Monday, December 31, 2012

Simple vs Complex Definitions 2

In my last post, I started listing the problems I have with simple, reductionist, essentialist definitions and suggesting ways that complex definitions provide better, more workable results. The list of issues that I want to present is in no particular order, as my thinking is not yet ordered enough. I mentioned in that post that I have problems first with definitions as an end-point rather than a starting point and then with definitions that disregard the human point of view rather than incorporate it. My next problem with simple definitions is that they aim for the absolute.

In the extreme case, people want definitions that are true for everyone, everywhere, for all time. I was raised in a fundamentalist Christian family, so I deeply understand the attraction of this desire. Once we have our sock drawer arranged (well defined), then we want it to stay put. Once we know the formula for either eternal salvation or the speed of light, then we want it to stay put, and we become very unsettled when anything threatens that order. More to the discussion: once we know the formula for tenure, then we want it to stay put. We post-structuralist academics may pride ourselves on being open and fluid, but just mess with one of our primary relationships, our favorite word processor, or our retirement strategies, and see how quickly the knot of fascism swells in our hearts. We all want definitions that persist in the face of Life's flux, and we will move heaven and earth to make Reality conform to our definitions.

This very human desire for the absolute is, of course, a part of Reality, but Reality doesn't appear to take it too seriously. Reality won't stay put, or as Robert Frost says it: something there is that doesn't love a wall. We have come to see that a stable Reality is the result of truncated vision. We think that the arrangement of continents is stable only because we cannot see over long enough periods of time. When we extend our vision through technology, then we see that the very ground of our being is constantly shifting beneath our feet. This is not good. We want St. Louis to stay where we put it, damn it.

Complex definitions, then, incorporate the heuristics for change and development. This is very much the way DNA works: we have a set starting point for any human being, but the way that DNA unfolds and blossoms within its environment is critical to that human being. The starting point is necessary for the definition of a human, but hardly sufficient. The process of emerging, which is an interaction of both internal and external processes, is just as important. The starting point limits an entity (it prevents a given zygote from becoming a rabbit or a chimpanzee rather than a human, for instance), but it does not define the entity. Complex definitions allow for infinite variations in snowflakes and humans. They allow for black swans.

Then, simple definitions mishandle boundaries. In reductionist thinking, a boundary is a line that separates one kind of entity from all other entities, rendering an entity discrete from its environment. In complex thinking, a boundary is a zone of engagement between the entity and its environment. This is a radical difference in visualizing Reality that cannot be overstated. A simple definition isolates an entity from Reality, while a complex definition integrates an entity within its environment. Complex definitions take into account the dynamic exchange of energy and information at the boundaries of an entity, recognizing that what a thing is depends a great deal on the kinds of energy and information it exchanges at its boundaries. This is obvious at the biological level, but it is just as true for rhetoric. This post, for example, acquires most of its meaning from the information it exchanges with other posts (both my own and other bloggers) and conversations. This post has no discrete meaning. Its meaning comes only from the interactions with its environment.

Finally, at least for today, I have trouble with simple definitions because they ignore networks. This is perhaps another way of saying what I just said about mishandling boundaries, but I think the concept is worth introducing into this discussion, and anyway, it's been inherent in much of what I've already said. Meaning is a function of complex, multi-scale networking. As near as I can tell, all Reality is a function of complex, multi-scale networking, so definitions are as well. The definitions we have in our minds are networks of neurons firing in a fractal pattern, and this may seem dynamic enough, but thoughts are more dynamic than that. The neuronal network that represents the concept of, say, Christmas is dynamic. If Olaf Sporns is correct, each brain recreates the Christmas neuronal network with whatever neuronal resources it has available to it at the moment. Thus, Christmas is not associated with a fixed set of neurons firing in a fixed pattern—certainly not across all our brains, but not even within a given brain; rather, Christmas is a somewhat fresh, self-similar firing of available neurons each time I think it. The physical substrate for the thought Christmas is a dynamic, multi-scale networking (I'm using the verbal form rather than the nominal form of network to try to capture the dynamic nature of the concept).

Simple definitions, on the other hand, try to reduce entities to discrete chunks, whole within themselves. I don't think such chunks exist except in the coarsest level of Reality. They exist in conversation only as a convenient shorthand, a manner of speaking, but we should never be surprised when our simple definitions have slipped their moorings and we have to map reality all over again.

Friday, December 28, 2012

Simple vs. Complex Definitions

Dave Cormier's post A review of rhizomatic learning in Mendeley led me to an engaging conversation about definitions, especially a definition of rhizomatic learning. This is a topic that keeps returning to me, and I have not sufficiently worked through it, but I keep trying because I think it is important to the discussions about connectivism and rhizomatic learning.

Definitions are important to any discussion, for without a working definition, conversation is almost impossible. In many ways, definitions are the bedrock of traditional education, especially to what Cormier calls "the basics." Much class time from kindergarten all the way through baccalaureate higher education is spent on defining colors, times tables, history dates, science terms, parts of speech, and literary genres. The problem, it seems to me, stems from our standard method of defining, which I believe is reductionist and essentialist in nature. What do I mean by that?

