Espace lisse et espace strié
Two models of space that Deleuze and Guattari set against each other, then constantly bring into communication: the *striated* organizes through the interweaving of constants and variables (warp and weft, longitude and latitude), it is closed, measured, gridded; the *smooth* is a basic heterogeneity, open, non-metric, occupied without being counted (*felt* rather than weaving, *nomos* rather than *logos*). In fact, the two spaces exist only when mixed, endlessly translating into one another.
L’espace lisse et l’espace strié, – l’espace nomade et l’espace sédentaire, – l’espace où se développe la machine de guerre et l’espace institué par l’appareil d’État, – ne sont pas de même nature.
Here’s the translation, preserving all Markdown, links, italics, and symbols while aiming for idiomatic English:
The opening sentence of the plateau sets up three cascading oppositions—smooth and striated, nomadic and sedentary, war machine and state apparatus—without collapsing them into one. They don’t align term for term: in fact, the chapter’s entire effort is to show, through a series of models (technological, musical, maritime, mathematical, aesthetic), how these de jure distinctions actually intermingle—“the smooth space is ceaselessly translated, traversed into a striated space; the striated space is constantly poured back, returned to a smooth space.”
The technological model anchors the vocabulary: weaving interlaces two perpendicular sets of threads, the fixed warp and the variable weft, producing a necessarily closed and homogeneous space; felt, by contrast, is made by compressing tangled fibers without order, without top or bottom, a material proper to the nomad and their tent. The Greek model doubles this distinction with a political vocabulary: “The smooth is a nomos, while the striated always has a logos.” Nomos designates open, unpartitioned space—steppe, plateau, mountainside—the law of distribution in a boundless expanse; logos, that of the city, which measures, divides, and grids. Deleuze and Guattari finally trace this same division to the sea, “archetype of all smooth spaces,” which astronomical navigation gradually striates—then to the air and stratosphere, themselves smoothed in turn to better control the striated earth.
Distinct from the war machine, which occupies smooth space without being reducible to it: smooth and striated space is the geometric counterpart, the description of a milieu; the war machine is the collective assemblage that moves within it, with its own affects and becomings. One can inhabit a desert in striated fashion, or a city in smooth—so the distinction isn’t merely objective, unlike strata, which do effectively capture matter into stable units. The smooth doesn’t oppose the organized as the formless opposes the formed: it’s a space of continuous variation, not an absence of space.