The sea as a smooth space is a specific problem of the war machine. As Virilio shows, it is at sea that the problem of the fleet in being is posed, in other words, the task of occupying an open space with a vortical movement that can rise up at any point. In this respect, the recent studies on rhythm, on the origin of that notion, do not seem entirely convincing. For we are told that rhythm has nothing to do with the movement of waves but rather that it designates "form" in general, and more specifically the form of a "measured, cadenced" movement.25 However, rhythm is never the same as measure.
And though the atomist Democritus is one of the authors who speak of rhythm in the sense of form, it should be borne in mind that he does so under very precise conditions of fluctuation and that the forms made by atoms are primarily large, nonmetric aggregates, smooth spaces such as the air, the sea, or even the earth (magnae res). There is indeed such a thing as measured, cadenced rhythm, relating to the coursing of a river between its banks or to the form of a striated space; but there is also a rhythm without measure, which relates to the upswell of a flow, in other words, to the manner in which a fluid occupies a smooth space. This opposition, or rather this tension-limit between the two kinds of science—nomad, war machine science and royal, State science—reappears at different moments, on different levels. The work of Anne Querrien enables us to identify two of these moments; one is the construction of Gothic cathedrals in the twelfth century, the other the construction of bridges in the eighteenth and nineteenth centuries.
Gothic architecture is indeed inseparable from a will to build churches longer and taller than the Romanesque churches. Ever farther, ever higher ... But this difference is not simply quantitative; it marks a qualitative change: the static relation, form-matter, tends to fade into the background in favor of a dynamic relation, material-forces. It is the cutting of the stone that turns it into material capable of holding and coordinating forces of thrust, and of constructing ever higher and longer vaults.
The vault is no longer a form but the line of continuous variation of the stones. It is as if Gothic conquered a smooth space, while Romanesque remained partially within a striated space (in which the vault depends on the juxtaposition of parallel pillars). But stone cutting is inseparable from, on the one hand, a plane of projection at ground level, which functions as a plane limit, and, on the other hand, a series of successive approximations (squaring), or placings-in-variation of voluminous stones.
Of course, one appealed to the theorematic science of Euclid in order to find a foundation for the enterprise: mathematical figures and equations were thought to be the intelligible form capable of organizing surfaces and volumes. But according to the legend, Bernard de Clairvaux quickly abandoned the effort as too "difficult," appealing to the specificity of an operative, Archimedean geometry, a projective and descriptive geometry defined as a minor science, more a mathegraphy than a matheology. His journeyman, the monk-mason Garin de Troyes, speaks of an operative logic of movement enabling the "initiate" to draw, then hew the volumes "in penetration in space," to make it so that "the cutting line propels the equation" (le trait pousse le chiffre).
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