Different Species of Space – Jennifer-Lynn Crawford


Flat space is space that doesn’t breathe – it, quite literally, *is* not. We can say that it is a useful exercise in metaphor. There is a wonderful branch of mathematics called topology. I’m a fan, definitely on the amateur scale, but happily so. They discuss ‘space’ mainly – which I find quite useful for all sorts of things – dancing, thinking, imagining –  and one feature of topology that I really enjoy is the possibility of tidying spaces into named places (even though I also don’t believe that they remain in such boxes in the chaos that is live(d) space)… making maps, essentially. There is a branch on the topology tree that focuses on surfaces, something that can be referred to as flat-land, or 2-d space. We don’t live there, but we find it very easy to imagine things there. It gives us ‘perspective‘ – and we tend to have a bit of a cultural disposition to that in the West.

I find a particular species of topological space, called a manifold, very useful. When topology adopts a space like this (i.e., says it is a ‘topological’ space) it means that that space can be manipulated in certain ways, but mostly retains its identity. Confusingly, this is interchangeable with the ‘topology’ of the space: a set of defining characteristics = the identity of the space = the topology of the space.

(Perhaps a good example is the olde rubber sheet – we can stretch it, twist it, bend it so that it looks different – but as long as we don’t tear it, it will continue to have the same identity/topology. As soon as we put a hole in it, it takes on a new identity/topology.)

Geometry is a different kettle of fish that I’ll mostly sidestep for now, but just in case it is useful, we can do geometry on surfaces without the nature of the surfaces changing. Geometry is all the stuff that would change and shift about when we stretch/bend/twist a surface (i.e., measurable qualities of shape rather than nature). Caveat: beware amateur definitions… investigate for your self if this is of interest and forgive me my attempts if expert in the field!

Back to manifolds: manifolds have localized ‘properties’, even though they might be globally more diverse. Put another way: if you are on a surface that goes round a sphere (like we might be), you might find the neighbourhood to be flat… your immediate perception is not of slope. However, given the whole of the ‘space‘ – if we zoom out enough to apprehend the sphericality of the surface we are on (somehow) – it is indeed spherical. We could only find this out for ourselves (physically experience it) by planet-hopping, or figuring out how to jump into a 4-d universe.

Scale is important here – and since interplanetary missions/dimensional jumps are not really on my agenda, I propose that zooming in is possibly the only way that we can apprehend the global variation of the manifold, the many-folded space we are all simultaneously in, with pockets all differently-shaped. Rather than trying to get out of our manifold to ‘see’ it (get perspective, or flatten it into a visual), we have to get further in to it. A way to do this involves playing actively with depth and scale – disturbing our up-down orientation and our visually-dominant perception – in order to start grasping (literally, feeling with our hands and other tactile antennae) that there are many different spaces in what we generally consider to be ‘our’ space.

Time is also important here and it isn’t possible to avoid it. However, I’d like to at least propose that space isn’t (as it often is considered in this ‘global culture‘ aka capitalist-consumerist paradigm) a ‘historical queue‘ (as Doreen Massey puts it); not every space needs to be drawn up in terms of time. Some spaces are on mountain time, where we measure erosion in centuries. Some spaces are on TV prime time, where the cost prohibits anything longer than second-by-second measurement. Different spaces live in/at different times. We don’t need to tune time out to get a feel for spatial difference, nor do we need to measure spaces in a single (clock-based) temporal frame. There needn’t be any integration (of spaces into time); particularly the kind that masquerades (manifolds) as such – but is actually homogenization.

For example: measuring progress as development along a Western/Euro-centric axis requires that spatial difference is homogenized under the umbrella of temporal progress. It couldn’t be that other cultures might be different and that space shifts to promote and feed difference. The underlying paradigm here insists that surely they are just behind ‘us’ in the movement towards the fixed goal of globalization.

To draw this back to zooming in: it isn’t that the ants are moving slowly/quickly according to my human-scale space. They are moving relatively in ant-scale space.

Walking Stories and Space

Is it possible that we consider Walking Stories with its participatory emphasis as less fixed and more true mappings of lived and shared spaces? This could be a way (not *the* way) to zoom in rather than tune out.

My experience of the people who have tried the Walking Stories drafts in the past few weeks is that they find it immersive – rather than transcendent. They find themselves cohering IN the space rather than standing OUT from the space and maybe even starting to practice the environment/landscape we do the walk in.

Participant feedback seems to be that doing the walk changes their perception of self and of the environment the walk happens in. I can only agree – despite knowing the walk, having helped to shape the walk, I still get a different feeling for the environment we do it in, regardless of pre-exploration and strategizing. Of course, this has to do with a willingness and disposition on my part to get ‘lost’ in things. The proposal of he(a)r(e)/not-he(a)r(e) that the audio walk makes, where we aren’t quite sure whether what we are listening to is present or absent, whether it accords to our visual perception or not, invites disorientation and not-knowing. It gives us a human-voice and seriously satisfying compositional compass to get lost to. An invisible non-flat map.

As Cycle Stories continues, having moved through London, Hextable, to Kent, and most recently of Eastleigh, how do we embed ourselves as makers? How do we notice the channels in our perception that keep feeding Walking Stories even as we (out of necessity) map it out on paper, flatten it and fix it down so that others can find the same paths? I don’t think we are sure yet. I think we exercise cartographic skill here at a later point; we’ve come some distance, but we need to keep following our noses a bit longer before we pause to find out where we are/going. I’m feeling stretched by it all, in a good way, a meaty sort of stretch, whereby I think we are still twisting and bending the rubber sheet. We aren’t yet ready to do geometry on it. We are still figuring out what the topology of this thing is.

Seeing a slug trail (gastropoda – ‘travel by belly’ – which, thanks to the skills of Alex in feeding us so extremely well, we are happily very close to doing), I’m reminded that non-linear lines of ‘growth or becoming’ (as Tim Ingold puts it) are most definitely trajectories, and are still lines. Zooming in affords an opportunity to come in to space in all its shifting dimensions. A mountain is not shaped like a pyramid, nor a triangle. Paths are not straight line segments that run from A to B. The sun is not a big circle in the empty sky.

My own experience:

Zooming. Not only a visual space. I zoom in my perception to the ant-scale. This is a change of orientation, from bipedal, upright, human… Not simply a magnification – it is a movement along the horizon of my feeling for this space: Greenwich park/Swanley park/King’s Wood/Spinney Hollow… I change my involvement in the space and the space shifts – the grass is not a uniform blanket on the ground after all. This notion of the air – this thing that isn’t visible, but so open to smell. To skin. Fog = wet skin and ghostly visuals, mystery and slowed up time.

More Questions:

Continuing the idea of practicing space – which space?  It is possible to examine or explore from different levels or into different levels – zooming in our perception – space as folding, multi-valent possibility – foldable – fluid, unfixed.



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