Complex Classes: Heterogeneity and Homogeneity

Over the last few posts, I have characterized complex classes as a multiplicity of actants open to flows of Light and Word which animate dynamic interactions among the actants and other systems. In this post I explore heterogeneity, or diversity, with necessary discussion of homogeneity and unity. I think, too, that I will shift from the term actant to interactant which better expresses the dynamism that allows an actant to self-eco-organize itself into a functioning node in a system. In educational terms, interactant captures the dynamism that a learner and a class must have in order to learn.

Deleuze and Guattari say that the interactants in a rhizomatic system are heterogeneous. This heterogeneity, however, is much broader than classrooms full of diverse people from different socioeconomic and ethnic backgrounds. Though such a diversity is certainly included, it is still a collection of humans. Interactants are not limited to the human. Complexity thinking such as actor-network theory and object oriented ontology makes ample room for non-human interactants, which seem to be a part of all our complex systems. In his essay On actor-network theory, Bruno Latour corrects the misconception that actor-network theory, for instance, is mostly about human social networks:

[Actor-network theory] aims at describing … the very nature of societies. But to do so it does not limit itself to human individual actors but extend[s] the word actor -or actant- to non-human, non individual entities. Whereas social network adds information on the relations of humans in a social and natural world which is left untouched by the analysis, AT aims at accounting for the very essence of societies and natures. … Social networks will of course be included in the description but they will have no privilege nor prominence …. (p. 2)

An attempt to describe or understand or engage the modern complex class must account for the heterogeneity and diversity of its interactants. For instance, an account of modern learning must account for smartphones, which are potent interactants present in all modern classrooms. Chairs, desks, lights, books, tablets, lunch, recess, and hallway conversations are also interactants in classrooms, and the humans are constantly perturbed by the non-humans, constantly engaged in dynamic, nonlinear interactions. And yes, it must also account for different people speaking different languages from different contexts.

Even in those systems that we might think of as homogeneous—our own bodies, for instance—we find heterogeneity. Our bodies start as zygotes of rather homogeneous cells, but quickly differentiate themselves as they unpack their DNA and express themselves as hearts, lungs, brains, muscle, and skin in a unique configuration that distinguishes us from, say, mouse zygotes and from other humans. Be thankful for heterogeneity. Let us be thankful for heterogeneity and diversity.

Deleuze and Guattari explore heterogeneity in terms of language, which is "an essentially heterogeneous reality" (p. 7). They say:

A semiotic chain is like a tuber agglomerating very diverse acts, not only linguistic, but also perceptive, mimetic, gestural, and cognitive: there is no language in itself, nor are there any linguistic universals, only a throng of dialects, patois, slangs, and specialized languages. There is no ideal speaker-listener, any more than there is a homogeneous linguistic community. (p. 7)

Speaking of heterogeneity in terms of language is particularly important to me as it explains the necessity for heterogeneity and diversity within a complex system. Without diversity, a complex system cannot self-eco-organize. It cannot find its way through its ecosystem. It cannot grow, evolve, adapt. In short, it cannot learn. Heterogeneity is necessary for a language to thrive, to live, and to change in order for us to adequately respond to our complex, heterogenous world.

Said another way, a complex, diverse world requires an equally complex, diverse language to map it. Anthropologist Franz Boas was correct that a rich vocabulary maps a rich world. For example, Eskimos have so many more words for snow than we southerners do. That rich, heterogeneous vocabulary allows them to map a rich, heterogenous reality that most of us reduce to a simple, homogeneous snow. We southerners are the losers, as George Orwell explored so well in 1984: if you want to limit and control people, then limit and control their language. A healthy class needs more interactants with more languages to map more of the world. In his 2001 article "Diversity, Knowledge, and Complexity Theory: Some Introductory Issues", Pierpaolo Andriani says that "Ashby’s (1960) principle of requisite variety states that the internal variety of a system should match the variety of the external environment" (258). He says that diversity is important for adaptability, or the ability of the system to learn and to cope with changes in its environment. Especially relevant to school organizations, Andriani goes on to note that a distributed network based on self-organization principles is a diversity-increasing type of organization (265) whereas the firm type of organization is diversity reducing (267). Too many classes still play down or try to paste over the diversity within the class rather than cultivating that diversity. This is unfortunate.

