Atlas of Places
State space is “striated,” or gridded.
In view of this, it would be better to talk about simultaneous states of the abstract Machine. There is on the one hand an abstract machine of overcoding: it defines a rigid segmentarity, a macrosegmentarity, because it produces or rather reproduces segments, opposing them two by two, making all the centers resonate, and laying out a divisible, homogeneous space striated in all directions. This kind of abstract machine is linked to the State apparatus. We do not, however, equate it with the State apparatus itself. The abstract machine may be defined, for example, more geometrico, or under other conditions by an “axiomatic”; but the State apparatus is neither geometry nor axiomatics: it is only the assemblage of reterritorialization effectuating the overcoding machine within given limits and under given conditions. The most we can say is that the State apparatus tends increasingly to identify with the abstract machine it effectuates. This is where the notion of the totalitarian State becomes meaningful: a State becomes totalitarian when, instead of effectuating, within its own limits, the worldwide overcoding machine, it identifies with it, creating the conditions for “autarky,” producing a reterritorialization by “closed vessel,” in the artifice of the void (this is never an ideological operation, but rather an economic and political one).
The plane of consistency (grid) is the outside of all multiplicities. The line of flight marks: the reality of a finite number of dimensions that the multiplicity effectively fills; the impossibility of a supplementary dimension, unless the multiplicity is transformed by the line of flight; the possibility and necessity of flattening all of the multiplicities on a single plane of consistency or exteriority, regardless of their number of dimensions. The ideal for a book would be to lay everything out on a plane of exteriority of this kind, on a single page, the same sheet: lived events, historical determinations, concepts, individuals, groups, social formations. Kleist invented a writing of this type, a broken chain of affects and variable speeds, with accelerations and transformations, always in a relation with the outside. Open rings. His texts, therefore, are opposed in every way to the classical or romantic book constituted by the interiority of a substance or subject. The war machine-book against the State apparatus-book. Flat multiplicities of n dimensions are asignifying and asubjective. They are designated by indefinite articles, or rather by partitives (some couchgrass, some of a rhizome …).
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.”
Text: Gilles Deleuze and Félix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia, 1980