Quaternions and the manifold in Oceania
Susanne Kuechler (University College London)
Paper short abstract:
Simon Harrison (2006) has provided us with a convincing argument for the role played by the ‘fracturing of resemblance’ in island Melanesia, placing differentiation and dissociation rather than consociation and congruence at the core of identity politics. This paper will ask how an ontology of identity as manifold is made to work by exploring image based systems that make use of quaternions to rotate and deform spatial entities, while keeping their identity stable. It is this topological imagination, the paper will argue, which makes it possible to conceive of a propensity for relation to rest in the multiple iteration, or the manifold, of one (see Wagner 1991). The fractal images of Eastern Polynesian patchwork will provide the backdrop against which to throw a perspective on the material imagination that uses number sets not for exact measurement, but to draw out spatial relations such as neighborhood, insideness and outsideness, disjunction and connection. Mathematical ideas implicit in the cultural products of Eastern Polynesia constitute the conceptual framework for the political economy of its societies that have placed the transitive iteration of genealogical time at the center of considerations of affinity. Returning to island Melanesia, quaternions will be shown to be implicit, rather than explicit, driving the iteration of generative and composite images that display a being in relation permanently under construction. The implication of the recovery of quaternions in Oceania for a re-conception of ‘art and agency’ will conclude the paper.
Paper long abstract:
Beauty, order, harmony and design