By Trey Ratcliff,  http://www.flickr.com/photos/stuckincustoms/7821247204
(CC BY-NC-SA-2.0)

In short, heterogeneity is necessary both for a fuller, richer world and for a fuller, richer understanding of the world with a wider range of possible responses for those who want to engage their world as it is becoming. Diversity makes any complex system at most any scale more capable of making its way in the world. One of the wonderful things about being a human rather than a slime mold, for instance, is that we humans have a vastly wider range of possible responses to reality, and we have that range of responses in large part because we have a more complex neural fabric that enables us to comprehend more of reality, configure that reality in more ways, and respond in more ways. Slime molds see very little of the world and can respond in few ways. Though still complex creatures, they are far simpler than we humans are. Poor them. It confuses me, then, when groups of people want to limit what we can see and how we can respond. Who wants to be slime mold?

Denial of heterogeneity makes sense mostly when a group wishes to disengage from the world by reducing its understanding and its range of possible responses to the world. The problem with homogeneity, of course, is that all walls (even classroom walls) eventually crumble or become, at best, pleasant tourist destinations as the rhizome flows around them, eager to get on with the business of creating the world. Homogeneity will not hold on Earth—at least, not until we freeze into the cosmic heat sink a few billion years from now. Until then, heterogeneity far from equilibrium and damn-near chaos rules and enables not only life but learning.

That being said, homogeneity and unity are also necessary for life and learning. Like heterogeneity, homogeneity has its place and its affordances. It has its unity. As is the case with most characteristics of complexity, heterogeneity does not stand alone as a discrete, sanctioned quality; rather, it emerges in dialog with homogeneity. It is tempered, perturbed, and engaged by homogeneity. All complex characteristics of complexity must be conceived and worked with as dynamic interactions, not as static things or qualities. Thus, the characteristic under discussion here, for which I do not know a single term, is diversity in terms of unity, or unity in terms of diversity, heterogeneity in terms of homogeneity. Neither diversity nor unity alone is the correct understanding; rather, diversity and unity. That is the correct understanding, as Shunryú Suzuki might say.

I can understand this diversity in unity by considering my own body. I am, of course, me, a unity (Yes, the me is grammatically incorrect, but rhetorically it helps me make my point), but I am also a liver, heart, brain, lungs, skin, and more, a diversity. I am both unity and diversity.

Craig Alan, David Bowie, 48x48 oil on canvas,
http://www.renjeau.com/artist/alan-craig/

A shift in scale or perspective can also help me see this homogeneity within heterogeneity. The diverse people in the Craig Alan painting, David Bowie, become homogeneous dots, and while from this perspective I lose the heterogeneity and individuality of each person, I gain an image no one of those people could produce alone—unless, of course, a costumed David Bowie is in the crowd. The pattern, the new meaning, emerges from the inter-relationships of the interactants, and their heterogeneities are subsumed under a homogeneity that enables them to express something different and us to see something different.

This may seem no more than a trick of perspective, but I don't think that is the correct understanding. Rather, this is an instance of emergence, when the interactions of usually diverse interactants at a micro-scale lead to the emergence of new phenomena at a macro-scale. Get enough people, starlings, fish, neurons, or quarks together and interacting, and something new will emerge that cannot be reduced to an analysis of the constituent parts.

