Geo-Imaginaries: Topology vs Topography

New topological geo-imaginaries have to some extent supplanted landscape as a medium for theorising space and nature-culture realtions. Such accounts of space aim to challenge the static conceptions of space, measurement, distance, surface, and perspective developed by traditional landscape studies.

Those writing in a vitalist Deluezian-Bersonian vein, for example, express space as a matter of force, energy and process, and thus present geographies as being animated through their continual becoming (e.g. Thrift 2000; Dewsbury 2002; Marston et al 2005). While such accounts have done much to re-stress the dynamic materiality of space, its ‘entanglements’, these topological accounts of space (particularly those drawing on Actor-Network Theory (ANT)) are at risk reiterating the world as a flat grid-like surface; as Euclidean geometries have done for centuries.

 

Raphael's depiction of Euclid (in his fresco 'School of Athens) conducting a proof, with the back of tan-robed astronomer Ptolemy, holding a globe, beside him.

 

Some geographers, like Mitch Rose and John Wylie, therefore want to reinstate notions of ‘landscape’ or the ‘topographical’ back into topological and vitalist geographies. In their 2006 paper ‘Reanimating Landscape’ they argue that, in prioritising vectors, trajectories, and connections, topological and vitalist geographies present ‘a curiously flat and depthless picture of the world’ (Wylie and Rose 2006: 476).

Their reworking of the concepts of landscape and place in their paper can therefore be understood as a reaction against the topological conceptions of space forwarded by ANT and vitalist non-representational geophilosophies (e.g. Thrift 2000; Dewsbury 2002; Marston et al 2004) and by ‘new’ biogeographies of entangled nature-cultures (e.g. Whatmore 2002, Pile et al 2004; Greenhough and Roe 2006). While Wylie and Rose acknowledge that these topological conceptions of space have profitably critiqued and supplanted hidebound and static notions of space (in terms of territory, boundedness, area, scale, and so on) by ‘thinking space relationally’ (Massey 2004: 5), they also warn that the ‘topological imagination’ is ontologically over-flattening as it has ‘no middle terms of synthetics’ leaving ‘a surface without relief, contour, or morphology’ (Wylie and Rose 2006: 477).

To counter the flattening tendencies of topological accounts of space, they argue that notions of landscape, or the topographical, should remerge to reanimate the missing matter of topological geographies. To do so they present landscape as tension: ‘between presence and absence, and of performing, creating, and perceiving presence’ (Ibid: 475). In this way they present a conception of space that is attentive to both surface and relief – to the solid – and to the elemental and ephemeral.

I would like to suggest a simple exercise that merges topographical and topological imaginaries: making a Mobius strip out of a recycled map.

More specifically in this exercise we are merging the world of topology (that’s the science of the surface of a 3D shape) with topography (graphic representations of the surface features of a place).

Put basically, we could think of it as bringing together abstract notions of ‘Space’ with more concrete representations of ‘Place’.

 

Topographical Mobius Strip

 

1. Cut a narrow strip of a recycled map.

2. Hold both ends of the strip. In your left hand, twist the left side 180º.

3. Connect the two ends of paper together.

4. Tape the two ends together: you now have a mobius strip that merges both the topological and the topographical.

5. Draw a line down the centre of the strip – you will find that as you continue you cover all the surface of the strip and could continue to do so infinitely. Hence why the mobius strip is the symbol for infinity in mathematics and is described as a ‘non-orientable surface’: it has the unique property of having only one side and one edge.

6. If you now cut the line you have just drawn down the centre of the strip you will get an even larger mobius strip.

7. If you do the same again you will get two linking strips (because you have cut through two half turns).

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4 Responses to Geo-Imaginaries: Topology vs Topography

  1. cityperson says:

    Hey Merle,

    Have you read curator Nicolas Bourriaud’s little book “The Radicant”? Here’s a quote:

    “The major aesthetic phenomenon of our time is surely the intertwining of the properties of space and time, which turns the latter into a territory every bit as tangible as the hotel room where I am siting right now or the noisy street that stretches beneath my window. By means of the new modes of spatializing time, contemporary art produces forms that are able to capture this experience of the world through practices that could be described as “time-specific”–analogous to the site-specific art of the 1960s–and by introducing figures from the realm of spatial displacement into the composition of its works. Thus today’s art seems to negotiate the creation of new types of space by resorting to a geometry of translation: topology.” (p.79)

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