Two potential problems with this analysis immediately come to mind, the first having to do with underdetermination and the second with overdetermination. First – if, indeed, through an on-going, co-evolutionary process, our systems of geometry come to reflect and co-determine the architecture of the body/environment interface, how do we explain instances within the material-discursive environment which do not admit of description by invoking either the formal or abstracted elements of vision? How might this theory account for, for example, the sinuous streets of medieval cities or the network topologies of the digital economy when neither of these is given by the axioms of Euclidian geometry or the formal structure of the eye? And in a similar vein, how might such a theory explain the development of more recent geometrical systems such as topology and the related fractal geometry?
One possible response to this tri-partite question is that the architectures of medieval cities and digital networks are indicative of the existence of other geometrizing resources within the body in addition to those provided by the exteroceptive senses, such as sight or hearing. For example, both medieval and network architectures have been shown to exhibit fractal qualities such as self-similarity and scale invariance, properties which also describe various internal and external ratios of the body. In addition, the form of these towns or networks – distributed, self-organizing, byzantine – and their function – the concentration and amplification of intensity and duration at both the individual and social levels – is more redolent of the proprioceptive sensing system than of its exteroceptive counterparts. Thus, science writer, Clive Thompson describes his experience of one such digital network as being:
… like proprioception, [or] your body's ability to know where your limbs are. That subliminal sense of orientation [which] makes possible amazing feats of balance and dexterity…Twitter and other constant-contact media create social proprioception. They give a group of people a sense of itself, making possible weird, fascinating feats of coordination… It's practically collectivist — you're creating a shared understanding larger than yourself… [a] tactile sense of your community — and it makes the group more than the sum of its parts.
Proprioception monitors the position of the body from the inside-out making it possible for interactions between muscles, joints and the environment to direct most of the basic movements of the limbs without recourse to conscious control. As such, it can be credited with evoking the body’s “I” function, or sense of its own depth and boundedness, affects which it achieves through putting the body into motion.
Proprioception, then, constitutes one of the body’s primary resources for its enactment of space and time, with the understanding that the meaning conveyed by these constructs is inaccessible absent the body’s ability to locate itself within the coordinates they and it co-establish. The somatic schema proprioception instantiates and deploys – distributed, self-organizing and massively interconnected – differs significantly from that of the exteroceptive in its use of feed-forward as well as feedback looped architectures. Called to react within milliseconds, this entwined, looped architecture creates subperceptual zones of indeterminacy where past and future states of the system implicate one another and the muscle or limb stiffens in response to a signal that has yet to be sent.
Such a schema offers a potentially rich resource for intuitions of other possible geometries, geometries such as topology whose transformations and morphisms have proven useful both in developing the concept, and in exploring the qualities, of the spacetime manifold [SLIDE] thus making possible quantum theory and the related technologies of the digital economy. Born of the reflexive dynamic of the topological, we should then, perhaps, not be too surprised to learn that it is precisely the arrival of this new economy which theorists such as Mark Hansen and Brian Massumi credit with causing the on-going “shift from a vision-centered to a body-centered model of perception,” that is, to a proprioceptive model whose dynamic is best described topologically.
In response to our first question then, it would appear that the body does, indeed, offer resources other than those provided by its visual apparatuses for geometrizing our world, but these are more readily available at times and in places which are (or were) not dominated by the Western ocularcentric worldview – a worldview whose primacy is being challenged, at both the macro and micro-physical levels by technological developments in the field of digital media.
Turning to the theory’s second potential problem we note that, though there is compelling evidence to suggest that our visual apparatuses predispose us to project onto the world geometrical forms and relationships which are not necessarily there, and that they then lead us to (re)inscribe these forms, perhaps unwittingly, on the world through our material-discursive constructions, it might be overstating the case to say that they are the sole or even primary causal agent behind the geometrized world in which we find ourselves. It might, in fact, be more accurate to say that such perceptions and their (re)inscriptions are overdetermined by the countless numbers of other “natural” forces and formations which impose themselves on the consciousnesses of humans – from gravity, mountains and watersheds, in the case of hierarchies – to centripetal force, the revolution of the earth, and heavenly bodies, in the case of time represented as cyclical or circular [on a side note, only the grid seems to have no referent in the natural world, a topic for another day].
Carrying this thought further, it could be said that the body is as much a product of its material environment as is any feature or artifact to which it might be exposed. This would suggest that drawing distinctions between that which is inside the body and that which is outside (between invention and discovery, for example) is somewhat arbitrary, an observation which nicely sums up the dilemma facing those who would try to grasp the dynamic of the current cultural moment defined as it is by intensive/machine time, or what Hansen describes as “the time of e-mail and surfing, the time which eliminates space [and where] arrival and departure occur in the same moment.”
In an environment such as this, where time or the notion of forward movement has effectively come to a standstill as at the center of a vortex, we find the entanglement of subject and object, inside and outside, past and future to be at its peak. And we find that we, ourselves, occupy a metaphoric subperceptual zone of the proprioceptive, reacting to events before they’ve even happened. While such a dynamic is potentially productive in isolated instances, as when used to stabilize, for example: the body in space; a company’s reputation in the public eye; or the financial markets in a global economy, it can prove catastrophic if allowed to cut transversally through multiple scalar levels simultaneously. Such a scale-invariant dynamic is the very definition of turbulence as described in the literature on fluid dynamics and as captured in Deleuzes’s description of the cosmic maelstrom where, “Dividing endlessly, the parts of matter form little vortices…and in these are found even more vortices, even smaller, and even more are spinning in the concave intervals of the whirls that touch one another.” Such evidence of synchrony among differently-scaled elements within a system often indicates the onset of a phase transition from one state of matter to another.
