Academic journal article Environment and Planning D: Society and Space

The Surface and the abyss/Rethinking Topology

Academic journal article Environment and Planning D: Society and Space

The Surface and the abyss/Rethinking Topology

Article excerpt

Abstract

Through a critical deployment of the surface/depth metaphor, this article explores the catalytic potential of topological thinking to establish points of articulation between apparently opposed notions and canons of thought. Starting from a genealogy of mathematical developments and philosophical mediations toward the end point of geography, we address the interplay between the formal (axiomatic) and conceptual (problematic) dimensions of topology in suggesting some potentially alternative ways of re-imagining the role of topological thinking for spatial theory and human geography.

Keywords

Topology, surface/depth, mathematics, spatial theory, human geography

"Deafen yourself to the noise of the expressible! Listen instead for the whisper of the taken-for-granted!" (Gunnar Olsson, 1982: 224)

"The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite. Whenever we proceed from the known into the unknown we may hope to understand, but we may have to learn at the same time a new meaning of the word 'understanding'." (Werner Heisenberg cited in Majid, 2012: 98)

Introduction

Discussions invoking foundational issues are always a sensitive terrain. They often provoke tensions in the bundle of red threads underpinning the ontological status of disciplinary domains. Consequently, new ways of passage are sometimes exposed between familiar and less familiar places, often leading to the erosion of formalised categories and their assimilation into new architectures that challenge conceptual grounds once considered safe havens. This is also true for any plea for more inclusive approaches in current geographical conceptualizations of space, like the one emerged a few years ago with John Allen's call for a 'topological twist' (see, Allen, 2011; Coleman, 2011; Elden, 2011; Latham, 2011; Paasi, 2011a). Topology currently scores as one of the putative core topics in geography, but despite the proliferation of topological imaginaries of the past decade or so, it is not clear as yet whether what we are facing is the manifestation of a fashionable trend or something with more profound implications for spatial theory (for a tentative mapping of these see, among others, Martin and Secor, 2013). As such, we are still left with some important questions concerning for instance the issue of 'topological returns' (Paasi, 2011a; Phillips, 2013), or of how to make better sense of topology in analytical and methodological terms (Lorimer, 2007; Shields, 2013).

Arguably, there are many alternative ways to address these queries. Along the interventions that lament over the metaphorical treatment of topology (Shields, 2013) or the often superficial engagement with its 'genealogies of meaning' (Abrahamsson, 2012; Elden, 2011), we propose a genealogical exercise staged through a critical reflection on the surface/depth dichotomy, as a long-standing legacy in Western thought (Tuan, 1989). Echoing Heisenberg's quote above, our exploration may thus be conceived as a passage between the visible and the invisible, the known and the unknown, but also as an expression of the shifting spatialities articulated by appropriations of topology in geography. Working from a broad understanding of topology--which builds upon some key conceptual filiations to its establishment as a branch of mathematical endeavour--we address the interplay between its formal and problematic dimensions, emphasising the underrated potential of the latter for spatial thought.

Our main objective is thus to show how recourse to a tentative genealogy of topology in mathematics could unlock alternative venues for topological thinking in human geography and its approach to spatial theory. We attempt to do so first by reflecting on present-day treatments of topology in geography and by suggesting that a more direct reference to the mathematical tradition in topological thinking could prove useful for a broader geographical audience. …

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