Concrete Rules and Abstract Machines; Form and Function in A Thousand Plateaus

Chapter 15 Concrete Rules and Abstract Machines: Form and Function in A Thousand Plateaus Ray Brassier Introduction What relation between the abstract and the concrete is at issue here? How do ‘rules’ relate to ‘machines’? To answer this question, we first need to distinguish Deleuze and Guattari’s ‘machinic materialism’ from more familiar types of materialism, whether atomistic (Epicurus, Lucretius), mechanicist (Hobbes, d’Holbach), historical (Marx, Althusser), or physicalist (Quine, Lewis). Classical metaphysical materialism, whether atomistic or mechanicist, combines a theoretical proposition about the ultimate nature of reality with a series of practical injunctions about how best to live in accordance with that reality. Historical materialism rejects metaphysics but still attempts to derive a political programme from its account of socio-historical reality. As for physicalism, it is a theoretical proposition that eschews the prescriptive altogether, deferring to physics for its account of ultimate reality. But the materialism laid claim to in A Thousand Plateaus is unlike any of the above. It does not pretend to accurately represent an objectively existing ‘material reality’ (whether natural or social), just as it does not propose practical imperatives derived from universal laws (whether natural or social). It seeks to conjugate an ‘abstract matter’, conceived independently of representational form, with a concrete ethics, wherein action is selected independently of universal law. Here the abstract is no longer the province of the universal (invariance, form, unity) and the concrete is no longer the realm of the particular (the variable, the material, the many). The abstract is enveloped in the concrete such that practice is the condition of its development. It is this development which is rule-governed, but in a sense quite independent of the familiar juxtaposition of invariant rule to variable circumstance. Rules are

co n c re te rules a nd a bstract mach in es | 261 no longer abstract invariants that need to be applied to concrete or variable circumstances. ‘Abstract’ now means unformed and ultimately, as we shall see, destratified (we will try to understand what this term means below). But the unformed is endowed with positive traits of its own, traits which, from the viewpoint of the representation of ‘material reality’, are initially confounding. Thus abstract matter is described as constituting a ‘plane of consistency’ characterised by ‘continuums of intensities’, ‘particlessigns’ and ‘deterritorialised flows’. Moreover, Deleuze and Guattari insist that this plane of consistency (which they also call ‘multiplicity’) must be made, since it is not given: ‘it is not enough to say “Long live the multiple!”, difficult as it is to raise that cry . . . The multiple must be made . . .’ (ATP 6, translation modified, my emphasis). Consistency (or multiplicity) is made by mapping what is unrepresented in both thinking and doing. This mapping plays a key role in developing the abstract. To understand how concrete rules develop abstract matter, we have to understand both why A Thousand Plateaus retains a distinction between saying and doing and why mapping is a practice that fuses saying with doing. Thus the other sense that ‘concrete’ has here is practical: mapping the positive traits characteristic of the unformed is a practical matter; one that is constrained by certain rules. What sort of rules? Since abstract matter cannot be represented, the rules or practical injunctions governing its development cannot be read off some pre-existing ‘reality’. These rules will be concrete precisely to the extent that they effectuate the abstract. Practice and theory realise one another: theoretical concepts are effectuated in practice; practical imperatives are formulated in theory. Thus, for all its idiosyncratic novelty, A Thousand Plateaus conforms to a classical model of philosophising, wherein ontology, understood as the theory of what there is, is one with ethics, understood as a practice or ‘art of living’. This is not to say it is a traditional or conservative work: rather, it is an attempt at the contemporary reactivation of the classical task of philosophising, but one where contemporaneity is marked by the rejection of representation.1 This rejection entails a radicalisation of philosophical pragmatics (indeed, it construes philosophy as a generalised pragmatics) wherein neither the agents nor the functions of practices can be taken for granted. The referent of the communal ‘we’, constantly invoked by traditional pragmatists (James, Dewey) and their contemporary successors (Rorty, Brandom), is a starting point whose epistemic authority and socio-historical coordinates will be gradually disassembled and replaced by another ‘we’: that of a minoritarian ‘people to come’. By the same token, the habitual functions and goals established around this existing ‘we’ need to be suspended; normal functioning and established finalities are to be disrupted. This means that for machinic pragmatics, the efficacy

