Smooth & Striated

Definitions › Six models

Literature spine · ATP ch. 14 · outline from public sources

Six models of the smooth and the striated

Deleuze and Guattari test one distinction in six domains: textile, music, the sea, multiplicities, physics, nomad art. For each: what is smooth, what is striated, and how one passes into the other — as the sources we could read say it.

Status · outline, not a collation. This workspace does not hold A Thousand Plateaus in any printing. Every sentence below is tied to a public source fetched on 6 October 2026, or marked our gloss. Quotations of the chapter are given as those sources print them. Page numbers are always the citing source’s own, and the series are kept apart:

One frame for all six

The chapter, as Conte quotes it, says the two spaces in fact exist only in mixture: smooth space is constantly being translated, transversed into a striated space; striated space is constantly being reversed, returned to a smooth space Conte 474, while de facto mixes do not preclude a de jure, or abstract, distinction Conte 475. Lysen and Pisters put the same pair as de jure oppositional but de facto existing only in complex mixed forms L&P intro. The models are proposed as various aspects of the two spaces and the relations between them Anderson 475.

The movements are not mirror images. Anderson summarizes two nonsymmetrical movements, one of which striates the smooth, and one of which reimparts smooth space on the basis of the striated Anderson ~480; Harris: no simple reversibility Harris notes. Somers-Hall reads smooth and striated as tendencies we encounter in the world, rather than states or structures Somers-Hall p.243. Bonta’s outline, the teaching table we lean on, says the most realistic application lies in the mixings and passages and that a revision would add a middle passage between each opposition Bonta preface. His table has no middle column. The passage column below is assembled from what the sources say about crossings; it is not Bonta’s missing column.

  1. 1 · 475–77Technologicalfelt · woven fabric
  2. 2 · 477–78Musicaloccupy without counting · count to occupy
  3. 3 · 478–82Maritimevector · point to point
  4. 4 · 482–88Mathematicaldistance · magnitude
  5. 5 · 488–92Physicaldeclination, vortex · gravitational grid
  6. 6 · 492–500Aesthetichaptic, close · optical, distant

Bands are Bonta’s Minnesota 1987 page ranges, not checked in the book. Order and names: Bonta’s headings; Conte names the same six; Harris walks them in the same order on Continuum.

The technological model (textile)

Bonta band 475–77 · felt against fabric; patchwork against embroidery

The model starts from how cloth is made. Weaving crosses two sets of threads; felt is pressed into being. The difference is in the construction, not in how the surface looks.

Teaching figure · our gloss of Bonta 475–77 and Conte 475–77 · not a source plate

Felt, patchwork, and woven fabric Three swatches. Left: short fibres tangled in every direction, colour shifting continuously, edges fading on all sides, no centre. Middle: irregular patches of different sizes and patterns joined piece by piece, no central motif, edges fading. Right: a plain weave of vertical warp and horizontal weft strands passing over and under, with hard edges left and right and open top and bottom.
  • Felt · smoothentangled, not crossed; open on every side; no top, bottom, or centre
  • Patchwork · smooth, not homogeneouspiece by piece; no central motif
  • Weave · striatedwarp and weft; fixed and mobile; closed at the selvedges

Smooth

Felt, an anti-fabric: no separation of threads, no intertwining, only an entanglement of fibers obtained by fulling Conte 475.

In principle infinite, open, and unlimited in every direction; it has neither top nor bottom nor center; it does not assign fixed and mobile elements but rather distributes a continuous variation Conte 475–76 Somers-Hall ATP 475–6.

It is in no way homogeneous: it is nevertheless smooth Conte 475. Nomadic cloth, indexed to the outside Bonta 476.

Striated

Fabric: vertical and horizontal elements crossing at right angles, one fixed, one mobile; stake and thread; warp and woof; delimited on at least one side, with a top and a bottom Bonta 475.

The closed side is the width of the cloth; a top and bottom can be made by putting the knots on one side Harris notes.

Weaving was the paradigm for royal science Harris Cont. 525 — in Plato’s Statesman, the model for statecraft, which weaves courage and moderation like warp and weft Somers-Hall p.246.