What form such a shift might take at the social level, and whether we should expect to experience one ourselves, even metaphorically, remains to be seen, but returning to our discussion of the co-evolutionary dynamic of the material and the discursive, we find that some things can be stated with confidence: not all peoples at all times have privileged visual modes of perception and the ratios they inscribe in the same way as do modern Westerners, a fact which would suggest that physiology is not destiny; however, there also appears to be a nearly universal “alphabet” of geometrical form, (circle, square, triangle, for example) whose articulation into a social “grammar” is determinate upon differing paths of socio-historic technogenesis. It would also appear that modes of geometrized perception associated with the West (perspective drawing, for example) exert a powerful hold on those who have experienced their ratios, a fact which suggests they be understood to constitute, in this sense, one of perhaps but a few basins of attraction in the domain of visual perception.
The point in drawing attention to our geometrized material reality, in any event, is not to make a strictly causal argument about our modes of perception and the forms they necessarily lead us to reproduce. The goal is, rather, twofold. First, such an argument is meant to make us aware of just how deeply embedded in our psyche/somas, in our thoughts and feelings, are certain geometries, proportions, ratios and their resulting social and technological counterparts, and how this magnifies the difficulty of imagining how our material-discursive reality might be otherwise constructed. And second, it is meant to suggest that the move towards a “body-centered” rather than a “vision-centered” understanding of the world, a move which our technologies are making possible, if not inevitable, means that we might be freed in some small way from these long-lived ocularcentric geometrical constraints, a move which promises to remove at least one barrier to “envisioning,” or perhaps we should say, “enacting” reality as a material-discursive matrix of “constantly shifting relations between open-ended objects…reciprocal enfoldings gathered together in temporary and contingent unities” as theoretical physicist, Karen Barad and New Vitalist scholar, Mariam Fraser, would have.
To be clear, were the reigning, geometrized framing of reality to be displaced in favor of an episteme which recognized, as Fraser puts it, “the sensitivity of the world to our interest in it, and to the forms in which it is expressed” it should not be heralded as an example of the progressive nature of evolution. Various peoples, cultures, tribes, etc. have for millennia maintained something close to this understanding of reality as their cultural/technological artifacts might attest. But were our technologies to grant us greater access to, and a better understanding of, the post-visual topology that links our inner and outer worlds and which, in fact, calls this distinction into question, then it should certainly be characterized as an improvement in our modeling techniques, if not as an instance of outright progress, albeit of a local sort. I argue that topology and the related fractal geometry help us visualize the non-linear dynamic that animates all matter, thus offering us the means by which we might bridge the divide between moribund binaries of the inside/outside, vitalist/positivist sort. In short, these geometries would seem to offer the rational mind access to knowledge the body already possesses, knowledge best summed up perhaps, by cognitive scientist, Francisco Varela who maintains that, “we exist not in time but of it,” a shift in perspective whose radical nature is difficult to overstate.
In order to grasp something of what this might mean, we would perhaps do well to employ a fractal/embodied understanding of the organization of reality as revealed through the use of digital simulation technologies. This technology-enhanced understanding has made it possible for us to visualize how complexity does not diminish with scale, and how scales of organization might be considered both to be an artifact of the observer’s locatedness in spacetime and to extend indefinitely along what appears to us to be a scalar axis. Our bodies and world, in other words, consist of nested realms of equally complex entities differentiated vertically by the speeds at which they operate. Looking out we also look in, recursively, at an indefinite multitude of entities, each of which carries within itself the whole of that which it regards. Time and scale become as if two sides of a coin in such a reconfigured spatiotemporal environment, our understanding of the uniqueness and complexity of entities existing at “smaller” or “larger” scales, diminishing as they graduate away from us or us from them in “time.”
If our digital technologies are, indeed capable of altering our understanding of reality at this sort of fundamental level, then we are likely to see the discursive power of Euclidian-inspired rationalizing structures diminish along with that of the ocularcentric worldview which stabilizes them in the cultural imaginary. Such a shift seems to imply a syncretic melding of traditionally introspective Eastern and extrospective Western technological practices, an implication I hope to explore at a later date. Additionally, however, and of greater importance to the current discussion, this shift also signals a material-discursive move away from geometrized representations of subjects and societies that have more to do with Euclid and Democritus than with Mandelbrot and Bohr (geometers and physicists, respectively). Bounded atomic spheres and static relational hierarchies have little to tell us about the labile world of which we feel ourselves to be a part. We need ways of accessing and communicating the post-visual topology that is unfolding/enfolding before and within us. As Latour and others have noted, the moderns’ over-reliance on visual sources to establish empirical truths led them and us into, what Barad terms, a “representationalist trap of geometrical optics,” one which stems, at least in part, I argue, from the material constraints of the body itself. But other sensibilities of the body, the haptic and proprioceptive, for example, which the new digital technologies are allowing us to explore and better model, seem to offer us (Westerners) a way out of this particular trap. Accessing these we might be able to override our obsession with the solid geometries of the visible world which reinforce discourses of separation and hierarchy to enact the fluid boundaries and connections that the new post-visual topology in/de-scribes. Tracking this move from what Barad calls a “representationalist geometrical optics” to what I will call a “performative topological haptics” should help us think beyond the human condition, a move Bergson and Deleuze deemed essential in any attempt to develop a new philosophy of nature, as I believe it is necessary we do now, more than ever.