262 | a thousand pl ateaus a nd ph ilo s o ph y of performance can no longer be subordinated to pre-established standards of competence. So long as practice is subordinated to representation, it can only more or less adequately trace a pre-existing reality, according to extant criteria of success or failure. But machinic pragmatics is not geared towards representation; it is an experimental practice oriented towards bringing something new into existence; something that does not pre-exist its process of production. It decouples performance from competence. It does not engage in a utilitarian tracing of the real; it generates a constructive mapping (and as we shall see, a diagramming) of the real: ‘What distinguishes the map from the tracing is that it is entirely oriented toward an experimentation in contact with the real. The map does not reproduce an unconscious closed in upon itself; it constructs the unconscious . . . The map has to do with performance, whereas the tracing always involves an alleged “competence”’ (ATP 13). Competence is reproductive, but performance is productive. This contrast between tracing and mapping follows from the more fundamental difference between saying and doing proclaimed in the opening pages of A Thousand Plateaus (cited above). Three interrelated questions arise here. First, why does the overcoming of arborescent dichotomy still require a contrast between saying and doing, or representation and production, contemplation and practice? What is the status of this contrast? Secondly, what does performance freed from the constraint of competence actually do? Is performance to be understood as an act, an activity, an action, a production or a practice? These are all related yet distinct ways of conceptualising doing. Is mapping a variety of doing that is not normatively governed and achievement-oriented? Can one perform a mapping without any regard for competence? Competence need not be teleological: not all norm-governed doing is goal-oriented; nevertheless, an immanent standard is still a standard. Finally, if making the multiple is not susceptible to norms of competence, what is it that makes the difference between success and failure in constructing the plane of consistency? We will return to these questions below when we consider the way in which machinic pragmatism is supposed to operate a selective construction of the real (the plane of consistency). Stratification The disruption of utilitarian order, of the fixed goals, standards and practices through which reality is reproduced, cannot be immediately achieved. Since (as Deleuze repeatedly insists) we always start in the middle, we start stratified, organised, subjectified. Thus the practical challenge is to understand how we can de-stratify, dis-organise, and de-subjectify without

co n c re te rules a nd a bstract mach in es | 263 lapsing into religious self-abnegation: ‘to reach, not the point where one no longer says I, but the point where it is no longer of any importance whether one says I’ (ATP 3). But why would this point of apparent indifference between owning or abnegating one’s subjectivity be worth reaching? If such a point is worth reaching, it cannot be indifferent to this difference. Something must be retained: something of the subject, something of the sign, something of the organism: That which races or dances upon the plane of consistency thus carries with it the aura of its stratum, an undulation, a memory or tension. The plane of consistency retains just enough of the strata to extract from them variables that operate in the plane of consistency as its own functions. (ATP 70–1, my emphasis) What will be retained on the plane of consistency is the torsion of destratified intensities, particles, signs and flows. Yet because the point of torsion is indiscernible from the vantage of anyone invested in the importance of distinction between self and not-self, personal and impersonal, its approach requires caution, which is of course one of the book’s famous watchwords.2 Caution is required for the composition of the plane of consistency. This is the relevance of the concrete rules for its composition. Thus to understand how concrete rules are articulated with abstract machines we have to understand how the composition of consistency according to rules requires deformalising stratified functions and subjecting them to the torsion of absolute movement: ‘A movement is absolute when, whatever its quantity and speed, it relates “a” body considered as multiple to a smooth space that it occupies in the manner of a vortex’ (ATP 509). Absolute movement (or deterritorialisation) is attained through the deformalisation of stratified function. Deformalisation ensures the continuity of intensities, the emission of particle-signs, and the conjunction of deterritorialised flows on the plane of consistency. Thus abstract matter is de- or un-formed, which means destratified. Stratification is the source of all formalisation; conversely, deformalisation is the operator of destratification. But what is stratification? The theory of stratification is among the most impressive, but also most perplexing, achievements of A Thousand Plateaus. I think it is absolutely central to its entire conceptual construction; without it, nothing works. But its pivotal role is often overlooked. The theory of stratification is a theory of the self-organisation of matter. It is unabashedly metaphysical; indeed, it is perhaps the most ingenious and ambitious metaphysical hypothesis proposed by any twentieth-century materialists. Attempts to assimilate A Thousand Plateaus to the parameters of contemporary critical theory have encouraged the tendency to limit the scope of stratification to the experiential realm. But stratification cannot be confined to the phenomenological

264 | a thousand pl ateaus a nd ph ilo s o ph y or epistemological registers. It is not a function of representation; representation is a function of stratification. Thus the theory of stratification is not just an extension of Deleuze’s critique of the epistemology and metaphysics of representation in Difference and Repetition. It lays out the ontological conditions under which representation becomes possible. Already in Difference and Repetition, it was clear that representation is not an extrinsic grid which we superimpose upon reality. Reality generates its own representation. But representation remains a kind of transcendental illusion; a cavern within which an inverted image of the real holds sway, one that prevents us from penetrating to the imperceptible conditions of perception (the virtual). The theory of stratification lays out the real processes through which this cavern, this inversion and this image are successively generated on the same level as the real (rather than above or beneath it). It levels the superposition of planes through which Difference and Repetition maintained the virtual (the imperceptible) in a position of transcendence vis-à-vis the actual (the perceptible). Stratification explains the genesis of representability as a facet of the auto-production of the real as such, rather than as a consequence of the transcendent hiatus between virtual and actual.3 Stratification is the double-articulation of content and expression. This double-articulation is the condition of all order, structure and regularity. But stratification is complex. Both the articulation of content and that of expression are bifurcated. At the elementary physical level, content is articulated by splitting material flows into successively coordinated molecular units. Molecular substance is formally coordinated: this is the substance and form of content. Expression is articulated by establishing ‘functional, compact, stable structures’ (ATP 41), and constructing molar compounds on to which these structures are superimposed. Molar compounds are formally structured: this is the substance and form of expression. Stratified content is formed matter; stratified expression is structured function. Both articulations are segmented and the bi-univocal relations between segments of content (formed matters) and segments of expression (structured functions) are the source of every real structure, whether physical, biological or sociopolitical. Thus material reality comprises three fundamental types of strata: physico-chemical, biological and anthropomorphic (or allomorphic, because the anthropomorphic strata have the power to colonise the others). Only the first gives molar expression to molecular content: biological and allomorphic contents are not necessarily molecular, nor are their expressions necessarily molar. But what is common to every stratum is the coordination of structured function (expression) and formed matter (content). Matter is assigned a determinate function on the basis of its formation (whether physical, organic or sociocultural); function is assigned a determinable form on the basis of its substance (whether