Passage & mixture

Knitting and crochet are interlacings between the two types: in knitting the needles take turns as warp and woof; crochet draws an open space in all directions but keeps a centre Harris notes. Bonta files crochet as smooth (but with center) Bonta 476.

Patchwork shows that smooth does not mean homogeneous, quite the contrary: it is an amorphous, nonformal space prefiguring op art Anderson 477 Conte 477. Embroidery has a central motif Bonta 476; Harris notes the two can come to look alike, but patchwork still has no centre Harris notes.

Reading notes. Somers-Hall says felt fibres are rolled so that they intertwine Somers-Hall p.245. The chapter, as Conte quotes it, says felt has no intertwining Conte 475. The chapter’s word is entanglement our observation. Conte himself parts company with D&G and argues that felt tends toward homogeneity Conte essay. That is his view, not the chapter’s.

The musical model

Bonta band 477–78 · after Pierre Boulez

Somers-Hall calls Boulez the figure who first developed the distinction. Temperament will striate the surface, the musical space; where pitch can be divided at will, the ear will lose all landmarks Somers-Hall p.251, quoting Boulez (1975: 85).

Teaching figure · our gloss of Bonta 477–78 and Anderson 478 · not a score

Counting in order to occupy, and occupying without counting Left: a grid of evenly spaced horizontal pitch lines cut by regular vertical bar lines; notes sit only on intersections, some stacked vertically as chords. Right: no grid; dots spread thinner and thicker across the panel, and one continuous diagonal line rises across faint horizontal and vertical axes.
  • Striated · count in order to occupyfixed pitch steps, regular bar lines; notes only on crossings, melody along, harmony stacked
  • Smooth · occupy without countingno grid; points thin and thicken; one diagonal across the vertical and the horizontal

Smooth

In a smooth space-time one occupies without counting Conte 477.

Non-metric multiplicities; frequencies distributed statistically without breaks — evenly (nondirected smooth space) or thinner and thicker (directed) Bonta 477 Harris Cont. 527. A nomos Bonta 478.

The continuous variation, continuous development of form … the fusion of harmony and melody in favor of the production of properly rhythmic values, the pure act of the drawing of a diagonal across the vertical and the horizontal Anderson 478.

Striated

In a striated space-time one counts in order to occupy Conte 477.

Metric multiplicities; breaks fixed by a standard; frequencies in intervals between breaks, in modules — constant (straight) or regularly or irregularly variable (curved) Bonta 477. A logos, e.g. the octave Bonta 478.

Intertwines fixed and variable elements, produces an order and succession of distinct forms, and organizes horizontal melodic lines and vertical harmonic planes Anderson 478 Harris Cont. 528.

Passage & mixture

Boulez cared how the two spaces communicated, melded together, corresponded: the octave replaced by non-octave scales that spiral, texture made without fixed and homogeneous values, the sonic equivalent of op art Harris notes. Bonta: non-octave-forming scales reproduced through spiraling Bonta 478.

Even without breaks the smooth may keep intervals, as intermezzi Harris notes.

Reading note. Somers-Hall argues that Boulez’s smooth space, a field with no figure, is not phenomenological perceptual space, since for Merleau-Ponty perception is always a figure on a ground Somers-Hall p.251. Smooth is not simply “lived” space.

The maritime model

Bonta band 478–82 · the model that dates the plateau

The sea is a smooth space par excellence, and the year 1440, when Portuguese discoverers introduced the first nautical charts, marked a turning point in the striation of the sea — though D&G note it took hold progressively L&P Ath. 479. Anderson reads the chapter as citing the Portuguese argument for 1440, then a longer history Anderson ~479–80.

Teaching figure · our gloss of Anderson 481 and Bonta 478–80 · not a chart

One sea, two ways of crossing it A single sea. On the left a grid of meridians and parallels and a straight course drawn from one port to another. The grid fades out toward the middle. On the right there is no grid: small marks show local wind and swell, and a course bends with them; its stops lie on the line itself.
  • Striated · the line between two pointsmeridians and parallels; a course from port to port
  • Smooth · the point between two lineslocal wind and swell; the course bends; stops fall on the line

Smooth

Points subordinated to the trajectory; the stop follows from the trajectory; the line is a vector, not a dimension or metric determination Harris notes Bonta 478.

The point is between two lines; directional, with open intervals; one distributes oneself in an open space, according to frequencies and in the course of one’s crossings (nomos) Anderson 481.

In the smooth, materials signal forces and serve as symptoms for them Anderson 479 Somers-Hall ATP 479. Navigation by wind, noise, and the colour and sound of the water Bonta 478–80.

Striated

Lines subordinated to points: the line is between two points; dimensional, closed intervals; one closes off a surface and allocates it (logos) Anderson 481.

Filled by formed and perceived things and properties Somers-Hall ATP 479; optical; extensive, a space of measures Bonta 478.

The sea is striated by bearings and the map, latitude and longitude, first by commercial cities, then by States Bonta 478–80, which impose a dimensionality that subordinated directionality Harris Cont. 529.

Passage & mixture

The sea is smooth again with the fleet in being Harris Cont. 530 and the strategic submarine — but for the purpose of controlling striated space more completely. The smooth always possesses a greater power of deterritorialization than the striated Anderson 480.

The city is the striated space par excellence and also reimparts smooth space, down to shantytowns combining the smooth and the holey Anderson ~481.

The differences are not objective: it is possible to live striated on the deserts, steppes, or seas; it is possible to live smooth even in the cities, to be an urban nomad Somers-Hall ATP 482. To think is to voyage Harris Cont. 532.

The mathematical model (multiplicities)

Bonta band 482–88 · Riemann, Bergson, fractals

Here the distinction becomes two kinds of multiplicity. Riemann’s multiplicity, Harris reports, brought the end of dialectics Harris Cont. 533. The model closes on a six-point definition built from fractals Anderson 488.

Teaching figure · our gloss of Anderson 488 and Conte 486 · not the chapter’s diagram

A whole-number grid beside the Koch construction Left: a square grid with two arrows marking constant directions. Right: a curve built by replacing the middle third of each segment with two sides of an equilateral triangle, shown large and, along the bottom, at steps zero to three.
  • Striated · whole-number dimensionsconstant, assignable directions
  • Smooth · the Koch constructioneach middle third becomes two sides of an equilateral triangle; length grows by 4/3 a step; dimension log 4 / log 3 ≈ 1.26, more than a line and less than a surface
Harris reports that the chapter gives the curve’s dimension as log 4 / log 3 Harris Cont. 538 (he rounds it to 1.2). The four-place value 1.2619 and the 4/3 growth per step are our arithmetic our gloss. Anderson says the chapter draws the Koch curve and the sponge Anderson 487. The large curve steps through stages 1–4; with reduced motion it shows stage 4.

Smooth

Distances, not magnitudes: a temperature is not the sum of two smaller temperatures, a speed is not the sum of two smaller speeds Anderson 483; a distance cannot divide without changing its nature each time Harris Cont. 533. Gallop, trot, walk Bonta 483.

The numbering number, ordinal, directional, and nomadic Harris Cont. 535. Riemannian space is a patchwork of local pieces, joined in an infinite number of ways Harris notes Bonta 485.

A line with a fractional number of dimensions greater than one, or … a surface with a fractional number of dimensions greater than two; a line that fills a plane without ceasing to be a line; occupy without counting Anderson 488.

Striated

Metric magnitudes: a quantitative difference does not change quality Bonta 483. Bergson’s pair: one multiplicity qualitative and continuous, the other numerical and homogeneous, discrete Harris Cont. 534.

The number is the correlate of the metric; geometry with arithmetic and algebra makes up major science Harris Cont. 534–5.

We shall call striated or metric any aggregate with a whole number of dimensions, and for which it is possible to assign constant directions Anderson 488.

Passage & mixture

Translation runs both ways. Striation is subjugating, overcoding, metricizing smooth space, but also giving it a milieu of propagation, extension, refraction, renewal, and impulse without which it would perhaps die of its own accord Anderson 486 — like a mask without which it could neither breathe nor find a general form of expression Somers-Hall ATP 486.

