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!
Kauffman 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.
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.
The 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.
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.
Larval Subjects . 
August 5, 2009 at 1:37 pm
Hey LS,
Great post, but I’m having a problem understanding what you mean by “negentropy” and “entropy” when used in a onticological sense.
For it seems to me that when you state, “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,” you are in fact tying the loss of uncertainty to the creation of an assemblage.
But wouldn’t this cause problems for onticology? For if we think of entropy as information, then an assemblage as negentropic would (perhaps eventually) cease to communicate or make differences. With a decrease in uncertainty, the assemblage becomes reliable in its communications, in effect communicating nothing. In other words, it’s like if you told someone that you loved them every hour on the hour. Your words decrease in uncertainty, and therefore decrease in meaning – effectively communicating nothing. In this sense, a negentropic assemblage then is a closed system, a reliable series of arrows from one to the other with nothing new to say.
Or to put this another way, Assemblages become negentropic because they communicate nothing new, they simply repeat the same thing over and over to each other.
And in an attempt to answer your question at the end of your post, as to how entropy is introduced, couldn’t we simply recognize that any form of communication always requires an “n-object”, that is, an object which always defers/differs itself – passing on information rather than closing off the system therefore increasing entropy? If so, this means that there can be no assemblage which does not make a difference, no completely negentropic assemblage, right?
I hope this isn’t as confusing as I think it sounds.
August 5, 2009 at 7:38 pm
Way cool.
“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.”
Yes, exactly.
August 5, 2009 at 8:26 pm
Hey NrG,
Thanks. Luhmann makes a similar point in his charming, and surprisingly clear for him, little book The Reality of the Mass Media. Drawing on Bateson’s definition of information as the “difference that makes a difference”, he observes that a stimuli can only function as information once insofar as it no longer makes a difference or modifies a system state once it is repeated. Compare, for example, someone screaming “fire!” in a crowded movie theory with the subsequent exclamations that follow. After you have heard the first exclamation the subsequent exclamations no longer have information value or modify your system state. An important point to keep in mind is that the information-value of a stimuli resides not in the stimuli itself, but in the system. Thus, one in the same stimuli can cease to be information for one system, yet when video footage is reported on the news later that night, the stimuli can take on information-value for other systems.
I am not familiar with the intricacies of entropy as the concept functions in information theory, but as I understand it the issue revolves around signal-to-noise ratios in transmissions. For example, the transmission of a message or signal across electric lines. The issue was one of how to reduce the noise so the receiving end contained the information of the sending end. Negentropy would refer to those processes through which this is insured. This issue is distinct from the ontological thesis of onticology, because the thesis that if something makes a difference then it is is not a thesis about the reception of messages for a system. When subsequent people shout “fire!” differences are nonetheless produced despite the fact that this utterance no longer produces a difference for the systems in the vicinity. For example, sound-waves vibrate. The issue of information, by contrast, is an issue of translation or interaction between one object and another.
I think it’s important to note that the concept of entropy is a concept that is broader than that of the reduction of uncertainty. The reduction of uncertainty is an issue that revolves specifically around issues of information. By contrast, entropy revolves around issues of distribution and organization in a collection of elements. The ten-second video clip illustrates this point nicely. In the initial moments of the interaction, the particles are highly localized, but then they drift all throughout the glass chamber. The question then becomes on of how elements come to maintain a particular organization across time. Self-maintenance is negentropic in that it maintains its organization across time. However, organization does not mean unchanging. Returning to buttons nine and ten in the diagram in the post, button nine produces a difference in button ten. In doing so, a system state is selected that modifies the behavior of the system. But ten produces a response, causing a shift to occur in the system state of button nine. And so it goes. Each interaction modifies the two elements in the system like moves in a conversation.
