience involves the total body. In general, the more senses a lesson can engage, the better. Too many teachers seem to believe that their lecturing is a sufficient sensory experience for student learning. Lecturing is, in fact, a sensory experience, but when I think back to most of the lectures I endured, then I realize how displeased my senses were with the experience: a droning voice, dry, dusty chalk smells, drab rooms and lecture halls, an aching ass from sitting too long (I have lower back problems), my bouncing legs, the unexpected discovery of discarded chewing gum. The lecturer's words were seldom engaging enough to overcome all those other sensory impressions. The world simply drowned out the droning don, and god forbid a pretty girl should be in class—then I couldn't even take notes. If the lesson is not engaging the student's senses, then the class will. Fortunately, my writing classes have a built-in sensory experience: writing. Unfortunately, that doesn't work for everyone, so I use texting, drawing, discussing, games, reading, contests, group work, and more to engage students' senses. My classes are noisy, bordering on happy. This has troubled some of my superiors.
• WAITING FOR UNITY: Helping people comprehend their experience - "Reflection is searching for connections—literally!" Students need time to bounce their experiences around in their heads to build the connections necessary to integrate information into their own neural networks. This is how we create knowledge. Knowledge is not imparted, given, or transferred. That's a harmful metaphor. Knowledge is not even in our brains—that's an even more harmful metaphor. As Diane Laflamme says in her essay Ethics and the Interplay Between the Logic of the Exluded Middle and the Logic of the Included Middle (in Basarab Nicolescu's Transdisciplinarity: Theory and Practice, 2008), "The body does not contain consciousness" (150).  Rather, consciousness and knowledge are emergent properties, epiphenomena, of the interplay of neural networks. Better: it's what emerges when our brains fire in synchronicity with our body's sensing and acting within a rich ecosystem that is also firing. This bubbling of concepts is called reflection. The brain is looking for useful, recognizable patterns in its sensory data to integrate with the patterns that it already has. Even dreaming is an important part of reflection, but since we can't use dreaming as an instructional strategy in most classes (most of us work hard to counter daydreaming), then we use language for reflection. Actually, we should be encouraging our students to use language through discussion and writing, rather than falling into the easy habit of us talking all the time. Again, my writing classes have a built-in advantage, but only if I'm giving my students time to reflect on a lesson's sensory experience. 
• THE COURAGEOUS LEAP: Creating knowledge by using the integrative frontal cortex - Though related, short-term memory and long-term memory are not the same, nor are they necessarily linked. We can sometimes hold prodigious amounts of information in short-term memory without transferring that information to long-term, and sometimes we transfer powerful experiences directly to long-term memory, bypassing short-term. Students must be allowed to form their own long-term memory ideas, and this takes time and ownership. Short-term memory is powerful, but limited and easily replaced with new sensory data; thus, we cannot overload short-term with too many facts or too much feedback. To learn, students must hold limited information in short-term memory, and then have time to manipulate and play with that information to form connections in their own minds. Teachers who are in a briskly-paced rush to cover the material seldom allow the time and conditions for students to build the connections necessary for moving raw data from short-term memory into the knowledge centers of long-term memory. Students must have time and activities to attend to relevant bits of info and organize the learning task, task management, for themselves. They must develop a sense of probability, or an innate sense of statistical reasoning. This is critical thinking, and without it, most students don't learn, especially those who do well on the test.
• TEST BY TRIAL: Using the motor brain to close the loop of learning - Learning is active, action. Learners must be able to test their ideas to see if reality pushes back, or in Nicolescu's terms if reality resists our ideas. Good ideas bump up against something real, bad ideas don't. As Zull puts it: "It is this encounter with the reality of the world that leads to learning. The magic isn't in the action; it's in the testing" (219). What is active learning? "asking questions, drawing, writing, taking notes, checking out a reference, taking a test, and even reading. Anytime a learner tests out her ideas, she does it through action, and that action generates learning" (218). This is a good, educationist way of talking about Deleuze and Guattari's concepts of cartography, mapping, and decalcomania. This is perhaps the weakest part of my writing classes. I need to find ways to incorporate real-world writing into my classes: real writers writing to real readers about issues that are important to them. This is a tough one, and I welcome your suggestions.
• WE DID THIS OURSELVES: Changing the brain through effective use of emotions – Learning must involve the emotions. Engagement is an emotional response, depending on the learner's feelings about the importance and relevance of the lesson. We encourage engagement through arranging for success. When people repeatedly fail, they disengage; whereas, success (but not too easy) engages people. The balance between too easy and too hard is where the teacher's art comes in. Also, we encourage engagement when we enable a sense of control (emotional base) in students. Self-evaluation and ownership of task engage people emotionally; whereas, loss of control disengages people. When students have no control, then we teachers must resort to extrinsic motivations (which at heart are always violent uses of power) to get them to perform, and the performance is seldom satisfying.

I'm confident that I will refer to Zull's work a great deal in the future, and I recommend it to anyone interested in education.

