Magazine article Queen's Quarterly

Crossing the Threshold: Towards a Philosophy of the Interior

Magazine article Queen's Quarterly

Crossing the Threshold: Towards a Philosophy of the Interior

Article excerpt

Grid

THERE are lines and vectors, and so there are boundaries and insides. There is, too, a new map of space itself: the infinitely flexible grid of Cartesian planar space.

What Descartes adds to traditional Greek geometry is the systematic biaxial--eventually triaxial--plotting of position. The basic fact of human existence in space is that there are always six directions created by being: in front and behind, above and below, left and right. These are not always the terms of directionality but its possible namings. The grid takes that irreducible three-dimensional reality and renders it two-dimensionally. But it does more than this. In its various acts of dimensional reduction, the grid is also creative; it alters our idea, and therefore our experience, of space. Now we can map and grid virtually anything--or, to be more precise, virtually map and grid anything.

The very idea of the map, though preceding the Cartesian moment by long centuries, is given new life and direction now: no longer the conceptual fantasies or cautionary fables of earlier ages, where a map might express the rule of Fortune's wheel or the chastening fears of the dragons lying beyond the boundaries, but instead a cluster of imperatives about "precision" and "accuracy." And as with space, so with time: it is well to remember that the navigation of mapping of the seas would not have been possible without the reliable timepieces that enable useful longitudinal measure. You can fix latitude by the stars, and thus get a reading on north and south; but east and west resist measurement as long as there is no precise, measured time-telling.

These norms of measurement, as always both driven by and driving political and commercial desires, themselves create a driving inner logic of representation. This is, to be sure, reducible at the margins to absurdity, as in Lewis Carroll's tale of the county so bent on accurate mapping that it commissioned a 1:1 map which, when completed, lay over the ground like a carpet. All maps, even highly accurate ones, remain fantasies of representation, and the concepts of accuracy and precision themselves subject to important limits. Maps only make sense insofar as they are used, and use structures the meaning of both precision and the act of representation itself. Fractal mathematics reminds us that a given stretch of coastline, for example, no matter how short in miles, is infinitely long. Every inlet and crevice can be mapped, but then can be mapped again at some even higher degree of minuteness; and so on, and so on. At a certain point, a point which can only ever be determined by our purposes, the notion of accuracy, with its implicit wispy normativity, becomes self-defeating.

The Cartesian grid is an abstraction, then, but one of the most powerful ever imagined. In addition to map-making and all that it implies, the grid makes possible the calculus and hence the powerful mathematics of twentieth-century physics. It structures--you could accurately say invents--the peculiar space and time characteristic of Modernity--a space and time I am not defending but analyzing. And though its proximate roots are mathematical, its genealogy is more complicated. Just as innovations in optics and epistemology mapped over to bold new techniques in painting after Descartes, enabling the hyper-realism of the Dutch seventeenth century, so earlier struggles to achieve realistic perspective made possible the abstract refinements of Descartes' notional universe of infinity.

But make no mistake. Infinity, with its swift extensions into transnational capital exchange and information access, has not really transcended the limits of the physical, where body and geography are still inextricable from soul and spirit. A nation-state such as Canada, described so witheringly by Voltaire as "a few acres of snow," may be more a state of mind than a sensible territory, but its borders are still lines to be crossed--and defended. …

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