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 becom-
Ing itself a model, and no longer a secondary charac-
tertsttc, a copy; in the Timaeus, Plato raises this possibil-
icy, but only in order to exclude it and comure it away in
the name of royal science. By contrast, in atomism, just
such a model of heterogeneity, and of passage or becom-
ing 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 for 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 predif ferential calculus.
In the field
of
interaction of the two sciences, the ambulant sciences
confine themselves to inventing problems the soiution of
which is linked to an entire set of collective, nonscientific
activities, but the scientific solution of which depends, on
the contrary, on royal science and the way it has transformed the problem by introducing it into its theorematic
apparatus and its organization of work. This is some. I
what like intuition and intelligence in Bergson, where
only intelligence has the scientific means to solve for mally the problems posed by intuition, problems that
intuition would be content to entrust to the qualitative
activities of a humanity engaged in following matter..
Problem 2: Is there a way to extricate thought from
the State model?
Theorematic: "I would say that my second example overlaps my first one: I will call, if you will, “deductive” or “theorematic” conception the conception which goes beyond the spatial representation towards the power of abstr … towards the symbolic power, and I will call “problematic” the Desargues, Pascal, Monge… Poncelet’s conception which goes beyond the spatial representation towards a trans-intuition or a trans-spatial intuition. And, that the two intermix … It’s possible that at some level, the two intermix, but every time, there are tensions."
Whenever this primacy is taken for granted, nomad
science is made out to be a prescientific, or parascientific,
or subscientific agency. And most importantly, it is no
longer possible to understand the relations between
science and technology, between science and practice,
because nomad science is not a simple technology or
practice, but a scientific field in which the problem of
The War Machine 29
these relations is brought out and resolved in an entirely
different way than from the point of view of royal
scrence.
These numbers appear as soon as
distributes something in space, instead of dividing up
space or distributing space itself. The number becomes a
subject. The independence of the number in relation to
space is not a result of abstraction, but of the concrete
nature of smooth space, which is occupied without itself
being counted. The number is no longer a means of
counting or measuring, but of moving: it is the number
itself that moves through smooth space. There is un-
doubtedly a geometry of smooth space: but as we have
seen, it is a minor, operative geometry, a geometry of the
trait. The more independent space is from a metrics, the
more independent the number is from space. Geometry
as a royal science has little importance for the war
machine (its only importance is in State armies, and for
sedentary fortification, but it leads generals to serious
defeats66). The number becomes a principle whenever it
occupies a smooth space, and is deployed within it as
subject, instead of measuring a striated space. The num-
ber is the mobile occupant, the movable (meuble) in
smooth space, as opposed to the geometry of the im-
movable (immeuble) in striated space. The nomadic
numerical unit is the ambulant fire, and not the tent,
which is still too much of an immovable: "The fire takes
precedence over the yurt." The numbering number is no
longer subordinated to metric determinations or geo-
metrical dimensions, but has only a dynamic relation
with geographical directions: it is a directional number,
not a dimensional or metric one. Nomad organization IS
indissolubly arithmetic and directional; quantity is every-
where, tens, hundreds, direction is everywhere, left'
right: the numerical chief is also the chief of the left or the
67 The numbering number is rhythmic, not har-
right.
But why does Husserl see this as
a protogeometry, a kind ot half-way point and not a pure
science? Why does he make pure essences dependent
upon a passage to the limit, when any passage to the limit
belongs as such to the vague? What we have, rather, are
two formally different conceptions of science, and, ontologically, a single field of interaction in which royal
science is perpetually appropriating the contents of vague
or nomad science, and nomad science is perpetually
releasing the contents of royal science. At the limit, all
that counts is the constantly moving borderline.
One does not pro-
ceed by specific differences from a genus to its species,
nor by deduction from a stable essence to the properties
deriving from it, but from a problem to the accidents that
condition and resolve it. This involves all manner of
deformations, transmutations, passages to the limit, op-
erations in which each figure designates an "event" much
more than an essence; the square no longer exists inde-
pendently of a quadrature, the cube of a cubature, the
straight line of a rectification. Whereas the theorem is of
the rational order (de I'ordre des raisons), 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 that 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.
It is also true of differential calculus: for a long time, it had only parascientific status, it was labeled
a "gothic hypothesis," royal science only accorded it the
value of a convenient convention or a well-founded
fiction; the great State mathematicians did their best to
improve its status, but precisely on the condition that
all the dynamic, nomadic notions—such as becoming.
heterogeneity, infinitesimal, passage to the limit, con•
tinuous variation, etc.—be eliminated, and that civil,
static and ordinal rules be imposed upon it (Carnot's
ambiguous position in this respect). Finally, it is true of
the hydraulic model: for it is certain that the State itself
needs a hydraulic science (there is no going back on
Wittfogel's theses on the importance of large-scale water-
works for an empire). But it needs it in a very different
form, because the State needs to subordinate hydraulic
force to conduits, pipes, embankments which prevent
turbulence, which constrain movement to go from one
point to another, and space itself to be striated and
measured, which makes the fluid depend on the solid,
and flows proceed by parallel, laminar layers.
