I’m experimenting here so hopefully the more mathematically knowledgeable among us won’t give me too hard a time. Perhaps one of the ways the argument of my previous post could be understood is in terms of mathematical categories. What mathematical categories allow us to think are functional morphisms or relations between sets. I’ll say more about this in a moment. In playful jab at my friend Nate, I wrote the following in my previous post:

Rhetorically Nate seems to think that it’s of no significance that his post was written on the internet, requiring fiber optic cables, a particular platform, news feeds, electricity, etc., that created the opportunity for our thoughts to be brought together and preserved despite the fact that we live an hour apart.

Drawing on the formal resources of category theory we can construct an external diagram of the point that I was trying to make, depicted in the upper lefthand corner of the post. In this diagram we notice that there are upper and lower case letters and arrows. The upper case letters are what are referred to as objects in category theory, and are essentially sets. Thus, for example, the set composed of Levi and Nate constitutes what category theory refers to as an object (not to be confused with what OOO refers to as an object). We can denote this set with the name “conversants” or communicants, or simple “C” for short. The lower case letters refer to rules defining relations, morphisms, transformations, or correlations between sets. The relation between f and g connected by a small circle (I can’t figure out how to make the symbol here) is referred to as a composition of functions or morphisms and is read “g following f”. Thus, if we follow the arrows we have X pointing to Y governed by the morphism f and we have Y pointing to Z governed by the morphism g. We note that there is an arrow pointing directly from X to Z with the composition of g and f (g circle f, read as g following f)) which is to be read as the composition of these two morphisms for the three objects or sets involved.

read on!

If this is referred to as an external diagram, then this is because we are told nothing of the internal states of our objects or sets. We know only of the morphological relations between our objects. If we wanted to open up these “black boxes”, producing an internal diagram, we might draw three circles (labeled X, Y, and Z respectively), draw the objects that belong to each one of these sets, and the morphisms that lead from one object to another object in each one of these circles. For example, set X might contain Nate and I. Set Y might contain different activities (going to get a beer, reading group, eating fast food, exercise, gardening, etc), and set Z might contain different states of health. The morphism f between set X and Y would consist in the rule “do what you most want to do”. The arrow for Nate, according to the rule, today leads to gardening. The arrow from X to Y for me leads to getting a beer. When set Y, in turn, is mapped on to set Z (composed of elements like good health, poor health, various states of mental health, etc), gardening leads to good health, a diminution of stress, happiness, and getting a beer leads to poor health, weight gain, and an increase in depression. Now we attend to the composition of morphisms f and g, drawing a direct relation between X and Z. This allows us to simplify the complex relations between X, Y, and Z. Now we can draw a direct relation between Nate’s good health and my poor health, or between X and Z.

An internal diagram let’s us map what is going on between the elements inside the sets. Whereas an external diagram only shows us the relations between the sets without telling us anything about how the objects that belong to each set are mapping on to each other. As an aside, I here find a marvelous overlap between OOO and category theory. In external diagrams the objects are withdrawn from one another, their interiority or internal composition completely opaque, yet in the assemblage of these objects we are nonetheless able to trace morphisms between these objects correlating the manner in which they affect one another.

In and of itself this doesn’t sound particularly interesting. However, take the following example of a concrete category from the Lawvere Schanuel’s outstanding introduction to category theory, Conceptual Mathematics: A First Introduction to Category Theory. “Suppose you take your sleeping baby on a brief walk [around the city of Buffalo], first walking in the hot sun, then through the cool shade in the park, then out in the sun again” (27). The diagram for this event is identical to the one at the beginning of the post. Let set X be the interval of time. Let set Y be the City of Buffalo. And let set Z be the variations in temperature (where variations in temperature are the qualitative states the infant experiences, not numbers on a thermometer). f will be the wandering walk or the function that correlates a point in time with a position in the city. g will be the numerical variations correlating positions in the city with qualitative temperature experiences of the infant. The composition of g and f will express the correlation between the point in time and the qualitative experience of temperature for the infant.

Now in this particular example, it’s with the composition of g and f that things really become interesting. And if this is so, then this is because the composition of g and f doesn’t simply express a relation between points in time and states of the baby, but also expresses something about the experience of the baby. And in particular, something about what the infant does and does not know. For the dozing infant knows nothing about her position in the city, nor about numerical temperatures. All the infant encounters or experiences is the interval of time and the qualitative temperature states it experiences. What’s interesting here is that this category is both able to capture how the infant experiences its milieu and what withdraws from the infant (the shifting positions in the city). It is thus able to express a withdrawn condition for the given.