co n c re te rules a nd a bstract mach in es | 265 molecular, cellular or semiotic). This is the crux of all stratification as immanent principle of the self-organisation of matter. Yet stratification is also a process of division. Strata ‘shatter the continuums of intensity, introducing breaks between different strata and within each stratum’ (ATP 143). This division is real, not ideal (it is not dialectical). Strata split and segment, but they also conjoin and connect. Thus Deleuze and Guattari insist on the real (as opposed to formal) distinction between content and expression. It is a difference in being, not just a difference in thought. Stratification is a real synthesis establishing a common root for expressive form and expressed content. Thus there is an isomorphism of content and expression: ‘their independence does not preclude isomorphism, in other words, the existence of the same kind of constant relations on both sides’ (ATP 108). This isomorphism makes of stratification an instance of ‘divine judgment’, which is to say, ontological as opposed to cognitive (or transcendental) synthesis: ‘Indeed, the significance of the doctrine of synthetic judgment is to have demonstrated that there is an a priori link (isomorphism) between Sentence and Figure, form of expression and form of content’ (ATP 108). Where Kant’s doctrine of synthetic judgement traced the isomorphy of intelligible form and sensible content back to the activity of the transcendental subject, stratification anchors the isomorphy of expressive form and expressed content in the functioning of the abstract machine, the ultimate source of stratic synthesis. Concrete assemblages presuppose the articulation of structured function and formed matter. But they do so insofar as each envelops an abstract machine. Abstract envelopment What is an abstract machine? Here are two definitions: ‘The abstract machine exists enveloped in each stratum, whose Ecumenon or unity of composition it defines, and developed on the plane of consistency, whose destratification it performs (the Planomenon)’ (ATP 73, my emphasis). ‘We define the abstract machine as the aspect or moment at which nothing but functions and matters remain’ (ATP 141, my emphasis). The abstract machine is Janus-faced: on one side, it accounts for the unity of composition (i.e. synthesis) proper to strata, insofar as these allocate structured functions to formed matters. This is to say that it performs a stratificatory function. But on the other side, it decouples structure and substance, form and content, deforming both expressive function and expressed matter. This is its destratificatory role. Stratification and destratification are two aspects of a single, indivisible machinic process, straddled by every abstract machine.

266 | a thousand pl ateaus a nd ph ilo s o ph y In its destratifying role, the abstract machine draws the plane of consistency by articulating a non-formal function with a formless matter. What it retains of stratic expression is the tensor, the a-signifying sign which indexes a continuum of intensive variation. What it retains of stratic content are heterogeneous intensities, or more precisely, different degrees of different intensive qualities: degrees of temperature, speed, conductivity, resistance, dilation, etc. These are the expressive traits of unformed matter. Thus the non-formal function is composed of tensors expressing different degrees of different qualities of intensity. It does not coordinate constants and variables, measuring continuous degrees of difference, but conjugates different kinds of differences in degrees. This is why it composes a continuum of variation, where variation is no longer subordinated to a fixed, homogeneous domain of variables. Instead, it distributes discontinuous differences in the kinds of degree (different degrees of heterogeneous qualities). Bonta and Protevi (2004: 48) give the following examples of non-formal functions: the channelling of differences in temperature by a heat engine and the imposition of conduct by a discipline. To diagram a complex phenomenon, whether epidemic, market or swarm, is to draw its non-formal function. Thus abstract no longer means universal, ideal, or eternal; it is a function of variation: ‘there is no reason to tie the abstract to the universal or the constant, or to efface the singularity of abstract machines insofar as they are constructed around variables and variations’ (ATP 92–3). Tensors quantify continuous variation, not through unities of measure but through multiplicities of measurement. Quantity is no longer subordinated to invariant units of measure (number as unity); it indexes the qualitative particularity of heterogeneous intensities such as speed, temperature, conductivity, etc. (number as multiplicity). Consequently, magnitude varies according to the variation of the qualities it measures: Number is no longer a universal concept measuring elements according to their emplacement in a given dimension, but has itself become a multiplicity that varies according to the dimensions considered (the primacy of the domain over a complex of numbers attached to that domain). We do not have units of measure, only multiplicities or varieties of measurement. (ATP 8) This is to say that there is no fixed unit of measure for the differences in dimension of a multiplicity, only a variety of measurements; a nonmetric multiplicity numbering the qualitative heterogeneity of dimensions without referring to a common element or numerical base. Tensor signs are indices of this qualitative heterogeneity or continuous variation of intensities. Thus the tensor sign expresses the diagrammatic function of deformalised expression. This deformalisation of expression is

