The point is that a rhizome or multiplicity never allows itself to be overcoded, never has available a supplementary dimension over and above its number of lines, that is, over and above the multiplicity of numbers attached to those lines. All multiplicities are flat, in the sense that they fill or occupy all of their dimensions: we will therefore speak of a plane of consistency of multiplicities, even
though the dimensions of this "plane" increase with the number of connections that are made on it. Multiplicities are defined by the outside: by the abstract line, the line of flight or deterritorialization
according to which they change in nature and connect with other multiplicities. 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 ...)