Rewiring Student Brains

James Zull's book The Art of Changing the Brain contends that neuroscience can guide our teaching practice by revealing to us how our brains actually learn. I think his insight is reliable, and I'm particularly satisfied that he views the brain as a complex, multi-scale network and learning as changing, extending, and strengthening the connections within those networks. This fits quite nicely with connectivism, which defines learning in similar networking terms.

This definition of learning puts the student/learner at the center of the learning process, unlike traditional education, which puts the teacher/authority at the center of the learning process. Why? Because if learning is the development of new connections within existing neuronal networks, then learning depends overwhelmingly on the engagement of the student. No teacher can directly touch a student's brain. Development of neuronal networks absolutely depends on the student exercising her own brain, and her teachers cannot do it for her, any more than a fitness trainer can exercise her muscles for her. The student must sweat and exert herself and must want to sweat and exert. If the student is emotionally, physically, or intellectually incapable of learning a given lesson at a given time, then there is little the teacher can do. At best, teachers can create an environment that is engaging for a student and that encourages them to exert themselves, but the teacher cannot do it for them.

Then, each student comes with different neuronal networks. We teachers can often rely on rather gross similarities among student perceptions, neuronal processes, and responses, but the multi-cultural, inclusive nature of many modern classes shows how unreliable our dependence on these gross similarities can be. Our brilliant lectures and lessons, then, may engage one student and not the next. Neuroscience tells us why. If learning is a process of developing existing neuronal networks, then learning must start with each student's existing neuronal networks, and they ain't all the same. Some are positively alien, and ALL are different from the teacher's. Ground Zero for learning is NOT the teacher's knowledge, then, but her students' alien neuronal structures.

Traditional education views the teaching/learning process as a teacher writing a concept on the chalkboard of the student's mind. This is a radically false notion of education, and yet it is still the basis for too much instruction, even if the chalkboard is now a computer screen and the lecture involves a PowerPoint. The teacher's job is crucial but not essential to learning. The skillful teacher can create an environment that focuses, encourages, and enables students to stretch their minds to create new neuronal networks, but the teacher cannot create those neuronal networks for the student.

Moreover, the teacher cannot prevent students from learning. Most of the stuff that I remember learning in middle school—dealing mostly with sex—was never taught in the classroom. I suspect that most of what is learned in school is never taught from a lesson plan.

So what's the lesson for this teacher? First, I must start with the student and with their existing neuronal networks. That means that each program of study should begin not with what I know (the course content) but with what they know. I must build in to my classes time to discern what my students already know and do not know. The flipped classroom and just-in-time teaching techniques allow for this, and I use them.

Second, given the variety of neuronal structures I'm likely to encounter in any class, I must create a flexible environment that allows for a variety of engagements, processes, and responses. There is no one-size fits all. I know where I want my students to end-up, but I cannot assume one highway to travel or one vehicle. Some come from the cane fields near Belle Glade, some from the tenements of Lake Worth, and quite a few from Haiti, Jamaica, and Europe. Some take the bus, some walk, and some drive different cars. Some are here in a few minutes, some drive an hour or more each way. Getting everyone to West Palm Beach is a very messy business, and many teachers simply don't want to take that on. I think that's why they focus on simply delivering their content. It's much easier. It's also largely ineffective.

Third, I must monitor frequently, and not only to discern what they are not learning, but also what they are learning. I must check their progress along their different highways, monitoring where they are going and how fast they are travelling. If a particular lesson calls for a very specific destination, then I must be able to encourage those on-track to continue even if they can't see the destination, and I must be able to nudge those off-track to make new turn. If a particular lesson has no specific destination, as is the case with many cMOOCs, then I must delight in learning where they are going and encourage them to share their snapshots with me.

Rewiring Our Feelings

James E. Zull's book The Art of Changing the Brain makes a very useful connection between emotions and learning. Traditional education and scholarship has worked hard to minimize emotions within the Academy, and if Zull is correct, then this is most unfortunate. Our brains are wired for emotions, and teaching and learning suffer when we ignore or minimized emotions both in teachers and students. Humans cannot help but respond positively to things that enable pleasure and control and respond negatively to those things that enable pain and loss of control. Learning involves emotions. As Zull says, "Not only is knowing a feeling, getting to knowing [italics in original] is a feeling" (73).

Our feelings determine our attitudes about a teacher, a class, a subject, and those feelings are fixed by the brain before we are even aware of them. Zull explains how sensory impressions bypass our conscious brain and go straight to the amygdala, where they are assessed for threats. For anything that threatens pain or loss of control, the amygdala throws us into fight or flight mode, immediately and without question. The resulting feelings are very difficult to change through the conscious mind. If we don't like a class, teacher, or subject, then we just won't like it.

The problem is that the brain is a battleground for competing attention centers, and reason does not compete so well with emotion. It is hard to attend to a lesson when the amygdala senses loss of control or painful experiences ahead. We teachers can help a student's brain focus its attention through pleasure and movement, connection with people, awareness of the relevance of the material to the brain's identity, a sense of control, and other techniques. People can respond when, first, they are not distracted by threats of failure, pain, and loss of control, and second, when they sense relevance, control, joy, and play in what they are asked to do.

