In Mille Plateaus, Gilles Deleuze and Félix Guattari distinguish between two kinds of spaces: smooth space and striated space. This distinction coincides with the distinctions they draw between the nomadic and the sedentary, between the space of the war machine and the space of the state appparatus. 

While Deleuze and Guattari consider these two spaces to differ fundamentally in nature, they also believe that the two spaces in fact exist only in mixture. (see abstract / concrete ) 


Other terms of the smooth / striated opposition are:

felt / woven fabric 

non-metric / metric multiplicities ( Pierre Boulez) 

nomos (law) / logos (word, thought, rational structure --"logic" in the largest sense of the word.) 
...although the meaning of nomos that Deleuze and Guattari are interested in describes the outskirts as opposed to the city -- "a mode of distribution" see p 380--an open space as opposed to a closed space of parcellization 

primacy of the line (vector) / primacy of the point 

Riemann space / Euclidean space

minor science / royal science

becoming / progress 

"free action"(or play?) / work 

haptic / optic( is perspective a model of striation?) 

local / global (?) 

reading / writing? (De Certeau) 

quality / quantity? 

"The primary determination of nomads is to occupy and hold a smooth space." ( p.410) 

According to Deleuze and Guattari, smooth space is occupied by intensities and events. It is haptic rather than optic, a vectorial space rather than a metrical one. Smooth space is characteristic of sea, steppe, ice and desert. It is occupied by packs and nomads. It is a texture of "traits" consisting of continuous variation of free action. The characteristic experience of smooth space is short term, up close, with no visual model for points of reference or invariant distances. Instead of the metrical forms of striated space, smooth space is made up of constantly changing orientation of nomads entertaining tactile relations among themselves.

Smooth does not mean homogeneous, however, but rather amorphous non-formal (cf formless) in fact, striation creates homogeneity. Homogeneity is the limit-form of a space striated everywhere and in all directions. According to Deleuze and Guattari, striation is negatively motivated by anxiety in the face of all that passes, flows, or varies and erects the constancy and eternity of an in-itelf. Thus A Thousand Plateaus recounts an "extended confrontation between the smooth and the striated in which the striated progressively took hold." 

The sea and the desert are examples of smooth spaces that became striated (cf the clock and navigation) (cf. also time) Striation seems to be, at least in part, the effects of technological mediation resulting in mathematical quantitiesas opposed to qualities. Striation makes the measurable. Examples of striation include warp and woof, harmony and melody, longitude and latitude. (cf also aggregate / systematic )

the town as force of striation upon countryside "invents agriculture" For D+G the essential enterprise of the state is its conquest of the war machine. In the eighteenth and nineteenth centuries it subjugates it to the work-model of the construction site and factory, and imposes the interrelated concepts of physicoscientific work and socioeconomic labor. (cf. clock) "The war machine was perhaps the first thing to be striated. That is where free action in smooth space must have been conquered." (Thousand Plateaus, p.490) "The war machine does not in itself have war as its object, but necessarily adopts it as its object when it allows itelf to be appropriated by the State apparatus." (p.513)

Although they never mention it, the grid must stand as both the emblem and diagram of striated space. The effect of the grid was always to say of something that it was this, not that; it belonged here, not there. The metrics of striated space is indispensable for the translation of smooth multiplicity. In describing the fractal as a way of translating the strange data of smooth space into a striated one, Deleuze and Guattari emphasize the way in which the space and that which occupies it become identified, rather that one containing the other. (see also field) (This description ressembles Henri Focillon's comparison between the "system of the series" and the "system of the labyrinth" in the relation of ornament to void space.) D+G find smooth space in the spatial organizations of systems far-from-equilibrium: in the clinamen and vortex.

what is relationship of smooth/striated to space/place

Is the "everyday" a form of the smooth? (see also time of aeon / time of chronos) 

see De Certeau's description of the "trajectories" of consumers -- their tactics and "traverses" which remain heterogeneous to the systems they infiltrate in which they sketch out the guileful ruses of different interests and desires. (p.34) see also de Certeau's descriptions of reading as poaching and of writing as capitalist conquest. 

cf also visuality vs sensuality. Smooth, continuous mapping is also a mathematical / scientific concept.
Smooth mapping does not occur at singularities

How to map the " morphology of the amorphous?" 

what is a "granulated continuum?' 
The "Great Chain of Being" upheld the principles of continuity and plenitude. "Nature makes no leaps." --Leibnitz. 
The continuum for the Stoics was the pneuma 
"Architecture is an art of distinctions within the continuum of space." (W.J. Mitchell, The Logic of Architecture, p.1) 

In One River, an account of ethnobotanical exporations of the Amazon by Richard Evans Shultes and his students, Wade Davis describes the Kogi tribe of the High Sierra, a thriving agricultural people still living in relative isolation. For the Kogi, the loom is a metaphor both both their wanderings and their thoughts. For them, the sacred infuses the material world. In passing over the earth, the Kogi weave a sacred cloak over the Great Mother, each seasonal migration becoming a prayer for the well-being of the people and the entire earth. (p.52) 

Deleuze describes Riemannian space as a sort of space which involves setting up little neighboring portions that can be joined up in an infinite number of ways, which made possible the theory of relativity: ("Mediators" in Negotiations, p. 124) an amorphous collection of pieces that are juxtaposed but not attached to each other. pure patchwork. 

Is smooth "better", more desirable? What about the smooth "machinic enslavement" in which capitalism operates by a complex qualitative process bringing in to play transportation, urban models, the media, the entertainment industries, ways of perceiving and feeling ... to reconstitute a sort of smooth space in which the destiny of human beings is recast. (p.492) In integrated world capitalism a new smooth space is produced. Multinationals. Never believe that a smooth space will suffice to save us 

Manuel Castells calls the new space of multinational capitalism the new space of flows. (see space / place ) Michael Hardt and Antonio Negri call the new smooth space Empire . They remind us that capitalism, which may have emerged from striation, tends to smooth out all spatial boundaries, to open up markets, to deterritorialize production. (Post- fordist restructuring) "Capital tends towards a smooth space defined by uncoded flows, flexibility, continual modulation, and tendential equalization." (Empire, p. 327) 

Michel Serres points out that topology treats space in a non-metrical way. It uses the concepts of open and closed, of the between, towards, in front of, behind, etc. It uses prepositions in the analysis of what Leibnitz called analysis situs(Atlas, p. 71) If geometry makes the house, topology describes the forest. "J'habite la géométrie alors que la topologie me hante " (p. 74) The theme of haunting in architecture has been recently taken up by Vidler, Wigley, and others. (see unheimlich)

The voluntary muscles are the striated muscles. Are the involuntary muscles smooth?