Lately I have been rereading Stuart Kauffman’s At Home in the Universe as my bedtime reading which perhaps accounts for why I have been unable to sleep and am nearly psychotically tired as it is a rich book full of all sorts of fascinating ideas that keep me tossing and turning as my mind spins. Dealing specifically with issues of self-organization, Kauffman’s work strives to theorize the conditions under which we get self-sustaining and organized matter such as we see in the case of living systems. A number of his claims are generalizable to a wide variety of phenomena beyond cells and organisms. Similar principles, for example, would apply to ecosystems, economy, social systems, brain organization and so on. And indeed, Kauffman approaches organization at a high level of abstraction, focusing on self-sustaining or autocatalytic chemical processes while also providing a wealth of formalizations that refer to no specific material substrate in particular. I have made no secret of the fact that I am generally hostile to relational ontologies that reduce objects to their relations. While objects certainly enter into relations, onticology begins from the premise that objects are independent of their relations and can pass out of and enter into new relations. Thus, for example, while being sympathetic to the Saussurean conception of language as a system, onticology nonetheless refuses the thesis that anything is its relations. In short, onticology begins with the hypothesis that being is atomistic or composed of discrete, autonomous, and independent objects that can pass in and out of relations. Yes, there are systems or forms of organization, but these forms of organization are assemblages of objects that enter into certain relationships with one another.

The consequence of this thesis is that one of the central issues for onticology becomes the problem of entropy. Roughly, entropy is a tendency of systems to move from states of higher organization to states of lower degrees of organization, or, alternatively, to move from states of non-equilibrium to equilibrium. The video below illustrates this idea nicely:

At the beginning, the system is in a state of non-equilibrium in the sense that all of the particles are concentrated in a particular region of the chamber. With the passage of time– a mere ten seconds –the particles wander throughout the chamber such that you have an equal probability of finding particles in any particular region of the chamber. The big question for onticology then becomes if being is composed of discrete and autonomous objects, then how is it that certain objects form assemblages that resist this increase in entropy, instead maintaining an organized state across time? A while back I suggested that this is how we should pose questions about the nature of society. There the question was that of how it is that humans bodies just don’t fly off in entropic ways, but instead enter into organized relations that sustain themselves across time. Of course, in order for any system to maintain itself in an organized way work is required. No system maintains itself without work. So the real issue lies in discovering the sort of work through which this organization is re-produced across time. This really gets to one of the central problems with French inflected structuralism and Luhmannian systems theory. Both identify the organization of a social system, how it is put together and how its elements are related, but they remain at the level of social physiology, giving only the skeleton of social systems or how the “bones are put together”. What they don’t give us is the work by which this physiology is maintained. They tell us that these systems somehow resist entropy, but not how. Given that many of us are interested, above all, in the question of how change is possible, the issue of how a social system resists entropy becomes a crucial strategic issue for political engagement. However, even if one is not interested in these political questions of change, the question remains fascinating on its own terms.

read on!

buttons_sketchKauffman provides some interesting tools for thinking about how networks both arise and resist entropy. In a simple thought experiment he asks us to imagine buttons– say twenty –spread out across a table top. Begin attaching two buttons at a time to one another using bits of thread. At a certain point we find that a critical threshold is reached where if we lift one button, most of the other buttons come up as well. This threshold or phase transition is represented in the graph to the right.fig3_4 What we have here is the beginning of an interdependent system, where the elements composing the system, come to rely upon one another in a specific way. The system, as it were, has become “negentropic” or an assemblage. At around the fifty percent mark we see that there is a sharp rise in connectivity among the elements, such that probability random distributions decreases dramatically.

rbn1The full force of this thesis does not hit home very strongly in the case of buttons and threads, in that buttons and threads are very static things. Instead of fixed and static buttons, imagine that the buttons are processes— not unlike Leibniz’s famous monads and Whitehead’s “actual occasions” –and that processes are also occurring among these buttons as depicted in the image to the left. In a diagram not unlike those we find in mathematical category theory– no surprise here –we find a particularly clear example of such a system in the relationship between buttons nine and ten. On the one hand we have what the category theorists call “identity arrows” which consists of the curved arrow that points away from button 1 and then back to itself.basic_category1 This refers to the manner in which an object maintains itself across time. For example, in the case of a cell it would refer to the manner in which it maintains a particular organization or pattern of activity despite the fact that the matter that composes it is constantly changing. For living things, just as for signs, there’s a very real sense in which the being of the thing is incorporeal as it is the pattern that persists, not the matter. This is perhaps true even of non-living matter in that at the atomic level electrons and whatnot are constantly being exchanged. In the relationship between buttons nine and ten we notice arrows pointing to one another. This indicates the manner in which the two objects have come to depend on one another to sustain themselves. Thus ten draws on nine to maintain its identity or pattern across time and nine draws on ten in order to maintain its pattern or identity across time. Buttons one through eight depict a far more complex network of relationships where the relationship of dependence is more round-about. Interestingly the identity arrows do not appear for each button in this network, suggesting that the elements aren’t maintaining a patterned identity across time.

The point is that in entering into these relations a phase transition takes place in which the elements come to form a system, assemblage, or organization where the elements are dependent on one another to maintain a particular mode of existence. All of this is highly abstract, but it is readily applicable in a wide variety of different domains. The relationship between buttons nine and ten, for example, could be taken to illustrate Lacan’s understanding of dual imaginary relations between two subjects– a bad therapist and an unfortunate patient –where both subjects maintain a rigid and fixed imaginary identity, enter into antagonistic relations with one another, and draw on this antagonism as a way of perpetuating that particular specular identity. Alternatively, the relation between buttons nine and ten could be taken to represent the relationship between the South Side and North Side of Chicago where we have a fairly strict economic, ethnic, and class differentiation, but where each side of this relation depends on the other to maintain it: The North Side requiring the South Side to produce its goods, do its data entry, clean its bathrooms, and so on, the South Side requiring the flow of wages that come from the North Side. Yet again, buttons nine and ten could be treated as a highly formal diagram of what Bateson called “schismogenesis“, which we witness so often here in the theory blogosophere.

The complex network depicted in the relations among buttons one through eight could be taken as anything from the relations of interdependence in an ecosystem, to the interplay between warm water flows and cold water flows in the ocean “conveyor belts” that regulate weather patterns, to relations of production or infrastructure, superstructure, and economy in various social systems. Indeed, I am fairly convinced that Marx was engaging in a sort of “actor-network” analysis of social systems where we get an interplay between these various elements in the organization of a particular social system. All of this begs for a rewriting of the later books of Plato’s Republic, where he outlines the different types of social organization in contrast to the Republic, along the lines of network interdependencies and how they produce various forms of social organization. This would be a sort of “transcendental sociology” examining the “diagrams” of various network forms in such a way that influxes of energy (environmental conditions, food sources, energy sources) were analyzed in relation to communication networks (media of communication, roads, and so on) and the role they play in emergent distributions of human bodies.

The key point, however, is that when “buttons” enter into relations of dependency such as this, they become negentropic or resistant to interventions that disrupt these tendencies. Not unlike the emergent patterns in the Game of Life, you get, as it were, systems that can only evolve diachronically according to the synchronous relations of interdependence through which the elements of the social system reproduce themselves across time. The question then becomes that of how you introduce entropy into entropy-resistant systems to produce change. As Aleatorist likes to say, sometimes you have to shut down the highways for a protest to work.

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