co n c re te rules a nd a bstract mach in es | 267 a prerequisite for the quantification of writing proclaimed at the beginning of A Thousand Plateaus: ‘quantify writing. There is no difference between what a book talks about and how it is made’ (ATP 4). To quantify writing is to conjugate expression and construction, structured function and deformalisation, stratification and destratification. This is the function of the diagram. Thus non-formal functioning is diagrammatic: A diagram has neither substance nor form, neither content nor expression . . . Whereas expression and content have distinct forms, are really distinct from each other, function has only ‘traits’, of content and of expression, between which it establishes a connection: it is no longer even possible to tell whether it is a particle or a sign. A matter-content having only degrees of intensity, resistance, conductivity, heating, stretching, speed, or tardiness; and a function-expression having only ‘tensors’, as in a system of mathematical, or musical, writing. Writing now functions on the same level as the real, and the real materially writes. The diagram retains the most deterritorialised content and the most deterritorialised expression, in order to conjugate them. (ATP 141, my emphasis) The diagramming of informal functions and formless matters not only conjugates signs and particles on the plane of consistency; it expresses the auto-construction of the real, the machinic unconscious. Thus the alternative to stratic synthesis is not analysis – the formal disintrication of the abstract and the concrete as invariant form and variable content – but another kind of synthesis; which is to say, an alternative intrication of the abstract and the concrete. This synthesis is not cognitive but practical: it is the diagramming of the junction between non-formal functions and unformed matters. Tensors perform a diagrammatic function: they are the operators of torsion through which deformalisation composes intensities, sign-particles and flows on the plane of consistency. Diagrammatic composition is the identification of these points of torsion. But this composition requires concrete rules: ‘There are rules, rules of “plan(n)ing”, of diagramming . . . The abstract machine is not random; the continuities, emissions and combinations, and conjunctions do not occur in just any fashion’ (ATP 70–1). Thus it is the rules of planification (‘planing’) that ensure consistency, not decoding, deterritorialisation or destratification as such. These rules extract deformalised functions from strata: ‘the plane of consistency is occupied, drawn by the abstract Machine . . .’ (ATP 70). Concrete development It is concrete rules that effectuate the abstract. They develop the abstract machines enveloped in the strata. But this development hinges upon the

268 | a thousand pl ateaus a nd ph ilo s o ph y distinction between stratification and assemblage (agencement). Because stratification is the precondition for every machinic assemblage, and assemblages are at once territorial and deterritorialising, assemblage is the practical condition for the development of the abstract. Agencer is a verb: to assemble. It is because concrete assemblages already envelop abstract machines that they can develop them: planification or planing is the concrete development of the enveloped abstract. It cuts across physical, biological and anthropomorphic strata to compose unformed matters, anorganic life and non-human becomings. Thus rules of destratification = rules of planing = development of the enveloped. Nevertheless, the distinction between Sentence and Figure, expression and content, saying and doing, remains necessary precisely insofar as it is not only a real consequence of stratic synthesis but also a condition of development or planing. Consequently, destratification is not the abolition of the difference between saying and doing, or competence and performance; it is their informal re-articulation, one which retains an expression that has been decoupled from organic function, just as it retains a content that has been released from its organising form. Development renders performance indissociable from competence. But how then are we to understand selection? How does performance operate a selection between greater or lesser degrees of connectivity (or dimensions) on the plane of consistency? How can it discriminate between greater or lesser degrees of development? How are we to measure the extent of construction? Here again the answer is: through concrete rules. Concrete rules orient us in the composition of consistency; they provide an immanent measurement for the degree of continuous variation: ‘Constant is not opposed to variable; it is a treatment of the variable opposed to the other kind of treatment, or continuous variation. So-called obligatory rules correspond to the first kind of treatment, whereas optional rules [règles facultatives] concern the construction of a continuum of variation’ (ATP 103). Thus concrete rules are optional, which is to say that they are neither universal imperatives nor context-sensitive directives. While the former presuppose the stratified distribution of constants and variables, through the constancy of principles and variety of circumstances, the latter presuppose an empiricist pragmatism that merely relativises principles to the constancy of organic or psychological self-interest. But optional rules cannot simply be contrasted with necessary or categorical imperatives as if they were merely contingent or hypothetical imperatives. They are not hypothetical imperatives because they cannot be formulated with regard to any pre-established practical goal or utilitarian objective. Their form cannot be: ‘If you want X, do Y’, where X is relatively constant with regard to the variable Y, because the functional coordination of Y as means to

co n c re te rules a nd a bstract mach in es | 269 end X remains entirely beholden to the stratification of function, whether physical, organic or subjective. Nor are optional rules merely ‘contingent’, since contingency is merely the stratic obverse of necessity. Concrete rules are ‘optional’ to the extent that they are constituted by their own selection, ‘as in a game in which each move changes the rules’ (ATP 100). This is why concrete rules are formulated in the shape of questions, the answers to which transform the assemblage within which they have been formulated. They are rules of assemblage that operate a selection according to the ways in which the assemblage under construction conjoins saying and doing, function and matter. Thus concrete rules of assemblage are distributed along two axes of questioning. The first axis asks: Which content? (i.e. which regime of signs?) Which expression? (i.e. which system of bodies?): ‘In each case, it is necessary to ascertain both what is said and what is done’ (ATP 504, my emphasis). The second asks: What are the cutting edges of deterritorialisation? What abstract machines do they effectuate? The concrete rules of assemblage thus operate along these two axes: On the one hand, what is the territoriality of the assemblage, what is the regime of signs and the pragmatic system? On the other hand, what are the cutting edges of deterritorialisation, and what abstract machines do they effectuate? (ATP 505) The answers to the first set of questions specify the assemblage’s type of signification and its degrees of territoriality: its expression and its content, or what it says and what it does. The answers to the second set of questions specify the assemblage’s type of abstract machine and its degree of deterritorialisation: its non-formal function and its unformed matters. In answering this second set of questions, we identify the point of indiscernibility between saying and doing. Thus, for instance, itinerant metallurgy is the content of which nomadism is the expression; the mode of signification proper to the nomad war machine is numerical, or counter-signifying, while its territoriality consists in smoothing space. Numbering number is the tensor of nomadic distribution, which occupies space without categorising it. Counting without measuring is constructive deformation; hence the war machine’s high index of deterritorialisation, both social and cognitive. Practical mediation Consequently, in answering both sets of questions, we determine the concrete rules and perform the diagramming function. Specifying our

