Spatio-Temporal Topology– A Brief Remark

One of the issues that tends to give me headaches within the object-oriented ontologies of Harman, Latour, and Whitehead are the questions of time and space. It seems to me that all of the object-oriented ontologists are more or less agreed in rejecting the notion of time and space as containers. If objects are, to use Bogost’s gorgeous term, the primitive “units” of being (which isn’t to say they are simple or indivisible), then it follows that time and space cannot be more primitive than objects, that they cannot be containers within which objects reside, but rather time and space must be generated by or arise from objects somehow. But how, precisely, to conceive these processes or the genesis of spatio-temporal fields and relations among relations? Of the object-oriented ontologists, Whitehead strikes me as having the most well developed account of spatio-temporality, though sadly I have a bear of a time understanding just what he is claiming (perhaps Shaviro can flesh this out for us some day). Whitehead was led to a similar conclusion precisely because he treats being as composed of actual occasions and nothing else.

I’m on the run so my comments will have to be brief, but it seems to me that one way spatio-temporal relations might be conceived is in terms of a sort of network topology pertaining to paths or vectors of relations among objects. Speaking in the context of spatiality, consider the difference between the three-dimensional geometrical plane in the diagram to the left above and the network diagram to the right. The geometrical plane above represents the standard notion of space as a sort of container for objects. Proximity and distance is a function of where objects are located with respect to one another in a coordinate system. Two objects are near or far when their coordinates share a close proximity to one another. Here the space precedes the objects.

read on!

A network topology, by contrast, is entirely different. Take the decentralized network (B) in the network diagram to the right. If we look at the lower two branches of the network cluster at the bottom of the dencentralized network we notice that they are, in Euclidean terms, very close to one another spatially. However, if we begin from the premise of topological network space, despite this close proximity, there are tremendously distant from one another. Why? For the node that is closest in Euclidean space to reach the closest node in the next branch it must pass through three other nodes. By contrast, the lowest node in this network only needs to pass through two other nodes to reach the central node in diagram (B). Space would thus be generated by objects through these sorts of network relations defining paths of accessibility or relatability. Rather than a Euclidean space where distance is defined by proximity, instead proximity would be an issue of paths.

To make this point more concretely, Graham and I are far closer in network space than I am with my neighbor. Despite the fact that my neighbor lives only a few feet from me, he is topologically very distant as there are few paths for us to relate to one another. By contrast, I tend to talk to Graham a few times a week despite the fact that he’s all the way in Egypt. We can think of time in a similar fashion. Times can be vastly distant for, say the Amish, in that the Amish occupy a different temporal horizon than someone living in the midst of post-industrial media culture. The paths between these two times can be very difficult to connect because of these different temporal plateaus or horizons.

One might object that this conception of time only pertains to the human, but this is not necessarily the case. No doubt there are specific ways in which human social systems are structured that organize time and space in this sort of networked fashion, but we find similar network structures of spatio-temporality in the biological world as well. There is, for example, a frozen lake in Siberia (I forget the name) that has not been exposed to the outside environment for thousands of years. Currently biologists are trying to figure a way to drill through the ice so as not to contaminate the environment underneath. Here we quite literally have a different temporality where the paths between life outside this lake and inside this lake require a number of mediating steps to meet up. They appear to be “contemporaneous” or simultaneous, but where the temporal distance between this ecosystem of life and others is quite divergent. In addition, we could ask how such a network structure of time might be thought in terms of nonorganic physico-material entities that do not have a dimension of memory (organic or cognitive). Time to scoot.