Complexity scientists are working on this issue of emergence. For instance, in her article "A Theory of Reality as More than the Sum of Its Parts", Natalie Wolchover covers neuroscientist Eric Hoel's concept of causal emergence which mathematically accounts for how agency at a macro-scale emerges out of the interactions at micro-scales. Let's say we want to explain how an idea emerges in the brain as a pattern of firing neurons. If we look at individual neurons, we can become hopelessly lost in the indeterminacy of the event. While the given idea requires a pattern across 12 neurons, the brain decides on the fly which 12 neurons (within certain constraints) to use. Hoel illustrates his concept with an approachable example of how it might work in our brains:

Imagine a network consisting of two groups of 10 neurons each. Each neuron in group A is linked to several neurons in group B, and when a neuron in group A fires, it usually causes one of the B neurons to fire as well. Exactly which linked neuron fires is unpredictable. If, say, the state of group A is {1,0,0,1,1,1,0,1,1,0}, where 1s and 0s represent neurons that do and don’t fire, respectively, the resulting state of group B can have myriad possible combinations of 1s and 0s. On average, six neurons in group B will fire, but which six is nearly random; the micro state is hopelessly indeterministic. Now, imagine that we coarse-grain over the system, so that this time, we group all the A neurons together and simply count the total number that fire. The state of group A is {6}. This state is highly likely to lead to the state of group B also being {6}. The macro state is more reliable and effective; calculations show it has more effective information.

In other words, some new, and more useful information has emerged at the macro-scale that did not exist at the micro-scale. This is not just a trick of perspective. Rather, something emerges that did not exist before. The constituent parts at the micro-scale, of course, are necessary for the emergent property at the macro-scale, but they are not sufficient to fully explain it. If physicist Lee Smolin is correct, then even new physical laws can emerge at macro-scales. I confess that I do not know very well how to cultivate and engage a class of diverse individuals into a unified, functioning whole and to attend to the learning and properties that emerge both at the individual scale and the class scale. This scale shifting is difficult for me, and understanding and expressing the dynamics between the scales is even more difficult. I'm glad Hoel is working on it.

Of course, we can focus at any time on either diversity or unity, heterogeneity or homogeneity. As Edgar Morin explains, we can reduce the complexity of any system either to a whole or to parts. Such a focused reduction has its affordances. Homogeneity and unity, for instance, can be a convenient shorthand to reference any group with some shared characteristic that we are focusing on, and we humans do it all the time. Homogeneity is quite likely a necessary mental construct to help us cope with the overwhelmingly rich diversity of our complex world. When I'm driving along a wooded road in central Georgia, the trees are homogeneous: just a bunch of trees. This is a benefit while I'm driving, as too careful a consideration of the heterogeneity of the trees will distract me from driving. We simply cannot process all the information flooding our senses every moment; so we ignore what we can and lump much of the rest together into coarse categories that homogenize the swarm and reduce its collected interactants to one or two characteristics that we can manage.

Likewise, heterogeneity and diversity can, among other things, help us focus on smaller and smaller parts to explore the interactions among them. We can come to understand how muscle is attached to bone and how the muscle fibers twitch. The last three centuries of Western science have had an unparalleled run of successes based on such a reductionist approach to reality.

However, such reductions to either the part or the whole eventually lead to wrong understandings when pursued exclusively. Homogeneity alone leads to stereotype and loss of individuality; heterogeneity alone leads to fragmentation and loss of unity. The affordances of both unity and diversity are short-term, provisional, and limited, but we want to make them permanent and absolute.

The problem is compounded because we usually cannot see both at the same time. At any one time, we can see people as diverse individuals or as homogeneous members of groups. For me, this limitation of vision is something like Heisenberg's Uncertainty Principle which says that "we cannot measure the position (x) and the momentum (p) of a particle with absolute precision." Likewise, we can see either the individual or the group, but we have difficulty seeing both at the same time. Too often, we forget that we are seeing only part of the picture, and we fall into error when we insist that the part we see is the whole picture. It never is. We must allow the whole to inform the parts and the parts to inform the whole. They do anyway.

Instructional ethics, then, must map the heterogeneity and homogeneity of complex learning. It must map whatever emerges from the dynamic interaction between diversity and unity that hums within every heart, every student, every class.