270 | a thousand pl ateaus a nd ph ilo s o ph y signifying regime and measuring our degree of territorialisation is the condition for diagramming the interaction of function and matter beyond the strata. Thus diagramming is akin to engineering: it is a cognitive operation carried out with a view to effectuating certain practical imperatives under specific material constraints. It lets us see to what extent a line of flight is liberatory for us insofar as we find ourselves in between strata and metastrata: ‘In effect, consistency, proceeding by consolidation, acts necessarily in the middle, by the middle, and stands opposed to all planes of principle or finality’ (ATP 507, my emphasis). Acting in the middle, diagramming deformalises stratified signs and substances to achieve consistency. This is why Deleuze and Guattari repeatedly insist that the distinction between territorial and deterritorial, smooth and striated, strata and body without organs, is not the difference between good and bad, let alone a matter of good versus evil.4 Deterritorialisation is not a theological imperative. There is no transcendence vis-à-vis the strata; consistency is not oriented towards an end-point or final state where territories, codes and signs have been definitively eliminated and the strata abolished. Since we are always in the middle – in between the organic, subjectified, signifying and the inorganic, a-subjective, a-signifying – the consolidation of consistency can only proceed from a certain stratified vantage point, whence different possibilities of action become assessable. The resort to the notion of ‘possibility’ is certainly awkward here given Deleuze and Guattari’s Bergsonism, which entails rejecting possibility as an artefact of representation. But it is difficult to avoid, just as it is difficult to unyoke the term ‘practice’ from the notion of ‘action’, which seems to invite an appeal to a disavowed notion of subjective agency. Yet agencement is not without agency. The concept of machinic assemblage decouples agency from subjectivation and reallocates it to pre-individual collectivities. Assemblage is a-subjective agency. The need for concrete rules of assemblage is a consequence of the fact that our power of assemblage, our capacity for assembling, for connecting and consolidating consistency, is constrained both by our degree of territorialisation and our type of signifying regime. Territories, signs and codes are conditions of consistency. But they are enabling conditions. This is why ‘alloplastic [i.e. anthropic] strata . . . are particularly propitious for the assemblages’ (ATP 514, my emphasis). Thus A Thousand Plateaus does not wholly revoke the privileging of the human standpoint. It does not simply jettison philosophical humanism and the problematic of the subject (as elaborated from Descartes to Kant, Hegel and Heidegger) the better to plunge directly into the inhuman maelstrom. Its methodological sophistication, which is to say its account of diagramming as the real materially writing itself, precludes appeals to the ‘intuition’ or ‘lived experience’ of the real. Deleuze and Guattari

co n c re te rules a nd a bstract mach in es | 271 understand that we cannot simply jump out of the strata on to the plane of consistency (whether we ought to accept the metaphysics of stratification is another matter, which we will return to below). We cannot simply nullify everything that distinguishes the human from the non-human by philosophical fiat. This is where Deleuze and Guattari’s careful cartography of the layers of stratification exposes the uninterrogated phenomenological biases of certain strands of posthumanist metaphysics. Machinic pragmatics starts from a stratified vantage point that is unavoidably anthropocentric; yet it is precisely the preservation of a certain strategic anthropocentrism that prevents it from lapsing into anthropomorphism and projecting human properties on to non-human reality. Such projection is characteristic of every metaphysics that believes it can simply disregard Kant’s access problem – what are the conditions under which human beings can think and know about non-human reality? Rather than ignore the constraint of human subjectivation in a way that only reinforces it and transplants human characteristics into the non-human, Deleuze and Guattari propose to use our stratified condition – our organic, subjectified, signifying state – as a leverage point for the development of consistency. The problem of selection The development or consolidation of consistency is inherently selective. As we know, it is concrete rules that operate the selection and ensure the consolidation. Two questions immediately arise pertaining to selection: ‘What is being selected?’ and ‘How is it being selected?’ The answer to the first question is: Whatever increases the degree of connectivity and the dimensions of consistency. The answer to the second is: Through the concrete rules that allow us to discriminate between increases or decreases in degrees of connectivity and dimensions of consistency. But now it becomes apparent that the answer to the first question is already the answer to the second. The selected ‘what?’ is also the selecting ‘how?’ This is to say that it is the plane itself that is the operator of selection: The plane sections multiplicities of variable dimensions . . . The plane is like a row [enfilade] of doors. And the concrete rules for the construction of the plane obtain to the extent that they exercise a selective role. It is the plane, in other words, the mode of connection, that provides the means of eliminating the empty and cancerous bodies that rival the body without organs, of rejecting the homogeneous surfaces that overlay smooth space, and neutralising the lines of death and destruction that divert the line of flight. What is retained and preserved, therefore created, what consists, is only that which increases the number of connections at each level of division or composition, thus in descending as well as ascending order (that which cannot be divided without changing in

