Stem_cell_embryo_20x_01In a terrific response to my post on exo-relations, Caemeron writes:

I wonder if people are scared to comment on this? The topic here does get pretty obscure and daunting, but I would like you to say more.

I remain unconvinced by your claim that there are objects that aren’t related to any other object.

To begin, I’ll take your example of yourself in relation to planet earth. Isn’t planet earth the way it is because of its gravitational relations with the rest of the solar system, and the solar system with the galaxy and so on?

Secondly, what is your take on “the butterfly effect”, or the idea that miniscule events on the other side of the world can create large impacts through a serial progression? To the point, perhaps: by relation do you mean only direct relation?

you say:

This is one reason that we are able to claim that two objects can be spatially unrelated. If enough time has not elapsed for light to travel to the other object, then there is no gravitational relation between these objects.

Could we not add the word ‘yet’ to the end of this? doesn’t that give us a temporal relation?

Insofar as you want to say that objects create spatiotemporal relations rather than vice versa, I’m with you, but I simply find the notion of an object which is unrelated to anything else to be unthinkable (wouldn’t thinking about it place it into a relation?) And, if it is thinkable through Gaussian manifolds, which I know woefully little about, I don’t see how that might justify us in claiming that there actually are such objects (to throw your criticism of Badiou back at you)

‘Relation’ seems to me to be a very broad term. A number like 47 may not be in space or time, but is certainly related to many things conceptually, metonymically, mathematically, etc. It seems to me that we can even conceive of non-relation as a form of relation.

Is your claim that 1) an object is not necessarily related to every other object or 2) there are objects which are not related to any other object?

I think Caemeron here raises a number of points that are worth briefly expanding upon and clarifying. First, my thesis is not that objects are unrelated to anything else or that there are objects that are unrelated to anything else. Like Caemeron, I hold that objects maintain a variety of exo-relations with other objects. My body, for example, has the shape, height, and consistency it possesses because of the exo-relations it has with other objects like the planet earth, the molecules presiding over air pressure etc. Consequently, there are a number of qualities belonging to my body that would not exist as they do without exo-relations or relations to other objects.

read on!

What I am railing against is not the thesis that objects have exo-relations with other objects, but rather the thesis that an object is determined or thoroughly defined by its exo-relations. Put otherwise, I reject the currently fashionable thesis that an object is its exo-relations. I reject this thesis based on two arguments drawn from Graham Harman’s Guerilla Metaphysics. First, argues Harman, the thesis that objects are thoroughly defined by their relations is “…too reminiscent of a hall of mirrors” (82). If objects are nothing but their relations to other objects, then objects end up evaporating altogether as each object is but a reflection of the other objects without any substantivity to anchor relations. In other words, the problem with the relational model of objects is that objects become, under this model, nothing at all. Consequently, the thesis is not that objects do not entertain relations with other objects, but rather that objects cannot be reduced to there relations. In order for ontology to be coherent, it is necessary that objects have a substantivity that is not simply a function of their relations.

Second, argues Harman, the ontological thesis that objects are their relations renders change incoherent. If the being of an object is its relations, then it is impossible to see how change is possible as there is nothing held in reserve to explain that from whence change comes. In other words, relational ontology gives us what I refer to as a “crystalline universe”. That is, just as a crystal is a fixed and static structure, the thesis that entity is nothing but its relations leads logically to the conclusion that the universe is fixed and unchanging. This, I take it, is an unacceptable conclusion.

It is for these reasons that I distinguish between endo- and exo-relations. Exo-relations are the relations objects entertain with one another in interacting with one another such that qualitative change is produced in one or both of the objects (exo-relations can be symmetrical or asymmetrical depending on the case). By contrast, endo-relations pertain to the being of the object in-itself independent of its exo-relations to anything else. In other words, the endo-relations of an object are its internal composition or its being, independent of how it is affected by other objects. My thesis is that endo-relations are the condition for the possibility of exo-relations. That is, an object must already have a substantivity of its own and a capacity to be affected for exo-relations between objects to be formed. For this reason, my tentative hypothesis is that the endo-relations presiding the internal composition of an object consist of affects. By “affect” I am not referring to emotions, but rather to the capacity to act and be acted upon, the capacity to affect and be affected, belonging to an object.