First, traditional definitions reduce a concept—let's pick the four major learning theories—to a few usually salient and so-called essential features. A recent infographic from Edudemic entitled A Simple Guide To 4 Complex Learning Theories lists and defines the theories this way:
  1. Behaviorism: Learning is a process of reacting to external stimuli.
  2. Constructionism: Learning is a process of acquiring and storing information.
  3. Cognitivism: Learning is a process of constructing subjective reality based ???
  4. Connectivism: Learning is a process of connecting specialized nodes or information sources.
For the moment, let's ignore whether or not we think these definitions reliably capture the essential features of each theory. Let's note instead that they are standard definitions. They reduce complex theories to a couple of essential characteristics. A traditional education course might say: if you want to understand connectivism, at least well enough and long enough to pass the test, then learn an eleven-word formula that effectively reduces the life's work of Siemens, Downes, Cormier, and countless other scholars to a process of connecting specialized nodes or information sources. Well, if that's all it is, then why didn't George just say that to begin with and save us all this work and talk? Of course, this is not connectivism, and if you are like me, you find this kind of reductionism repugnant and inadequate. It takes us almost nowhere. It takes those poor students almost nowhere, at least, nowhere beyond a grade on a test.

So why do we do this? I think we are seeking clarity, stability, and control. The flux of life is troubling and troublesome to most of us, and we want to define it away. We want clarity, or clear boundaries between this and that. So we say that behaviorism is reacting to external stimuli, and connectivism is connecting nodes—as if behaviorists can't connect things and connectivists can't react to external stimuli. This is little more than arranging your sock drawer—not a bad thing to do, but hardly sufficient to build a life or an education around. And we want stability. Once we define light socks on this side and dark socks on that side, then we don't want anybody messing with those categories. We can be outraged at those who will re-arrange our drawers (I'm thinking of a certain spouse here) putting cotton socks here and synthetics there, or dress socks for dark shoes, dress socks for brown shoes, casual socks, and athletic socks all in different piles. Don't these other people understand the inviolable order of the Universe? And finally, we seek control. When I reach for a certain pair of socks, I want to know exactly where they are and just which pants they go with.

So am I ridiculing this drive toward clarity, stability, and control? Absolutely not. Life is much easier with clarity, stability, and control, and much of our time and energy is spent blocking out well-ordered social, economic, political, religious, and familial spaces for ourselves. In terms of Dave Snowden's Cynefin framework, which Dave Cormier uses in his post Seeing rhizomatic learning and MOOCs through the lens of the Cynefin framework, we are constantly trying to move as much of life as possible from the chaotic, complex, and complicated zones into the simple zone. If my socks are arranged as I want them in my sock drawer, then I don't have to think much about them anymore. The sock realm of my life is now simple, which reduces my expenditure of cognitive and physical energy for an issue that I don't really want to engage much anyway. As with our socks, we want to move connectivism into the simple zone. Once I've made connectivism simple by reducing it to couple of essential characteristics and creating distinct, stable boundaries between it and other theories, then I don't have to think about it much anymore. I've nailed it. This gives me a sense of clarity, stability, and control.

So what's wrong with clarity, stability, and control? Nothing, except the Universe doesn't seem to be arranged that way. Reality has a way of becoming un-nailed and slipping out of our comfortable categories, of fleeing down lines of deterritorialization in what Deleuze and Guattari call asignifying ruptures. Modern physics seems to suggest that very little of the Universe is simple and that all of that most interesting and salient part of the Universe that we call Life exists in the complex zone between the merely complicated and the radically chaotic. Certainly, connectivism and rhizomatic education exist in the complex zone. By the time they have moved securely into the simple zone, most of us will have lost interest in them. And look at what has happened to MOOCs. We early participants in cMOOCs thought we had them fairly well defined, and then Coursera and edX came along to re-arrange the sock drawer. Life does that, and we shouldn't have tried to reduce MOOCs to a single thing anyway.

So the big problem for me is that definitions based on reductionism and essentialism try to move complex things into the simple zone, obscuring a thing rather than clarifying it. How so? First, a reductionist definition treats the definition as an end point rather than a beginning point. It stops conversation rather than starts it. Most teachers know that the quickest way to end a classroom discussion is for the teacher to give the answer. After you have the right answer, what else needs to be said? That issue is closed. Unlike simple, reductionist definitions, complex definitions take a definition as a starting point, as DNA which is constantly unfolding into a new entity, like a snowflake: recognizable as a snowflake, and yet totally unique. If snowflakes are that complex an entity, then how much more complex are humans and societies? We need definitions of snowflakes and people and theories that start with a few elements and processes (DNA) and work outward to an infinity of forms, not definitions that work inward toward one form with a few distinguishing features. Of course, this approach to defining really messes with the whole regime of multiple-choice tests.

Then, simple definitions remove the person from the definition. One of the great lessons of modern physics is that no observation or calculation or definition can be made aside from an observer, calculator, or defining agent. We can't leave people out. Any definition of connectivism must account for the point of view of the person defining it. I value the Oxford English Dictionary for its inclusion of writers who have used a given word in a given way. That's a step in the right direction. Complex definitions recognize the issue of point of view and build it into the definition.

I'll write more tomorrow about definitions.