272 | a thousand pl ateaus a nd ph ilo s o ph y nature, or enter into a larger composition without requiring a new criterion of comparison . . .) (ATP 508, my emphasis) An enfilade is a series of communicating rooms each connected to the other by a single adjoining door, so that one cannot enter a room or move from one to the next by means of an external corridor. The corridor is the supplementary dimension of transcendent overcoding with regard to the series of interconnected rooms. To characterise the plane of consistency as an ‘enfilade of doors’ is to say that there is no extrinsic dimension (corridor) by means of which its intrinsic dimensions (rooms) could be related to one another. What connects each room is its door or threshold. The threshold or limit of a multiplicity or assemblage is accessible only from within it. Each threshold is a mode of connection from room to room, multiplicity to multiplicity. But the mode of connection is the plane itself. It is the plane that connects the dimensions through which it is composed. This means that the criteria of selection (concrete rules) are discernible only from the vantage of an assemblage (dimension) already composing the plane. Recall that the selection is operated by diagramming content and expression, what is said and what is done within an assemblage, but in such a way that this diagramming determines a non-formal function and a formless matter that have become indiscernible, performing a saying that is also a doing. This is diagramming as the consummation of machinic pragmatics: to achieve a thinking-doing that develops the real while the real envelops it in turn. Selection becomes creation as participation in the auto-construction of the real. Thus it is the plane (i.e. the mode of connection) that selects itself through the concrete rules of assemblage: connection (consolidation) is the selection of connection. This is a-subjective agency insofar as every selection operated by concrete rules within an assemblage is also the self-selection or auto-consolidation of the plane itself. There is a troubling circularity here, although it is one deliberately engineered by Deleuze and Guattari. Consistency is consolidated by increasing its number of connections and thereby its dimensions. The consolidating selection is effected through concrete rules, which are in turn determined by us, for who else can answer the questions that determine the rules? Since the plane does not pre-exist its practical construction, we decide what increases or decreases connectivity on the plane; yet the plane also decides through us. But this seems to introduce a fatal reversibility into the relation between concrete assemblage (the stratified) and abstract machine (the destratified). The real’s auto-selection through us is just as much our selection of the real. Our decisive role in the composition of consistency, which is supposed to be the concrete development of the enveloped (the

co n c re te rules a nd a bstract mach in es | 273 destratified), requires re-enveloping the abstract within the concrete (the stratified). The absoluteness of relativity (connection) becomes indistinguishable from the relativity of absoluteness (the body without organs as disconnection). But then are we not absolutely relativising the absolute? And if we are, doesn’t machinic pragmatics risk lapsing into its less glamorous, more prosaic majoritarian cousins, either pragmatic individualism or liberal pragmatism? The qualities of power This reversibility or relativisation is symptomatic of a more fundamental difficulty: How do we determine the measure of consistency? One cannot construct without increasing, even if this increase is not measured in units. So how do we select what to increase given that it cannot be measured in fixed units? What are we constructing, given that we must proceed by subtracting unity, so that the extent of our constructive activity cannot be gauged in terms of constancy, regularity or order? How do we measure the dimensions of a consistency devoid of constancy? Two successive passages seem particularly relevant here. The first occurs on the book’s penultimate page: [T]here is a whole process of selection of assemblages according to their ability [aptitude] to draw a plane of consistency with an increasing number of connections. Schizoanalysis is not only a qualitative analysis of abstract machines in relation to the assemblages, but also a quantitative analysis of the assemblages in relation to a presumably pure abstract machine. (ATP 513, my emphasis) In this passage, Deleuze and Guattari seem to affirm the possibility of attaining a quantitative measure of an assemblage’s capacity for increasing degrees of connectivity and dimensions of consistency. If this capacity can be assigned a quantitative measure, then selection operates on the basis of this measure: assemblages are selected or deselected according to the magnitude of their ‘ampliative’ capacity (i.e. increasing degrees of connectivity and dimensions of consistency). Capacity would presumably be cashed out here in terms of a Spinozist notion of power: the power to affect and be affected. Assuming a rough equivalence between modes and assemblages, every assemblage would be characterised by a degree of reality (consistency) corresponding to its power of affecting and being affected. As Deleuze writes of Spinoza: ‘A thing has all the more reality or perfection insofar as it can be affected in a great number of ways: quantity of reality always finds its reason in a power that is identical to essence’ (Deleuze