All progress is made by and in striated space, but all becoming occurs in smooth space Anderson ~486 Harris Cont. 537.

Sierpiński’s sponge, less than a volume but more than a surface, is the mathematical presentation of the affinity between free space and a holey space Conte 487.

Reading notes. Bonta, Conte, and Anderson (inside a quotation) all spell it “Sierpensky”. That is probably the translation’s spelling our observation. Harris asks whether the fractal is really a rigorous example of a smooth space in mathematical terms Harris notes. We leave that open and make no claim beyond the arithmetic above.

The physical model

Bonta band 488–92 · gravity, work, capital

The various models confirm a certain idea of striation: two series of parallels that intersect perpendicularly … roughly the case for the warp and the woof, harmony and melody, longitude and latitude Anderson 488. Harris calls the section equally baffling Harris notes.

Teaching figure · our gloss of Anderson 488–9 and Bonta 488–89 · not a physics diagram

Gravitational striation, and the escape by declination and vortex Left: parallel vertical lines with small downward arrows pass through a body; its centre of gravity is marked; a second set of parallels, rotated to horizontal, crosses the first through that point, making a grid. Right: a vertical line leans by a very small angle, curves away from the vertical, and winds into a spiral.
  • Striated · the gravitational gridparallel verticals; a centre of gravity; the verticals rotated into a grid through that point
  • Smooth · declination and vortexa vertical that leans by a hair, curves away, and winds into a spiral

Smooth

Heterogeneity — felt, patchwork, rhythm, Riemann — a continuous variation that exceeds any [regular] distribution of constants and variables, the freeing of a line that does not pass between two points Harris notes.

Space escapes striation by declination, the infinitely small deviation between a gravitational vertical and the arc of a circle to which the vertical is tangent Harris notes, linked to Lucretius’ clinamen Anderson ~489, and by spirals and vortices Bonta 489 Harris Cont. 540.

Free action, not work Bonta 490.

Striated

The more regular the crossing, the tighter the striation and the more homogeneous the space Bonta 488.

An imaginary, elementary physics in six steps: parallel gravitational verticals; their resultant at a centre of gravity; that point unmoved when the forces turn perpendicular; gravity as attraction along straight lines; work as force times displacement; and so an increasingly perfect striated space … in every direction subordinated to points Anderson 488–9.

Labour performs a generalized operation of striation of space-time, a subjection of free action, a nullification of smooth spaces Anderson 490–91.

Passage & mixture

Homogeneity is not smoothness, but when the striated attains its ideal of perfect homogeneity, it is apt to reimpart smooth space, by a movement that superposes itself upon that of the homogeneous but remains entirely different from it Anderson ~488 Harris Cont. 539.

Physics meets sociology in abstract labour and the standard-man: physics had never been more social Harris Cont. 541.

Capitalism, having perfected striation, reconstituted a sort of smooth space; what matters is the difference between striated capital and smooth capital Anderson ~492 Bonta 492.

Reading note. Anderson flags that Massumi renders travail sometimes as “work” and sometimes as “labor”, citing a translator’s note at 573n25 Anderson note. His pin; not checked here. In Bonta, “(free-form jazz)” is his own parenthesis Bonta 488.

The aesthetic model: nomad art

Bonta band 492–500 · Riegl, Worringer, the abstract line

The last model takes its terms from art history: close and distant vision, haptic and optical space (from Riegl), the abstract line (from Worringer) Bonta 492–93 Harris notes. Haptic here does not mean touch alone; vision can be haptic too Harris notes Anderson summary.

Teaching figure · our gloss of Anderson 494, 499 and Bonta 494–98 · not an artwork

Central perspective, and a line that describes no contour Left: a horizon line with a single vanishing point; floor lines converge on it and a framed rectangle stands on the floor. Right: no horizon; one long line keeps changing direction, spirals, zigzags and crosses itself, running off the edges without enclosing any shape.
  • Striated · long-distance, opticalhorizon, vanishing point, a framed form: central perspective
  • Smooth · close-range, hapticno horizon; one line of variable direction that describes no contour

Smooth

Close-range vision; haptic space Bonta 492. Orientations in continuous variation; it operates step-by-step Harris Cont. 544. No outline, horizon, background, limit, perspective, form, or centre Bonta 494.

