This essay is part of the Volumetric Sovereignty forum.

he ground has volume. It is a voluminous surface. As such, it cannot be an object of sovereignty. My argument here follows three steps. First, I shall bring out the original sense of volume as the rolling up or turning over of material, thanks to which its lower and upper regions are continually inverted. Second, I shall demonstrate that this kind of rolled-over surface is incompatible with the logic of the state, which requires that the ground be levelled. Third, I shall show how the exercise of volumetric sovereignty by the state therefore means relinquishing the ground for spaces above and below, respectively aerial and subterranean, contained within an abstract grid of three dimensions.

I begin with an exercise in etymology. The word ‘volume’ has its source in the Latin verb volvere, ‘to roll’. Thus, it is cognate with such words as ‘evolution’ and ‘revolution’. The original volume was a scroll of papyrus or parchment, usually inscribed with writing. To read it, the scroll had to be unrolled, or evolved, after which it would be rolled up again, or revolved. Only later did the scroll give way to the handwritten codex, and eventually to the printed book we know today. In the codex, the continuous length of the scroll would be folded into sheets, so that the reader, rather than unrolling the volume, would turn its pages, opening up each fold only to close its predecessor behind. Yet the codex itself was never closed but always remained open, in the reader’s hands or on his desk. Only later, as manuscript was replaced by the printed word, was the book finally closed. For in the printed book, the pages are laid one over another to form a stack. When you retrieve what you call a volume from your shelf, it is to this stack that you refer. Bound between covers, it takes on something of the character of a box. The volume becomes a container, and the words its contents. By extension, then, the volume of any form, whether material like a wooden box or ideal like an abstract geometrical figure, becomes the measure of its capacity to contain. And with that, the voluminous makes way for the volumetric.

Now let’s get back to ground. Can it be compared to a scroll? Can it be rolled up on itself, and unrolled, like a carpet? Well, not exactly. But it can be turned. Put yourself into the shoes of the medieval ploughman, who would turn the ground with every turn of the seasons in the agricultural calendar. There were three periods of ploughing in the medieval year: in April for spring crops, June for the late summer harvest, and October for winter wheat and rye. The purpose of ploughing is to bring to the surface nutrient-rich soil from deep down, while burying soil already drained of nutrients by previous cropping, along with any remaining weeds and stubble. Thanks to this continual turnover, the ground will continue to yield, year after year. It is repeatedly renewed, not by adding layer upon layer as in a stack, but by breaking it, cutting through with the share so as to raise the deep and bury the shallow. The same thing happens with the scroll. Roll up a carpet, and you will find that the underside lifts up over the topside, which now finds itself beneath. Similarly, when you turn the page of the codex, recto and verso are inverted: what had once been hidden beneath the fold is opened up, and what was open is now concealed beneath. That’s what makes the ground – like the carpet and the codex – into a volume. It’s a surface that turns with the seasonal passage of time, with the alternations of weather and the husbandry of crops, wherein the past rises up even as the present sinks below.

In the eyes of the state, however, the ground is not for turning. It is for occupation. The logic is territorial. As a bounded portion of territory, the ground is understood as a fundamental platform—level, void and hard—upon which everything stands, each in its proper location, as might be represented on a cartographic map. The state does not inscribe its ways into the land as does the husbandman, or like the penman into parchment, but rather imposes its sovereignty from above, much as in the printing press, letters are imposed upon the sheet. Every new impression, then, calls for a new sheet, or a new ground. Thus there can be no renewal without re-layering: ground is layered upon ground, as sheet on sheet, to form a stack. Time no longer rolls, folds or turns the ground into a volume. It rather cuts through successive grounds, going upwards from past to present, or downwards—as in archaeological excavation—from present to past. Yet the ground itself, thus conceived, has no volume, only area.

How then can the state, whose territory is confined to the ground of the present, simultaneously establish sovereignty over volume? It can do so only by taking leave of ground level. To the two dimensions of the horizontal it is necessary to add a third, of height above or depth below the zero point. One can go across, from place to place in the territory, but also vertically up and down, as in an elevator. For the prospector who would drill the earth for oil or gas, or for minerals, and for the architect who would pierce the sky with his constructions, the ground is not a surface to be turned but a level plane – a ground zero – to be either penetrated or transcended. Like the runway for the airliner, it is flat, hard-surfaced and completely free from obstruction. As it takes off, the plane enters the ‘air space’ of a state. But whether the domain of sovereignty be aerial or subterranean, above ground or below, it is in the containment of space, and not the revolution of time, that its volume is generated.