274 | a thousand pl ateaus a nd ph ilo s o ph y 1968b: 83–4, my translation). Power is identical to essence as actuality, not potentiality: essence is existence as act. Thus essence is the power of acting, of affecting and being affected, whose increase converts passivity into activity: ‘The power of acting is the only real, positive, and affirmative form of a power of being affected’ (Deleuze 1968b: 204, my translation). The reality of affectivity derives from the power of activity: the greater the power of acting, the greater the power of affecting and being affected. But what determines this increase in power? For Deleuze’s Nietzsche, the power of acting is a function of the quantity and quality of forces composing a body. Crucially, however, quality is that aspect of quantity ‘that cannot be equalised out in the difference between quantities’ (Deleuze 1983: 43–4). Thus quality is the intensity of force. Differences in the quantity of force are generated by different qualities of force, i.e. different intensities (speed, heat, resistance, conductivity, etc.) What Deleuze calls ‘the absolute genesis’ of the qualities of force is attributed to the will to power (Deleuze 1983: 51). Power is the being of force, its reality or actuality. But because power is will to power, self-intensification, it is the quality proper to the will to power that determines the qualities of forces. The qualitative difference proper to power is affirmative or negative; the qualitative difference proper to forces is active or reactive. Thus differences in the power of acting, in the capacity to affect and be affected, follow from the fundamental difference in the quality proper to power, which is either affirmative or negative. But if what is selected is difference in power, and the only quantity proper to power is determined by its quality as either affirmative or negative, then it is the quality of power that determines its quantity in terms of its capacity to affect and be affected. In other words, it is the affirmative will to power that selects between the affirmative and negative qualities of power. Assemblages that increase connectivity and consistency are those that select between increases and decreases in connectivity and consistency. The selection of assemblages reiterates the deliberate circularity in Deleuze’s account of the selection of will to power. The trouble, however, is that this difference in the quality of power is already actual. If differences in the capacity to act ultimately reduce to differences in the qualities of forces, as either active or reactive, then the difference in power on the basis of which selection is supposed to discriminate between assemblages has already been determined: it is already a difference in actuality (since the differences in modal power already correspond to differences in their attributive expression). This is to say that difference in power is already a difference in being. Flattening essence on to existence as power of acting effectively levels the distinction between making a difference in being (selecting) and accepting a difference in being as given, since the essential differences in degree of activity, which

co n c re te rules a nd a bstract mach in es | 275 is to say differences in the quality of power, have already been made (i.e. selected). Thus the distinction between affirmative and negative types of will to power threatens to slip into an essential difference between types of potency. Yet the distinction between types of power was supposed to be a function of selection: making is (supposed to be) selecting. The relative absolute Ultimately then, the quantitative difference in power on the basis of which selection is supposed to operate requires a qualitative difference whose reason or ground is ontological, which is to say already actual or in effect. Thus the operative criterion for selecting between degrees of actuality, or powers of acting, turns out to be rooted in the quality, not quantities, of power: affirmativeness. If selection is the affirmation of affirmation (as in Deleuze’s account of the dice-throw), then an assemblage’s self-affirmation is effectively indistinguishable from that of the plane of consistency. Given this ambiguity, one might ask: Can we distinguish between personal self-affirmation and the impersonal self-affirmation of the machinic unconscious? In the second of the two passages mentioned above (which occurs on the last page of the book), Deleuze and Guattari openly acknowledge the difficulty of measuring an assemblage’s degree of proximity or distance visà-vis the ‘pure’ abstract machine: On the alloplastic [anthropic] strata, which are particularly propitious for the assemblages, there arise abstract machines that compensate for deterritorialisations with reterritorialisations, and especially for decodings with overcodings or overcoding equivalents. We have seen in particular that if abstract machines open assemblages they also close them. An order-word machine overcodes language, a faciality machine overcodes the body and even the head, a machine of enslavement overcodes or axiomatises the earth: these are in no way illusions, but real machinic effects. We can no longer place the assemblages on a quantitative scale measuring how close or far they are from the abstract machine of the plane of consistency. (ATP 514, translation modified, my emphasis) Thus while conceding the difficulty of measuring degrees of connectivity and consistency, Deleuze and Guattari attribute this difficulty to the imperialism of the anthropic strata – in other words, to the anthropomorphisation of the earth. Yet the overcoding, enslavement and axiomatisation they allude to here may be symptoms of their own underlying equivocation between personal and impersonal self-affirmation; an ambiguity reiterating the reversibility between voluntarism and determinism, concrete and

276 | a thousand pl ateaus a nd ph ilo s o ph y abstract, relative and absolute, which we have already noted. The ‘pure’ abstract machine is consistency as point of indiscernibility between saying and doing, the absolute development of the enveloped. But the alloplastic strata generate abstract machines that re-envelop what has been developed on the physical and biological strata: every sign becomes signifying, every haecceity is subjectified, every smooth space is striated. This systematic re-envelopment renders it difficult if not impossible to measure an assemblage’s degree of development vis-à-vis the abstract machine or plane of consistency. A fatal indiscernibility is inaugurated such that it becomes impossible to say whether the absolute is in the relative (the abstract in the concrete), or the relative in the absolute (the concrete in the abstract). This predicament points to a still deeper problem. In order to stave off this indiscernibility, it must be possible to measure degrees of deterritorialisation relative to an absolute movement – the full body of the earth, the deterritorialised, the cosmic egg, etc.5 This is the absolute in terms of which we measure degrees of deterritorialisation and types of assemblage. Thus, the absolute expresses nothing transcendent or undifferentiated. It does not even express a quantity that would exceed all given (relative) quantities. It expresses only a type of movement qualitatively different from relative movement. A movement is absolute when, whatever its quantity and speed, it relates “a” body considered as multiple to a smooth space that it occupies in the manner of a vortex. (ATP 509) Absolute movement – the torque of a vortex – is qualitatively different from relative movement as well as the measure of relative movement. But the retention of this absolute movement seems to violate the prohibition on transcendence precisely insofar as relativity is defined negatively as a diminution, a limitation or relativisation of absolute movement. How can we measure the relativisation of movement negatively as a diminution of absolute movement unless we can specify the positivity of absolute movement independently of its limitation? Vortical torque may have the absoluteness of an intensive quality, but why should this particular quality of movement be the defining characteristic of the absolute? Its qualitative absoluteness remains relative to that of every other quality of movement. (Despite their Spinozism, Deleuze and Guattari reject the thesis that determination is negation.) Thus the distinction between relative and absolute remains relative because there is no immanent access to the absolute that would bypass the strata (which is to say, the absolute’s self-limitation). The question remains: why does absolute movement relativise itself? If the absolute is a quality of movement, rather than a quantity, what accounts for this difference in quality from the viewpoint of that which