The abstract line: nomadic, it passes between points, without outside or inside, form or background, beginning or end Bonta 496–98. The abstract line is the affect of smooth spaces, not a feeling of anxiety that calls forth striation Anderson 497.

In modern art, a line of variable direction that describes no contour and delimits no form Anderson 499. Repetition as power Bonta 498.

Striated

Defined by the requirements of long-distance vision: constancy of orientation, invariance of distance through an interchange of inertial points of reference, interlinkage by immersion in an ambient milieu, constitution of a central perspective Anderson 494.

Outline, horizon, background, limit, perspective, form, centre Bonta 494. The concrete line, rectilinear or regularly rounded, goes from point to point and draws a contour Bonta 496–98. Symmetry as form Bonta 498.

Passage & mixture

The haptic can itself striate: we will not define the haptic by the immobile background, by the plane and the contour, because these have to do with an already mixed state in which the haptic serves to striate Somers-Hall ATP 496.

Egyptian art, where Riegl and Worringer placed the haptic, is for D&G already captured for striation Anderson 495; Somers-Hall calls it a hybrid form of smooth and striated space Somers-Hall p.252. The optical can bring back the smooth by liberating light and modulating colour Harris notes Bonta 496.

Haptic and optical, near and far, are made subordinate to the smooth and the striated Anderson 496.

Not seven, not eight

Bonta puts Go against chess, and thought against ideology, inside the aesthetic band Bonta 499–500. The closing passage, as Harris quotes it, names them in order to decline them: Do not multiply models. We are well aware that there are many others: a ludic model … (for example, the smooth space of Go versus the striated space of chess); and a noological model … It then adds holey space and turns to the passages or combinations Harris notes. Conte and Anderson pin that sentence at 500 Conte 500 Anderson 500. The same paragraph ends on the caveat already given on Definitions: Never believe that a smooth space will suffice to save us Anderson 500.

Held, not mapped. These six models are literature. None is mapped here onto the TFS glyph, twist parity, sheaf cohomology, holonomy, or the heat map as φ. The teaching figures teach the chapter’s distinctions only. No Bridge locked. No joint-field claim.

Sources for this page

Bonta
Mark Bonta, “ATP 14: The Smooth and the Striated,” outline, May 1999, keyed to D&G 1987, University of Minnesota Press. Parentheses are his comments. protevi.com/john/DG/PDF/ATP14.pdf
Conte
Joseph Conte, “The Smooth and the Striated: Compositional Texture in the Modern Long Poem,” Modern Language Studies 27 (Spring 1997): 57–71. Cites the Massumi translation, University of Minnesota Press, 1987, 474–500. acsu.buffalo.edu/~jconte/SmoothStriated.htm
Anderson
Don Anderson, “A Thousand Plateaus, Chapter 14,” The Third Carriage Age (blog), 16 June 2025. Uses the Massumi translation; the printing is not named. A “~” before a pin means the quotation sits next to that pin without its own. thirdcarriageage.com/2025/06/a-thousand-plateaus-chapter-14.html
Somers-Hall
Henry Somers-Hall, “The Smooth and the Striated,” in A Thousand Plateaus and Philosophy (Edinburgh University Press, 2018), 242–259; author’s upload. “p.” = his page; “ATP” = his pin to the chapter. The volume’s edition key is not in the pages we fetched. henrysomershall.net (PDF)
L&P
Flora Lysen & Patricia Pisters, “Introduction: The Smooth and the Striated,” Deleuze Studies 6.1 (2012): 1–5. Cites D&G 1988, London: Athlone. pure.uva.nl (PDF)
Harris
Dave Harris, notes on D&G (2004) A Thousand Plateaus, London: Continuum, ch. 14. Continuum pagination. Open teaching notes. arasite.org/TPch14.html

Full working note, with every pin: lit/kb/six-models.md. Captures and checksums: lit/fetched/. Earlier pagination note (Minnesota 1987 vs Athlone 1988): Definitions → Six models.