Without a Trace – Drawing and the Failing Line

The failing line

A trace has neither subject nor object; it is made up of variously formed materials, of very different dates and speeds.

As soon as a trace is attributed to a subject, this working of materials and the exteriority of their relations is disregarded. A beneficent God is invented for geological movements. In a book, as in everything else, there are lines of articulation or segmentation, strata, territorialities; but also lines of a journey, movements of de-territorialisation and of de-stratification. The comparative rates of flow along these lines produce phenomena of relative slowness and viscosity, or alternatively of precipitation and rupture.

All this, these lines and measurable speeds, constitute an assemblage. A trace is such an arrangement and as such, un-attributable. It is a multiplicity – but we still don’t know what the multiple implies when it ceases to be attributed when it is raised to the status of a substantive. An operative arrangement is orientated toward the strata that undoubtedly make of it a kind of organism, either a signifying totality or a determination attributable to a subject, but it is orientated no less toward a line without traces that never ceases to break down the system, causing a-signifying particles to pass and circulate freely, pure intensities, and causing the attribution to itself of objects to which it allows no more than a name as trace of an intensity.

How can a drawing have lines without a trace?

There are several ways, according to the nature of the lines considered, their content or density, their possibility of convergence on a plane of dependability which would secure their assembly. There as elsewhere, the units of measure are the essential thing: the quantification of drawing.

There is no difference between what a line talks about and the way it is drawn. Thus, a line has no object either. As an assemblage, it exists only in connection to other assemblages, in relation to other lines without traces. We shall never ask what a line, signifier or signified means, we shall

not look for anything to understand in a line; instead, we shall wonder with what it functions, in connection to what it transmits intensities or doesn’t, into what multiplicities it introduces and metamorphoses its own, with what lines without traces it makes its own converge.

A trace only exists by means of an outside, a beyond. Thus, a trace being itself a little apparatus, what measurable relationship does this rhythmical apparatus have in turn with a writing apparatus, a musical apparatus, a performative apparatus, etc. – and with an abstract apparatus which drives them along? The only question when drawing is what other apparatus the rhythmical apparatus can be connected, and must be connected in order to function.

Drawing is an assemblage. Through drawing, we voice of nothing but multiplicities, lines, strata and segmentations, lines of journey and intensities, operative arrangements and their different types, lines without traces and their construction, their selection, the plane of dependability, and the units of measure in each case. Measures of stratification and measures of deletion, the lines without traces units of density, and the lines without traces units of convergence not only provide a quantification of drawing but define the latter as always being the measure of something else. Line alone has nothing to do with signifying, but components of land-surveying and mapmaking.

ACT I – Line as Threshold // Visible World

ACT II – Line as Language // Invisible World

ACT III – Line as Performer // Visible World

ACT IV – Line as Apparatus // Visible World

The acting line

The first type of line is the source-line. It is the classic line – organic, signifying, and subjective. This line imitates the world, by employing procedures that are peculiar to it and that carry out what nature cannot or can no longer do. The law of the line is that of reproduction, the One that becomes two. Each time we encounter this formula, whether expressed strategically or understood the most ‘dialectically’, we find ourselves dealing with the most classical conceptual account.

The second figure of the line, the index system or grammar-line forms a directory, from which our modernity gladly draws its inspiration. The line as an intellectual reality, the source as a sign endlessly develops the law of the One that becomes two the two that becomes four. Binary logic is the intellectual reality of the source-line.

This amounts to saying that this model has never understood multiplicity: it requires a strong principal unity as a presupposition in order to arrive at two following an intellectual method.

Then the line as reality operator, or performer-line, with its pivotal axis and surrounding bequeath. Where most methods for generating a series or extending a multiplicity are perfectly valid in one direction, linear, while a unity of totalization is asserted all the more in another dimension, that of a circle or a cycle. Each time a multiplicity is caught up in a structure, its growth is offset by a reduction in the laws of combination. Here the abortionists of unity are very much ‘chance makers’. This line of multiple sources, in effect, shatter the linear unity of the sign, or even of drawing, only by setting up a cyclic unity of the assemblage. The unity is endlessly thwarted and hindered in the object, whilst a new type of unity triumphs in the subject.