co n c re te rules a nd a bstract mach in es | 277 is already relative? The problem is that Deleuze and Guattari maintain a traditional qualitative conception of the absolute while insisting that this quality is neither negatively defined (as infinite vis-à-vis other finite qualities) nor wholly inaccessible and transcendent vis-à-vis the relative and immanent. They want to be able to specify absoluteness as a determinate quality of movement. But the differences in the qualities of intensity – intensive matter’s expressive traits – cannot be absolutised without absolutising the relations between bodies within which they manifest themselves. The notion of absolute intensity is limitative vis-à-vis the continuums of intensities, but Deleuze and Guattari want to invert the relation between absolute and relative to define relative intensity limitatively in regard to absolute intensity. Thus they have to give a positive account of limitation on the basis of a negative account of the unlimited, or the absolute, since the latter is precisely that whose positive characteristics are defined negatively in relation to its own limitation: de-territorialised flows, a-signifying particles, non-formal functions, formless matters. The body without organs does not lack anything, but what it does not lack can only be defined in terms of that which falls short of it, that which is not full, that which is limited with regard to it, i.e. the stratified. Thus destratification presupposes stratification; but stratification only makes sense with regard to a concept of the destratified whose positive characteristics are drawn exclusively from the strata. Conclusion The consistency of machinic pragmatics stands or falls with the theory of stratification. The latter is in many ways a magnificent construction, drawing creatively on an impressive array of scientific work (most notably that of François Jacob, Jacques Monod, René Thom and Ilya Prigogine).6 Yet it remains wholly speculative for all that. Its dazzling ingenuity should not blind us to the very obvious questions it continues to raise: How do they know? Why should we believe that reality is really like that? Dismissing these questions as Kantian hang-ups is a facile rhetorical manoeuvre, unworthy of the seriousness of the book’s philosophical ambition. Without stratification, the consistency of A Thousand Plateaus unravels: it is the single thread tying together its fantastically intricate lines of thought. Yet it is the thread that cannot be verifiably tethered to anything outside the book. Thus, for all its paeans to the primacy of exteriority, A Thousand Plateaus is ultimately a self-enclosed, self-sufficient construction; but one rooted in a gesture of negation that it cannot avow or integrate within itself. What it rejects is representation, together with its ‘arborescent’ dichotomies

278 | a thousand pl ateaus a nd ph ilo s o ph y between inside and outside, subjectivity and objectivity, truth and falsity. It tries to purify this rejection of negation by construing rejection as selection and negation as a quality of power. Thus the rejection of representation (together with all its dichotomies, oppositions and negations) is not supposed to be a denial but a mere effect or consequence of the book’s selection of affirmation over negation. Rather than seeking to justify itself, this is a book that insists on affirming its own power, which is precisely the power of affirmation. But as we saw, the attempt to reduce negation to affirmation and denial to selection rests upon the affirmation of a difference between affirmative and negative power which turns out to be all but essential. Differences in the quality of power (affirmative or negative) turn out to be fundamental differences in being. By the same token, making the difference between affirmation and negation turns out to be indiscernible from accepting it as something that is already given; which is to say, representing it. This indistinction testifies to a fundamental inconsistency, which might also be called a contradiction, between what the book says and what it does. Despite its extraordinary ingenuity, A Thousand Plateaus cannot give a wholly positive account of the limit between the relative and the absolute, the finite and the infinite. This is to say that its systematic disavowal of dialectics, negativity, interiority and transcendence leads it to hypostatise the difference between negative and positive, inside and outside, immanence and transcendence, into a brute given, an ultimately transcendent datum: stratification. Everything in the book relies on giving a positive sense to the de- in destratification, or delimitation, but this positive sense is merely the inversion of the limitation of absolute movement that it cannot but presuppose as its starting point: stratification. Thus the book absolutises limitation in a forlorn attempt not to define the absolute limitatively. Circumventing negation and mediation, which is to say the constraints of justification, it seeks to install itself immediately (or immanently) in between the relative and the absolute, but in doing so ends up absolutising in-between-ness. But can this absolute in-betweenness be so confidently contrasted with the utilitarian compromise which is the fabric of the everyday? Notes 1. