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The Smooth and the Striated Spaces
I was reading 'Deleuze and Guattari, A Thousand Plateaus: Capitalism and Schizophrenia' and couldn't resist sharing this particular chapter 'The Smooth and the Striated'. There's a lot more under this chapter in the book but shared the best of it. It's about smooth vs striated in a manner like local vs global or becoming vs progress or like minor science vs major science and so on. Read it to get illuminated. Best ever! Here's how it goes:
The Smooth and the Striated
Smooth space and striated space—nomad space and sedentary space—the
space in which the war machine develops and the space instituted by the
State apparatus—are not of the same nature. No sooner do we note a simple
opposition between the two kinds of space than we must indicate a
much more complex difference by virtue of which the successive terms of
the oppositions fail to coincide entirely. And no sooner have we done that
than we must remind ourselves that 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. In the first case, one organizes even the desert; in the second,
the desert gains and grows; and the two can happen simultaneously. But the
de facto mixes do not preclude a de jure, or abstract, distinction between
the two spaces. That there is such a distinction is what accounts for the fact
that the two spaces do not communicate with each other in the same way: it
is the de jure distinction that determines the forms assumed by a given de
facto mix and the direction or meaning of the mix (is a smooth space captured,
enveloped by a striated space, or does a striated space dissolve into a
smooth space, allow a smooth space to develop?). This raises a number of
simultaneous questions: the simple oppositions between the two spaces;
the complex differences; the de facto mixes, and the passages from one to
another; the principles of the mixture, which are not at all symmetrical,
sometimes causing a passage from the smooth to the striated, sometimes
from the striated to the smooth, according to entirely different movements.
We must therefore envision a certain number of models, which
would be like various aspects of the two spaces and the relations between
them.
The Technological Model. A fabric presents in principle a certain number
of characteristics that permit us to define it as a striated space. First, it is
constituted by two kinds of parallel elements; in the simplest case, there are
vertical and horizontal elements, and the two intertwine, intersect perpendicularly.
Second, the two kinds of elements have different functions; one
is fixed, the other mobile, passing above and beneath the fixed. Leroi-
Gourhan has analyzed this particular figure of "supple solids" in basketry
and weaving: stake and thread, warp and woof.' Third, a striated space of
this kind is necessarily delimited, closed on at least one side: the fabric can
be infinite in length but not in width, which is determined by the frame of
the warp; the necessity of a back and forth motion implies a closed space
(circular or cylindrical figures are themselves closed). Finally, a space of
this kind seems necessarily to have a top and a bottom; even when the warp
yarn and woof yarn are exactly the same in nature, number, and density,
weaving reconstitutes a bottom by placing the knots on one side. Was it not
these characteristics that enabled Plato to use the model of weaving as the
paradigm for "royal science," in other words, the art of governing people or
operating the State apparatus?
The Musical Model. Pierre Boulez was the first to develop a set of simple
oppositions and complex differences, as well as reciprocal nonsymmetrical
correlations, between smooth and striated space. He created these concepts
and words in the field of music, defining them on several levels precisely
in order to account for the abstract distinction at the same time as the
concrete mixes. In the simplest terms, Boulez says that in a smooth spacetime
one occupies without counting, whereas in a striated space-time one
counts in order to occupy. He makes palpable or perceptible the difference
between nonmetric and metric multiplicities, directional and dimensional
spaces. He renders them sonorous or musical. Undoubtedly, his personal
work is composed of these relations, created or recreated musically.
The Maritime Model. Of course, there are points, lines, and surfaces in
striated space as well as in smooth space (there are also volumes, but we will
leave this question aside for the time being). In striated space, lines or trajectories
tend to be subordinated to points: one goes from one point to
another. In the smooth, it is the opposite: the points are subordinated to the
trajectory. This was already the case among the nomads for the clothestent-
space vector of the outside. The dwelling is subordinated to the journey;
inside space conforms to outside space: tent, igloo, boat. There are
stops and trajectories in both the smooth and the striated. But in smooth
space, the stop follows from the trajectory; once again, the interval takes
all, the interval is substance (forming the basis for rhythmic values).