I’m a little nervous about the suggestion that networks require an “n-object” (sounds like you’re referencing Deleuze’s “empty square” in The Logic of Sense here). What makes me nervous is that on the one hand there are all sorts of networks that are pretty stable, evolving diachronically according to their synchronous organization with a fairly low degree of entropy. The introduction of organization changing disruption into a system seems to be a pretty unique event that only occurs under certain circumstances when, for example, there’s a large increase of energy into the system as in the shift from hunter-gatherer societies to agrarian societies where the increase in abundant foods pushed the social systems into new basins of attraction and new forms of organization, or when suddenly a source of energy upon which the network depends to continue its work of self-replication become absent as in the case of the evaporation of certain lakes in region of Africa making water rare. And, of course, there are all sorts of other aleatory events that can take place that aren’t simply matters of energy. For example, in Eyes Wide Shut, Nicole Kidman’s story about her desire to have a fling with the naval officer throws the communicative system her and her husband have formed into disarray, suddenly sexualizing Cruise’s entire universe of interpersonal relations as can be witnessed in the scenes subsequent to him leaving the house where he’s hit on by the new widow, mocked as gay by the frat boys on the street, solicited by the prostitute, and encountering the strange sordid sexual affair at the costume shop with the owners daughter. Where prior to his wife’s speech-act the underlying sexual innuendo of interpersonal relations was invisible to him (he gives breast exams to beautiful women without finding anything sexual in it at all), his wife shifts his psychic organization into a new and traumatic basin of attraction that oppressively haunts all human interactions. Indeed, the scenes involving the strange sexual ritual seem to recaptulate, in Levi-Straussian terms, the libidinal underbelly of society or how social relations are organized at the unconscious and libidinal level. I guess the point I’m making is that it’s important to avoid reductive abstractions that prevent us from seeing the specific organization of networks and those points at which they are subject to organization-shifting entropic events.
August 6, 2009 at 2:18 am
Dr Sinthome I have been avidly following your manic opus of late, and I am always edified by your sexy brains, although I have one crucial complaint:
it’s as though you’ve forgotten Lacan’s primary message – that language speaks us – and so the introduction of all these mathematical, physical, biological et cetera terms e.g. affordance already sets the tone of the kind of an interpretation that follows it.
August 6, 2009 at 4:05 pm
I’m beginning to suspect that onticology is in fact the larval form of…mathematical physics!
Particularly, on the latest showing, the kind that takes an information-theoretic view of just about everything – if an object exists to the extent that it “makes a difference”, and information is “differences that make a difference”, then an object’s extensive existence is an information pattern, and variations in the intensity of an object’s existence become variations in the strength and integrity of its information pattern.
August 6, 2009 at 5:05 pm
Yikes Dominic! Don’t tell me that! That would mean I’ve been studying the wrong discipline all these years!
August 6, 2009 at 5:52 pm
“then an object’s extensive existence is an information pattern”
That’s the core of Ladyman and Ross’s “ontic structural realism.” Says Nick in his very informativepost on L&R at Speculative Heresy:
“Undertaking an in-depth and extensive look at the various work being done in contemporary physics, they argue persuasively that individual things don’t exist. Rather, what exists are ‘real patterns’ – temporal and spatial patterns which are mapped by the mathematical structure of scientific theories.”
August 6, 2009 at 6:36 pm
Please tell me you’re not just figuring that out now… ;-p
August 7, 2009 at 4:21 am
“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.”
The most interesting aspect of the game of life is how a stable pattern will explode when a “glider” interrupts it.
You also get the same effect if you pause a stable pattern and then add a square to it and start it up again. A good example of this can be found here:
But in both cases the change requires something like transcendence. Something from outside of the stable pattern introduces the explosion.
Ever since I learned about Conway’s Game of Life I’ve never been able to think about history the same way. It seems to be the best way to imagine historical development. The Aztecs had a certain dynamic, one that was developing and changing but that still had a stable signature, until Cortez the glider came in from the East and exploded that pattern setting up new and different patterns (and of course the Spanish pattern wouldn’t be the same either).
One way to avoid any reliance on transcendence is to say that entropy develops internally because the entire universe can never become stable, only small sections of it can (for example, the political institutions of any given state). Over time those small sections will interact with developments that happen elsewhere and blow apart and reform into new patterns.
August 8, 2009 at 1:42 pm
“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.”
Kind of makes the whole nature-can’t-be-a-condition-of-mind-because-mind-is-a-condition-of-nature thing seem a little antiquated.