BaezNot all objects have the capacity to affect one another and therefore not all objects have the capacity to form exo-relations with each other. Thus, for example, I do not currently– much to my despair –have the capacity to be affected by advanced category theory. One will object that certainly, when I regard the category depicted to the right of this paragraph, I am affected and that therefore it is false to suggest that I cannot be affected by advanced category theory. However, this line of argument lacks precision, forgetting as it does the principle lesson of Husserl regarding the nature of intentionality. As I regard the diagram I do not intend the diagram as a category, but rather am conscious of it as a lusciously beautiful arrangement of lines, arrows, and functions without any access to the object for which this diagram stands. Like an ape, I point and gesture at the diagram with delight, wondering what it is all about, without, nonetheless, being affected by the category. In short, I am affected by the diagram as an aesthetic object not as a category. Interestingly, it is possible that I might develop the capacity to be affected by advanced categories.

Analogously, no matter how much I yell, scream, sing, and coo seductive words at a rock, the rock remains unaffected by my speech. Again, the physicalist will protest: “But certainly the sounds waves affect the rock!” Indeed, this is true. However, while the rock possesses the capacity to be affected by sound waves, it does not possess the capacity to be affected by speech. In other words, speech is not sound-waves. The rock is able to translate sound-waves in its own unique way, but it is not able to translate speech.

Finally, since both of these examples involve humans, we can refer to the example of the humble neutrino. The neutrino falls through most matter with an ease and slipperiness that is the envy of butter knives everywhere. So great is the neutrino’s capacity to slide through matter that, unlike butter knives, it does not touch or affect most other matter at all. In this respect, neutrinos have a very small number of affects. Not only do they have little capacity to act on or affect other types of matter, but they also have little capacity to be affected by other matter. This is why it is such a challenge to study these slippery neutrinos. To investigate anything it is necessary to form exo-relations with that thing so as to provoke or elicit the affects of which the thing is capable. The challenge posed by neutrinos is that of how to form an exo-relation with that which slips through nearly all matter.

My thesis is that ontology must simultaneously investigate objects in terms of their endo-relations, their exo-relations, and their genesis. The point about endo-relations is not that objects do not enter into exo-relations with other objects, nor, even, that we can find a single example of a totally relationless object in the universe, but simply that objects cannot be reduced to their exo-relations. When Caemeron points out that my body is dependent on gravity and air pressure, I think he is failing to distinguish between the internal composition of my body and the qualities of my body that result from being affected in a particular way as a result of the exo-relations it enters into. Suppose, for example, a diabolical correlationist, fed up with my harping about objects, catapults me into outer space. Clearly my body now undergoes profound qualitative changes. My eyes and blood vessels begin to bulge as a result of being plunged into a vacuum, the gasses in my body begin to boil and bubble, I scream out in agony yet without being able to make any sound. However, these qualitative changes are not my body as characterized by its endo-relations or its capacity to affect and be affected, but are rather qualitative changes produced as a result of the affects that compose my being. These qualitative changes are only possible through the endo-structural composition of my body.

300px-Riemann_sphere1When I claim that it is possible for an object to exist that possesses no exo-relations with any other object in the universe, I am not making the claim that such objects exist (how would I know?), but that insofar as objects necessarily possess an independent substantivity or being that cannot be reduced to their relations and is the condition for any exo-relations objects might enter into, there is nothing to prohibit the possibility of such a thoroughly un-related entity. Caemeron contends that it is impossible to conceive such an object, but I do not see why it is anymore difficult to conceive an object without exo-relations than it is to conceive a match that is not burning. Moreover, I believe that mathematically we have even developed the tools for analyzing the endo-relational structure of objects independent of their relations with the mathematical concept of multiplicity or manifold. As DeLanda so beautifully summarizes it,

…when Gauss began to tap into these differential resources, a curved two-dimension surface was studied using the old Cartesian method: the surface was embedded in three-dimensional space complete with its own fixed set of axes; then, using those axes, coordinates would be assigned to every point of the surface; finally, the geometric links between points determining the form of the surface would be expressed as algebraic relations between the numbers. But Gauss realized that the calculus, focusing as it does on infinitesimal points on the surface itself (that is, operating entirely with local information), allowed the study of the surface without any reference to a global embedding space. Basically, Gauss developed a method to implant the coordinate axes on the surface itself (that is, a method to implant the coordinate axes on the surface itself (that is, a method of ‘coordinatizing’ the surface) and, once points had been so translated into numbers, to use differential (not algebraic) equations to characterize their relations. As the mathematician and historian Morris Kline observes, by getting rid of the global embedding space and dealing with the surface through its own local properties, ‘Gauss advanced the totally new concept that a surface is a space in itself. (Intensive Science and Virtual Philosophy, 11-12)

The point here is not that the object does not have exo-relations or that the object is not the result of a genesis from other objects and prior states, but rather that the endo-structure of an object is subject to analysis independent of its relations.