The Mathematical Model. It was a decisive event when the mathematician
Riemann uprooted the multiple from its predicate state and made it a
noun, "multiplicity." It marked the end of dialectics and the beginning of a
typology and topology of multiplicities. Each multiplicity was defined by n
determinations; sometimes the determinations were independent of the
situation, and sometimes they depended upon it. For example, the magnitude
of a vertical line between two points can be compared to the magnitude
of a horizontal line between two other points: it is clear that the
multiplicity in this case is metric, that it allows itself to be striated, and that
its determinations are magnitudes. On the other hand, two sounds of equal
pitch and different intensity cannot be compared to two sounds of equal
intensity and different pitch; in this case, two determinations can be compared
only "if one is a part of the other and if we restrict ourselves to the
judgment that the latter is smaller than the former, without being able to
say by how much." Multiplicities of this second kind are not metric and
allow themselves to be striated and measured only by indirect means,
which they always resist. They are anexact yet rigorous. Meinong and
Russell opposed the notion of distance to that of magnitude. Distances
are not, strictly speaking, indivisible: they can be divided precisely in cases
where the situation of one determination makes it part of another. But
unlike magnitudes, they cannot divide without changing in nature each
time. An intensity, for example, is not composed of addable and displaceable
magnitudes: a temperature is not the sum of two smaller temperatures,
a speed is not the sum of two smaller speeds. Since each intensity is
itself a difference, it divides according to an order in which each term of the
division differs in nature from the others. Distance is therefore a set of
ordered differences, in other words, differences that are enveloped in one
another in such a way that it is possible to judge which is larger or smaller,
but not their exact magnitudes. For example, one can divide movement
into the gallop, trot, and walk, but in such a way that what is divided
changes in nature at each moment of the division, without any one of these
moments entering into the composition of any other. Therefore these multiplicities
of "distance" are inseparable from a process of continuous variation,
whereas multiplicities of "magnitude" distribute constants and
variables.
The Physical Model. The various models confirm a certain idea of striation:
two series of parallels that intersect perpendicularly, some of which,
the verticals, are more in the role of fixed elements or constants, whereas
the others, the horizontals, are more in the role of variables. This is roughly
the case for the warp and the woof, harmony and melody, longitude and latitude.
The more regular the intersection, the tighter the striation, the more
homogeneous the space tends to become; it is for this reason that from the
beginning homogeneity did not seem to us to be a characteristic of smooth
space, but on the contrary, the extreme result of striation, or the limit-form
of a space striated everywhere and in all directions. If the smooth and the
homogeneous seem to communicate, it is only because 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. In each model, the smooth actually
seemed to pertain to a fundamental heterogeneity: felt or patchwork rather
than weaving, rhythmic values rather than harmony-melody, Riemannian
space rather than Euclidean space—a continuous variation that exceeds
any distribution of constants and variables, the freeing of a line that does
not pass between two points, the formation of a plane that does not proceed
by parallel and perpendicular lines.
The Aesthetic Model: Nomad Art. Several notions, both practical and theoretical,
are suitable for defining nomad art and its successors (barbarian,
Gothic, and modern). First, "close-range" vision, as distinguished from
long-distance vision; second, "tactile," or rather "haptic" space, as distinguished
from optical space. "Haptic" is a better word than "tactile" since it
does not establish an opposition between two sense organs but rather
invites the assumption that the eye itself may fulfill this nonoptical function.
It was Alois Riegl who, in some marvelous pages, gave fundamental
aesthetic status to the couple, close vision-haptic space. But for the moment
we should set aside the criteria proposed by Riegl (then by Wilhelm
Worringer, and more recently by Henri Maldiney), and take some risks
ourselves, making free use of these notions.26 It seems to us that the Smooth
is both the object of a close vision par excellence and the element of a haptic
space (which may be as much visual or auditory as tactile). The Striated, on
the contrary, relates to a more distant vision, and a more optical space—
although the eye in turn is not the only organ to have this capacity. Once
again, as always, this analysis must be corrected by a coefficient of transformation
according to which passages between the striated and the smooth
are at once necessary and uncertain, and all the more disruptive. The law of
the painting is that it be done at close range, even if it is viewed from relatively
far away. One can back away from a thing, but it is a bad painter who
backs away from the painting he or she is working on. Or from the "thing"
for that matter: Cezanne spoke of the need to no longer see the wheat field,
to be too close to it, to lose oneself without landmarks in smooth space.
Afterward, striation can emerge: drawing, strata, the earth, "stubborn
geometry," the "measure of the world," "geological foundations," "everything
falls straight down" . . . The striated itself may in turn disappear in a
"catastrophe," opening the way for a new smooth space, and another striated
space...