Shifting back to my discussion with Nate and my catty little remark about the internet, we see that the diagram is the same. Let X be communicants. Let Y be various nonhuman technologies correlated with communications according to morphism f, and let Z be receivers according to sendings g. The sort of transcendental illusion that besets the traditional rhetorician (or cultural theorist) is encountered in the composition of g and f. In the arrow pointing from X to Z characterized by the morphism “g following f”, what we get is not simply the composite of X (communicators) to Y (nonhuman technologies) and Y to Z (receivers). No. What we get is the disappearance or withdrawal of Y for communicators and receivers relating to one another. And this withdrawal or disappearance is not without theoretical consequences. For where Y has withdrawn, the social theorist or rhetorician is now going to focus exclusively on the content of messages sent from X to Z, ignoring the role of actant Y.

Now why is the occlusion of Y going to have profound theoretical implications for how the political theorist, the social theorist, or the rhetorician approaches their questions? For the simple reason that the theorist will be led to focus on messages alone, to the detriment of what McLuhan called “media”, where media refers not to content but to all those nonhuman actants that function as conditions for content, defining as they do the form that content can take. And in focusing on the message alone (what Nate called “significance”) to the detriment of media, the theorist will look for the raison d’être of all collectives of humans— remember the nonhumans have withdrawn from the thought of our theorist –within the message or content. In other words, the theorist will perpetually look for something about the messages that brings humans together in this way or drives them apart in that way. And if the theorist is interested in changing these collectives, they will conclude that change is produced through the message or the content. Perhaps the theorist will practice the hermeneutics of suspicion, presenting an ideology critique aimed, like a virus, at exploding particular messages that are believed to lock X and Z in a particular relation with one another. Perhaps the theorist will seek to engage in a particular speech act that will transform the patterned relations belonging to the collective in Z.

What the theorist will find in many instances, much to his dismay, is that despite changes in the message, the elements in Z remain the same and nothing changes. Yet the theorist will continue endlessly looking for that one speech-act that would change the organization of the collective in Z. What is missing here is the role played by Y and how Y contributes to the continuation of certain patterns of social organization within a patterned collective. For example, perhaps the reluctance of Americans to overturn the oligarchies in the United States has less to do with them being “duped by ideology”, than the role Y plays in their individual lives (where Y refers to things like student loan debt, credit card debt, mortgages, law enforcement agencies, utilities, car payments, etc). Where agents in Z are caught in a sticky web of relations belonging to set Y that mire people in a particularly unpleasant form of life.

In his Critique of Cynical Reason Sloterdijk suggests that cynicism has itself become the reigning form of ideology today. Agents have become cynical of all ideologies, yet curiously this doesn’t make them immune to ideology but seems to mire them all the more in their situation as they can now no longer give themselves any plausible grounds for acting. The paradox is thus that they know they are doing it but are still doing it. There is something to Sloterdijk’s thesis, but nonetheless it still seems to misread the situation. Like the practitioner of suspicion, Sloterdijk is working on the premise that all social relations are a product of the discursive or signifying, the relation between X and Z. He is thus mystified when he notes that people know the reigning ideologies are bullshit, yet they still continue to do the same old thing. What is missing here is the dimension of Y that locks people in particular forms of life. Here Y shouldn’t be understood as deterministic, but rather more like a grooved surface along which marbles roll. This surface constrains and affords certain movements to the marbles without determining which paths the marbles will take. So too with the nonhuman actors in Y. These nonhuman actors play a key role in the form human collectives come to take. This is why Palahniuk’s novel Fight Club, in its own way, is far more clear sighted as to why collectives take the form they take than the critic of ideology. When the anti-heroes of the novel resolve to blow up the buildings containing all credit data they are taking out one of the key sets of actants presiding over how human lives are constrained. This particular constraint feeds in to a number of other human activities such as working for shit wages with few benefits or putting up with the brutal exploitation of corporations.

Let me hasten to add that the argument here is not that the actants contained in Y are the truly significant and important actants, the grand theory of everything, and that the messages issuing from X are just an illusion. The category includes all three of these elements. And were we to reverse the arrow between Y and X such that Y is now pointing at X rather than X to Y (as Mcluhan seems to often do in his worst moments), then the dimension of content, of the message, and the differences these actors introduce would disappear as well. The point is not to elide or illicitly bifurcate the category (between what belongs to nature and what belongs to culture) rendering the whole problem completely irresolvable altogether.