The apparatus-line is objective, n-dimensional, its multiplicities are a-signifying and a-subjective. They are designated by indefinite articles, or rather by partitives.

Though the line has lost its pivot,

the subject can no longer even make a dichotomy, but accedes to a higher unity of ambivalence and over-determination, in a dimension always supplementary to that of its object.The trace has become a chaos whilst the line

The trace has become a chaos whilst the line remains the sign, model-chaos instead of source-cosmos. Strange mystification, that of a trace all the more total when fragmented. The multiple must be made, not by continuously adding a higher dimension; but, on the contrary, and most simply, by force of restraint, at the level of dimensions already available, by making n-1. Only thus does the one become part of the multiple: by always being subtracted from it. Subtract the unique from the multiplicity city being constituted; write to the n-1.

The appearance of the trace

The principle of connection and heterogeneity: any point on a line can be connected to any point on a line can be connected with any other and must be. This is very different from a source-line, which fixes a point and thus an order. In a trace, on the contrary, each feature does not necessarily refer to a morphological feature: semiotic chains of every kind are connected in it according to very diverse modes of encoding, and that put into play not only regimes of different signs but also different states of matters. In effect, the collective assemblages of expression function directly in the operative arrangement and no radical separation can be established between the regimes of signs and their objects.In drawing, we remain inside a sphere of

In a drawing, we remain inside a sphere of discourse that still implies modes of arrangement and particular types of expression. The grammaticality of representation, the categorical symbols controlling all the visual instances, is first a marker of the convention before being a syntactic sign, a sort of separation between each statement into a nominal syntagm [phrase] and a verbal syntagm [the first dichotomy].

A trace never ceases to connect semiotic trails, compositions, and events. A semiotic trail is like a tuber gathering up very diverse acts – morphological, but also perceptual, mimetic, gestural, and cognitive. There is no language in itself, no universality of language, but an encounter of dialects, patois, argots and special languages. Trace becomes an essentially heterogeneous reality. There is no dominant line, but a seizure of structure by a dominant assemblage. Line can always be broken down into its internal structural components. There is always something genealogical about the line. A method of the trace, on the contrary, can only analyse signs by de-centring it onto other dimensions and into other registers.

Principle of multiplicity:

it is only when the multiple is treated as substantive or multiplicity that it no longer bears any relationship to the One as subject or as an object, as natural or intellectual reality. Multiplicities are traces and expose consequent pseudo-multiplicities. There is no unity that serves as a pivot in the object, nor that is divided on the subject; no unity that would abort in the object only in order “to return” in the subject. A multiplicity has neither subject nor object-only determinations, sizes, and dimensions which cannot increase without changing its nature (thus the laws of combination increase as the multiplicity does).

An assemblage is precisely this growth of dimensions in a multiplicity that necessarily changes its nature as it increases its connections. There are no points or positions in a trace, there are only lines.

There are no units of measure, but only multiplicities or varieties of measure. But a trace or multiplicity never allows itself to be over-coded, never disposes of a dimension supplementary to the number of its lines, which is, to the multiplicity of numbers attached to these lines. All multiplicities are flat, insofar as they fill up or occupy all their dimensions; we will speak therefore of a plane of dependability of multiplicities, although this “plane” increases in dimensions according to the number of connections that are established on it.

Multiplicities are defined by means of the outside: by the abstract line, the line of wander or of de-territorialisation following which they change nature by being connected with others. The plane of dependability (grid) is the outside of every multiplicity. The line of flight marks simultaneously the reality of a number of finite dimensions actually filled by the multiplicity; the impossibility of any supplementary dimension, unless the multiplicity transforms itself following this line; and the possibility and necessity of flattening all these multiplicities onto the same plane of consistency or exteriority, whatever their dimensions. The ideal for a trace would be to display everything on such a plane of exteriority, a broken chain of effects, with variable speeds, precipitations, and transformations, always in relation to an outside. Consequently, in stark contrast to the traditional, or even romantic approach, constituted by the interiority of a substance or a subject.

The principle of critical rupture: against the excessively signifying breaks that separate structures, or traverse one of them. A trace can be cracked and broken at any point; it starts off again following one or another of its lines, or even other lines. Every trace includes lines of segmentation according to which it is stratified, territorialized, organized, signified, attributed, etc.; but also lines of de-territorialisation along which it endlessly wanders. There is a rupture in the trace each time the segmented lines explode into a line of wonder, drifting away, but the line of wonder is part of the trace. These lines never cease to refer to one another, which is why a dualism or dichotomy can never be assumed, even in the rudimentary form of good and bad. A rupture is made, a line of wonder is traced.

How could the movements of de-territorialisation and processes of re-territorialization not be relative, perpetually branching onto one another and caught up with each other?

The line is de-territorialized by creating an assemblage, an exact tracing (copy) of an idea; but the line reterritorializes itself on this image. The trace is de-territorialized, however, by becoming part of the image, but it reterritorializes in the plane of dependability. It could be said that the line imitates the trace, whose image it reproduces in a signifying manner. This is true, however, only at the level of replica – reproduction. At the same time, it is a matter of something altogether different: no longer an imitation at all, but the capture of a code, a genuine becoming. There is neither imitation nor resemblance, but an explosion of two heterogeneous series in a line of wonder consisting of a common trace that can no longer be attributed nor made subject to any signifier at all. Yet, the trace is not the image of the world. There is a parallel evolution of the trace and the milieu; the trace ensures the de-territorialisation of space, but space effects a re-territorialisation of the trace, which is de-territorialized in its turn by being spatial.

Always follow the trace by rupturing, lengthening, prolonging, taking up the line of wonder, making it very, until if produces the most abstract and tortuous line in n dimensions and scattered directions. Combine the de-territorialized flows. Begin by fixing the limits of a first line according to circles of convergence around successive singularities; next see if new circles of convergence are established along the interior of this line, with new points situated outside its limits and in other directions. To draw, form traces, expand your own territory by de-territorialisation, extend the line of wonder to the point where it covers the whole plane of consistency in an abstract apparatus.

Watch the rain, as it trickles down a window pane, never ceasing to set off these lines of wonder — multiplicities of transformation.

The principle of cartographic trace: a trace is not answerable to any structural or generative model, being by nature foreign to the very idea of a genetic axis, or a deep structure. A genetic axis is like an objective pivotal unity on which successive stages are organized; a deep structure is rather like a base series decomposable into immediate constituents, while the unity of the product passes into another dimension, subjective and transformable. Thus there is no departure from the descriptive model, associated with a base sequence and representing the process of its generation. A variation on the oldest kind of thinking.Concerning the genetic axis or deep

Concerning the genetic axis or deep structure, we say they are before anything else principles of tracing (copy), reproducible. The whole logic of the line is a logic of tracing and reproduction. It has for its purpose the description of a state of fact, the exploration of an unconscious already there, lurking in the obscure corners of memory and language. It consists of tracing something given as already made, starting from an over-coding structure or supporting axis. The line articulates and establishes a hierarchy of tracings.

The trace is something altogether different, a map and not a tracing. If the map is opposed to the trace, it’s because its whole orientation is toward establishing contact with the real experimentally. The map does not reproduce an unconscious closed on itself; it constructs it. It contributes to the connection of fields, the freeing of lines without traces, and their maximal access onto the plane of dependability. It becomes itself part of the trace. The map is open, connectable in all its dimensions, and capable of being dismantled; it is reversible and susceptible to constant modification. It can be torn, reversed, adapted to montages of every kind, and taken by the hand by an individual, a group, or a social formation. It can be drawn, conceived, constructed as action or as a thought. Perhaps one of the most important characteristics of the trace is that it always has multiple readings. Nevertheless, hasn’t this argument just restored a simple dualism by opposing maps to tracings, but isn’t a map something that can be traced? Isn’t a trace something with overlapping lines, which sometimes merge with them? Doesn’t a map entail redundancies which are already like its own tracings?

Even the lines of wonder, owing to their eventual divergence, aren’t they going to reproduce the very formations that it was their function to dismantle or evade? But the inverse is also true, it’s just a question of method: the tracing must always be – transferred onto the map. And this operation is not at all symmetrical with the preceding one, for, strictly speaking, it’s not true that a tracing reproduces a map. A tracing is more like a photograph, it is always the imitator who creates his model, and who attracts it. The tracing has already translated the map into an image; it has already transformed the trace into lines. It has organized, stabilized, and neutralized multiplicities according to its own axes of significance and subjectivization. It has generated and structuralized the trace. The tracing only reproduces itself when it is reproducing something new. It injects redundancies and reproduces them. What the tracing reproduces of the map or trace are only the impasses, the blockages, the nodes and points of structuration.

There are different assemblages – tracing-maps, line-traces – with variable coefficients of de-territorialisation. Line structures exist in traces, but, inversely, a twigged line branch can begin to reveal itself into a trace. The distinction here depends on a pragmatism that puts together multiplicities or aggregates of intensities. An element of intensity begins to work on its own behalf, a hallucinatory perception or a mutation. The line inspires the image of a thought which endlessly imitates the multiple, starting from a superior unity, centre, or segment. These create hierarchical systems comprised of centres of significance, autonomous centres like organized memories. It presumes a topological explanation. The trace contrast these centred systems with a-centred systems. Consider the possibility of an acentred organization of a society of lines. The important thing is never to reduce the insensible, to interpret it or make it signify, but rather to produce the insensible, and, along with it, new utterances and other desires. The trace is precisely this production of the insensible.

There are anarchic deformations in the transcendent system of lines. What counts is that the line-tracing and the line-trace are not opposed like two models: the one functions as a transcendent model and tracing, even if it engenders its own wonders; the other functions as an immanent process that overturns the model and sketches a map, even if it constitutes its own hierarchies, even if it gives rise to a despotic canal. It is not a question of any particular category of mind, but rather of a model that is ceaselessly set up and that collapses, of a process that ceaselessly extends itself, breaks off and starts again. Perhaps a new or another dualism. Inexact expressions are absolutely necessary in order to designate something exactly. And not at all because one has to pass through them, nor because one can proceed only through approximations: in-exactitude is the exact path of what is done, and not at all an approximation. To invoke one dualism only in order to challenge another. To employ a dualism of models only to arrive at a process which would challenge every model.

There are different assemblages – tracing-maps, line-traces – with variable coefficients of de-territorialisation. Line structures exist in traces, but, inversely, a twigged line branch can begin to reveal itself into a trace. The distinction here depends on a pragmatism that puts together multiplicities or aggregates of intensities. An element of intensity begins to work on its own behalf, a hallucinatory perception or a mutation. The line inspires the image of a thought which endlessly imitates the multiple, starting from a superior unity, centre, or segment. These create hierarchical systems comprised of centres of significance, autonomous centres like organized memories. It presumes a topological explanation. The trace contrast these centred systems with a-centred systems. Consider the possibility of an acentred organization of a society of lines. The important thing is never to reduce the insensible, to interpret it or make it signify, but rather to produce the insensible, and, along with it, new utterances and other desires. The trace is precisely this production of the insensible.

There are anarchic deformations in the transcendent system of lines. What counts is that the line-tracing and the line-trace are not opposed like two models: the one functions as a transcendent model and tracing, even if it engenders its own wonders; the other functions as an immanent process that overturns the model and sketches a map, even if it constitutes its own hierarchies, even if it gives rise to a despotic canal. It is not a question of any particular category of mind, but rather of a model that is ceaselessly set up and that collapses, of a process that ceaselessly extends itself, breaks off and starts again. Perhaps a new or another dualism. Inexact expressions are absolutely necessary in order to designate something exactly. And not at all because one has to pass through them, nor because one can proceed only through approximations: in-exactitude is the exact path of what is done, and not at all an approximation. To invoke one dualism only in order to challenge another. To employ a dualism of models only to arrive at a process which would challenge every model.

 

wrap-up

The principal characteristics of a trace, unlike tracings or their lines, the trace connects any point to any other point, and none of its features necessarily refers to features of the same kind. It puts into play very different regimes of signs and even states of non-signs. The trace doesn’t allow itself to be reduced to the One or the Many. It is not the One that becomes two, or that might become three, four, or five, etc. It is not a multiple derived from One, nor a multiple to which the One might be added (n +1). It is not made of units but of dimensions, or rather of shifting directions. It has neither beginning nor end, but always a middle, through which it pushes and overflows. It constitutes linear, multiplicities in n dimensions, without subject or object, which can be laid out on a plane of dependability and from which the One is always subtracted (n – 1). Such a multiplicity does not vary its dimensions without changing its own nature and metamorphosing itself.

Unlike a structure defined by a set of points and positions, with binary relations between these points and hi-univocal relations between these positions, the trace is made only of lines: lines of segmentation and stratification as dimensions, but also lines of wonder or of de-territorialisation as the maximal dimension according to which, by following it, the multiplicity changes its nature and metamorphoses. Such lines are not to be confused with lines which are only localizable connections between points and positions. The trace is not an object of reproduction: neither external reproduction nor internal reproduction. The trace is an anti-genealogy. It is a short-term memory or an anti-memory. The trace proceeds by variation, expansion, conquest, capture, stitching. Unlike graphics, photography, or tracings, the trace refers to a map that must be produced or constructed, is always detachable, connectable, reversible, and modifiable, with multiple entrances and exits, with its lines of wonder.

The tracings are what must be transferred onto the maps, and not the reverse.

In opposition to centred systems (even multi-centred), with hierarchical communication and pre-established connections, the trace is an a-centred system, non-hierarchical and non-signifying, without a General, without an organizing memory or central autonomy, uniquely defined by a circulation of states.

An arrangement in its multiplicity necessarily works all at once on semiotic flows. There is no longer a tripartite division between a field of reality (milieu), a field of representation (line), and a field of subjectivity (drawing). The outside has no image, no signification, and no subjectivity. The trace is an assemblage with the outside, rather than the tracing of the world.

It’s not easy to perceive things from the middle, neither from top to bottom or the reverse nor from left to right or the reverse – everything changes. Drawing is always articulated from a sedentary point of view, and in the name of a unitary apparatus; or at least a possible one. These are models of nomadic representation, a drawing that embraces lines of wonder, and abandons segmentations and sedentarily. But why is a model still necessary? Isn’t the trace still an image? Isn’t a unity still retained? How can the trace determine an adequate outside, an outside with which it can establish heterogeneous connections, rather than a world to reproduce? As a cultural object, the trace is inevitably a tracing: already a tracing of itself, a tracing of the preceding trace by the same draftsmen, a tracing of other traces, whatever their differences, an unending transfer of established words and concepts, a tracing of the world past, present and future. The trace can be used for getting and not memory, for underdevelopment and not a progress to be developed, for nomadism and not sedentarily, for maps and not tracings.

A trace doesn’t begin and doesn’t end, but it’s always in the middle, between things, inter-being. The line is filiation, but the trace is arrangement. The line imposes the verb “to be,” but the trace is woven together with conjunctions: “and … and . . . and”.

In a trace what is at stake is all kinds of ‘becomings’.

 

Theoria:

line
wordings
detours