How do we orient ourselves within the space of the digital atlas?
How do we orient ourselves in a world without a compass, without a universal frame of reference like a horizon or Eurocentric modernist narrative?
In a previous post I discussed the notion of an anti-frame of reference, the confrontation with the modernist myth so that the stories of the marginalised are revitalised and re-inscribed into its narrative. But the modernist story must be infiltrated and retold from differing alternative perspectives. How are these different orientations represented on the map? More than this, how does the map shift and move between them?
What I would like to investigate, in the next few paragraphs, is the relationship between orientation and projection. I will do this via a short detour into the different ways we can understand and confiture space. What mathematicians refer to as topology.
Although the term topology sounds ancient as if it is etymologically related to the Greek topos meaning place and logy which denotes “the study of”, i.e. the logos. The terms itself, however, does not come into use until the late 19th century with the invention of the mathematical field of topology.
Topology is a mathematical subject that considers the organisation of space without having to think about calculation or metric. While geometry, for instance, tries to calculate the distance between two points on a line to find the middle point, topology only cares that there is a point between two points on a line. The idea of the middle is irrelevant since it’s fundamentally a measurable entity. It’s hard to eyeball the middle, for instance. In that sense, topology is a mathematical discipline that is sometimes accused of being qualitative and occasionally has trouble justifying its position as a science. The freedom from calculation, however, allows for the less constrained projective transformation from one topological space to another. In other words, it’s easier to mathematical change the configuration of space within the field of topology.
Transformative projection is the practice of faithfully transforming one geometric space into another. Some projections can take place between metric system such as that between the Cartesian coordinate system and the geographic coordinate system. Projections can occur, however, in topological space without recourse to any metric.
In some sense, we can think of projection as the shifting between frames, between perspectives from something quantitative metric, for instance, to another numerical system or to something that cannot be captured by the numerical, the lived experience or the topological.
In his book on Assemblage Theory Manuel Delanda recognises a hierarchy of geometric spaces between Eucledian and topological space. He goes on to rank them by borrowing terms from Gilles Deleuze, from greater extensity to greater intensity. The more complex or numerically differentiated the geometry. i.e. the more complex the metric, the higher its extensity and vice versa. In that sense, topology is the geometry with the highest intensity, making it more akin to energy or flow.
In the book, Delanda references intensive maps, which we could also refer to as topological maps. With intensive maps the idea is not to map borders or edges of entities like the ocean but rather thresholds between different intensities or between different geographical systems. To illustrate this point, he gives the example of the different thresholds of water, when it turns from gas into water and then into ice and so on. Each of these topological changes indicate a change in the molecular structure of water, the water quality of the water is transformed into quantity.
John Law in his discussion of network topology and Actor Network Theory (hereafter ANT) calls for a need to imagine a fluid topology that permeates the difference between a domain, or we can say field, topology that determines the study of field research and the network topology that is employed by ANT. For Law, topology is way to organise space in order to understand the social fabric of that space and so far, none of the topologies that he’s encountered satisfy some of the nuances that exist between.