The War Machine (IV)

by Biodun Iginla, BBC News  Analyst, New York

There is a kind of science, or treatment of science, that seems very difficult to classify, whose history is even difficult to follow. What we are referring to are not "technologies" in the usual sense of the term. But neither are they "sciences" in the royal or legal sense established by history. According to a recent book by Michel Serres, both the atomic physics of Democritus and Lucretius and the geometry of Archimedes are marked by it.16 The characteristics of this kind of eccentric science would seem to be the following: 

1. First of all, it uses a hydraulic model, rather than being a theory of solids treating fluids as a special case; ancient atomism is inseparable from flows, and flux is reality itself, or consistency. 

2. The model in question is one of becoming and heterogeneity, as opposed to the stable, the eternal, the identical, the constant. It is a "paradox" to make becoming itself a model, and no longer a secondary characteristic, a copy; in the Timaeus, Plato raises this possibility, but only in order to exclude it and conjure it away in the name of royal science. By contrast, in atomism, just such a model of heterogeneity, and of passage or becoming in the heterogeneous, is furnished by the famed declination of the atom. The clinamen, as the minimum angle, has meaning only between a straight line and a curve, the curve and its tangent, and constitutes the original curvature of the movement of the atom. The clinamen is the smallest angle by which an atom deviates from a straight path. It is a passage to the limit, an exhaustion, a paradoxical "exhaustive" model. The same applies to Archimedean geometry, in which the straight line, defined as "the shortest path between two points," is just a way of defining the length of a curve in a predifferential calculus. 

3. One no longer goes from the straight line to its parallels, in a lamellar or laminar flow,18 but from a curvilinear declination to the formation of spirals and vortices on an inclined plane: the greatest slope for the smallest angle. From turba to turbo: in other words, from bands or packs of atoms to the great vortical organizations.The model is a vortical one; it operates in an open space throughout which things-flows are distributed, rather than plotting out a closed space for linear and solid things. It is the difference between a smooth (vectorial, projective, or topological) space and a striated (metric) space: in the first case "space is occupied without being counted," and in the second case "space is counted in order to be occupied." 

4. Finally, the model is problematic, rather than theorematic: figures are considered only from the viewpoint of the affections that befall them: sections, ablations, adjunctions, projections. One does not go by specific differences from a genus to its species, or by deduction from a stable essence to the properties deriving from it, but rather from a problem to the accidents that condition and resolve it. This involves all kinds of deformations, transmutations, passages to the limit, operations in which each figure designates an "event" much more than an essence; the square no longer exists independently of a quadrature, the cube of a cubature, the straight line of a rectification. Whereas the theorem belongs to the rational order, the problem is affective and is inseparable from the metamorphoses, generations, and creations within science itself. Despite what Gabriel Marcel may say, the problem is not an "obstacle"; it is the surpassing of the obstacle, a pro-jection, in other words, a war machine. All of this movement is what royal science is striving to limit when it reduces as much as possible the range of the "problem-element" and subordinates it to the "theorem-element."