This suggests to me that my classes should begin with some task high in sensory input and something that students can almost certainly achieve, will want to achieve, and will enjoy achieving. I've been starting my writing classes by having students send text messages to someone outside of class, telling them what they are doing. The replies are often humorous, and the task is delightfully unexpected by the students. It demonstrates that they already know how to use writing as a tool for communicating with others. Now, they just have to learn how to use writing in a different, more academic context. I should be able to think of other opening tasks. Any suggestions?

Rewiring the Neuron

My good friend Bruce recommended that I read James E. Zull's book The Art of Changing the Brain (2002), and I'm glad that I followed his advice. The book has some important implications for connectivist, rhizomatic thinking.

The first section of the book establishes a direct correlation between brain form and functions and teaching and learning. As Zull says in the very first sentence: "Learning is about biology." For Zull, learning is the process of changing neuronal structures, and good teaching is aware of and works with the brain's innate structures and functions to enable those changes. I'm a bit uneasy about reducing learning to physical changes in the brain, but I can accept this as a useful focus for better understanding this aspect of learning. So what does this connection between brain structure and learning imply for connectivism and rhizomatic learning?

First, Zull understands the brain as a network. This is implicit in the first part of his book, but he later makes it explicit, devoting Chapter 6 to an exploration of neuronal networks. Moreover, he conceives the brain as a multi-scale, complex networking structure. For instance, individual neurons are networked to process certain sensory inputs, but then those individual networks are networked into larger networks to perform various integrative and meaning-making functions. Zull does not extend those networks into the larger networks of the body or our social and natural ecosystems, but that may be a result of his particular focus for this book rather than a specific belief. I find nothing in what he says that would exclude such an extension of our neuronal networks. It's easy for me to say, then, that Zull, like connectivists, sees learning as a network phenomenon. For Zull, learning is the process of shaping neuronal networks that map more or less well to reality. This process of neuronal mapping is quite compatible with Deleuze and Guattari's notions of decalcomania and cartography, and network structures are at the heart of both connectivism and the rhizomatics.

Zull provides some specifics about neuronal processes that are useful for connectivism and rhizomatics, that make cartography and decalcomania more practical. First, he outlines the basic sequence of learning:

1. sensing,
2. integrating (2 parts), and
3. acting.

For Zull, then, learning is grounded in sensing the physical world, integrating those sense impressions into our existing neuronal networks first through reflection and then abstraction, and then acting on, or testing, that new knowledge. This is a dynamic, complex process because the results of acting/testing is then fed back into the loop as we sense the consequences of our actions/tests, integrate those consequences, and act/test again. Through this process, our brains develop themselves, strengthening those neuronal networks that lead to somehow satisfactory results and weakening those networks that lead to unsatisfactory results. Of course, the loop is not this simple. We humans are often confused about which neuronal networks map satisfactorily to reality and which don't, and our brains can create and adhere to some awful mappings, but mostly it seems to work for us, and according to the latest neuroscience, this is the process most of us use.

The takeaway for me is that the educational process is improved if it begins with a concrete, sensory experience, includes time for reflection and abstraction of the experience, allows for action/testing of the new knowledge, and allows for feedback of the testing results into the loop. A teacher doesn't need to know anything about connectivism or rhizomatics to follow this teaching process, but this process can usefully inform connectivism and rhizomatics.

First, at the start of any lesson, students favor concrete, sensory experience. This is what they are learning. Unfortunately, that means most of our students are learning whether or not they like their teachers, whether or not the teacher is boring, whether or not the classroom is comfortable, whether or not this class fits into their eating schedule, and so forth. Our brains are wired this way, and our brilliant lectures can seldom overcome this sensory bias. Perhaps, then, we should capitalize on the sensory bias, and begin there. For instance, in my writing classes, I could start by having my students text someone on their smartphones about what they are doing in my class, and then launching into a classroom discussion of why people write to each other.

Second, students need time to integrate their new sensory experiences into their existing neuronal networks. Implications: if we march tenaciously through the content, we will lose most students. At best they will manage to register the content into short-term memory, which is a necessary step in learning, but hardly sufficient for any useful learning. The brain quickly flushes short-term memory to make room for the next short-term memory. Reflection and abstraction are the neuronal processes that move sensory experience into long-term memory and integrate it into existing neuronal networks. Most of the classes that I took provided little to no time for reflection and abstraction or for feedback of tests; thus, I have forgotten most of what I learned. What a sad waste of everybody's efforts and investments. So in my writing classes, I might allow my students to blog about the concepts I'm trying to teach, encouraging them to make the connections between the new stuff and what they already know. Class discussion is also a good tool for this reflection. I might encourage abstraction by having student bring in writing assignments from other classes and plan in groups how they might solve those assignments. We might also allow for feedback from those assignments, assuming there is time.

Then, short, shared writings in class are a good way to test new knowledge and feed the results back into our brains. Actually, I don't see why this wouldn't work in most any class. Maybe I'm just biased, but I think that writing is one of the best tools we have for integrating new information into our existing neuronal networks, thereby turning it into knowledge.