Source- Deleuze, Gilles, and Felix Guattari. A THOUSAND PLATEAUS: CAPITALISM AND SCHIZOPHRENIA. Trans. and Foreword by Brian Massumi. Minneapolis: U. of Minnesota Press, 1987.
The Smooth and the Striated
Smooth space and striated space—nomad space and sedentary space—the
space in which the war machine develops and the space instituted by the
State apparatus—are not of the same nature. No sooner do we note a simple
opposition between the two kinds of space than we must indicate a
much more complex difference by virtue of which the successive terms of
the oppositions fail to coincide entirely. And no sooner have we done that
than we must remind ourselves that 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. In the first case, one organizes even the desert; in the second,
the desert gains and grows; and the two can happen simultaneously. But the
de facto mixes do not preclude a de jure, or abstract, distinction between
the two spaces. That there is such a distinction is what accounts for the fact
that the two spaces do not communicate with each other in the same way: it
is the de jure distinction that determines the forms assumed by a given de
facto mix and the direction or meaning of the mix (is a smooth space captured,
enveloped by a striated space, or does a striated space dissolve into a
smooth space, allow a smooth space to develop?). This raises a number of
simultaneous questions: the simple oppositions between the two spaces;
the complex differences; the de facto mixes, and the passages from one to
another; the principles of the mixture, which are not at all symmetrical,
sometimes causing a passage from the smooth to the striated, sometimes
from the striated to the smooth, according to entirely different movements.
We must therefore envision a certain number of models, which
would be like various aspects of the two spaces and the relations between
them.
The Technological Model. A fabric presents in principle a certain number
of characteristics that permit us to define it as a striated space. First, it is
constituted by two kinds of parallel elements; in the simplest case, there are
vertical and horizontal elements, and the two intertwine, intersect perpendicularly.
Second, the two kinds of elements have different functions; one
is fixed, the other mobile, passing above and beneath the fixed. Leroi-
Gourhan has analyzed this particular figure of "supple solids" in basketry
and weaving: stake and thread, warp and woof.' Third, a striated space of
this kind is necessarily delimited, closed on at least one side: the fabric can
be infinite in length but not in width, which is determined by the frame of
the warp; the necessity of a back and forth motion implies a closed space
(circular or cylindrical figures are themselves closed). Finally, a space of
this kind seems necessarily to have a top and a bottom; even when the warp
yarn and woof yarn are exactly the same in nature, number, and density,
weaving reconstitutes a bottom by placing the knots on one side. Was it not
these characteristics that enabled Plato to use the model of weaving as the
paradigm for "royal science," in other words, the art of governing people or
operating the State apparatus?
The Musical Model. Pierre Boulez was the first to develop a set of simple
oppositions and complex differences, as well as reciprocal nonsymmetrical
correlations, between smooth and striated space. He created these concepts
and words in the field of music, defining them on several levels precisely
in order to account for the abstract distinction at the same time as the
concrete mixes. In the simplest terms, Boulez says that in a smooth spacetime
one occupies without counting, whereas in a striated space-time one
counts in order to occupy. He makes palpable or perceptible the difference
between nonmetric and metric multiplicities, directional and dimensional
spaces. He renders them sonorous or musical. Undoubtedly, his personal
work is composed of these relations, created or recreated musically.
The Maritime Model. Of course, there are points, lines, and surfaces in
striated space as well as in smooth space (there are also volumes, but we will
leave this question aside for the time being). In striated space, lines or trajectories
tend to be subordinated to points: one goes from one point to
another. In the smooth, it is the opposite: the points are subordinated to the
trajectory. This was already the case among the nomads for the clothestent-
space vector of the outside. The dwelling is subordinated to the journey;
inside space conforms to outside space: tent, igloo, boat. There are
stops and trajectories in both the smooth and the striated. But in smooth
space, the stop follows from the trajectory; once again, the interval takes
all, the interval is substance (forming the basis for rhythmic values).
The Mathematical Model. It was a decisive event when the mathematician
Riemann uprooted the multiple from its predicate state and made it a
noun, "multiplicity." It marked the end of dialectics and the beginning of a
typology and topology of multiplicities. Each multiplicity was defined by n
determinations; sometimes the determinations were independent of the
situation, and sometimes they depended upon it. For example, the magnitude
of a vertical line between two points can be compared to the magnitude
of a horizontal line between two other points: it is clear that the
multiplicity in this case is metric, that it allows itself to be striated, and that
its determinations are magnitudes. On the other hand, two sounds of equal
pitch and different intensity cannot be compared to two sounds of equal
intensity and different pitch; in this case, two determinations can be compared
only "if one is a part of the other and if we restrict ourselves to the
judgment that the latter is smaller than the former, without being able to
say by how much." Multiplicities of this second kind are not metric and
allow themselves to be striated and measured only by indirect means,
which they always resist. They are anexact yet rigorous. Meinong and
Russell opposed the notion of distance to that of magnitude. Distances
are not, strictly speaking, indivisible: they can be divided precisely in cases
where the situation of one determination makes it part of another. But
unlike magnitudes, they cannot divide without changing in nature each
time. An intensity, for example, is not composed of addable and displaceable
magnitudes: a temperature is not the sum of two smaller temperatures,
a speed is not the sum of two smaller speeds. Since each intensity is
itself a difference, it divides according to an order in which each term of the
division differs in nature from the others. Distance is therefore a set of
ordered differences, in other words, differences that are enveloped in one
another in such a way that it is possible to judge which is larger or smaller,
but not their exact magnitudes. For example, one can divide movement
into the gallop, trot, and walk, but in such a way that what is divided
changes in nature at each moment of the division, without any one of these
moments entering into the composition of any other. Therefore these multiplicities
of "distance" are inseparable from a process of continuous variation,
whereas multiplicities of "magnitude" distribute constants and
variables.
The Physical Model. The various models confirm a certain idea of striation:
two series of parallels that intersect perpendicularly, some of which,
the verticals, are more in the role of fixed elements or constants, whereas
the others, the horizontals, are more in the role of variables. This is roughly
the case for the warp and the woof, harmony and melody, longitude and latitude.
The more regular the intersection, the tighter the striation, the more
homogeneous the space tends to become; it is for this reason that from the
beginning homogeneity did not seem to us to be a characteristic of smooth
space, but on the contrary, the extreme result of striation, or the limit-form
of a space striated everywhere and in all directions. If the smooth and the
homogeneous seem to communicate, it is only because 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. In each model, the smooth actually
seemed to pertain to a fundamental heterogeneity: felt or patchwork rather
than weaving, rhythmic values rather than harmony-melody, Riemannian
space rather than Euclidean space—a continuous variation that exceeds
any distribution of constants and variables, the freeing of a line that does
not pass between two points, the formation of a plane that does not proceed
by parallel and perpendicular lines.
The Aesthetic Model: Nomad Art. Several notions, both practical and theoretical,
are suitable for defining nomad art and its successors (barbarian,
Gothic, and modern). First, "close-range" vision, as distinguished from
long-distance vision; second, "tactile," or rather "haptic" space, as distinguished
from optical space. "Haptic" is a better word than "tactile" since it
does not establish an opposition between two sense organs but rather
invites the assumption that the eye itself may fulfill this nonoptical function.
It was Alois Riegl who, in some marvelous pages, gave fundamental
aesthetic status to the couple, close vision-haptic space. But for the moment
we should set aside the criteria proposed by Riegl (then by Wilhelm
Worringer, and more recently by Henri Maldiney), and take some risks
ourselves, making free use of these notions.26 It seems to us that the Smooth
is both the object of a close vision par excellence and the element of a haptic
space (which may be as much visual or auditory as tactile). The Striated, on
the contrary, relates to a more distant vision, and a more optical space—
although the eye in turn is not the only organ to have this capacity. Once
again, as always, this analysis must be corrected by a coefficient of transformation
according to which passages between the striated and the smooth
are at once necessary and uncertain, and all the more disruptive. The law of
the painting is that it be done at close range, even if it is viewed from relatively
far away. One can back away from a thing, but it is a bad painter who
backs away from the painting he or she is working on. Or from the "thing"
for that matter: Cezanne spoke of the need to no longer see the wheat field,
to be too close to it, to lose oneself without landmarks in smooth space.
Afterward, striation can emerge: drawing, strata, the earth, "stubborn
geometry," the "measure of the world," "geological foundations," "everything
falls straight down" . . . The striated itself may in turn disappear in a
"catastrophe," opening the way for a new smooth space, and another striated
space...
Source- Deleuze, Gilles, and Felix Guattari. A THOUSAND PLATEAUS: CAPITALISM AND SCHIZOPHRENIA. Trans. and Foreword by Brian Massumi. Minneapolis: U. of Minnesota Press, 1987.
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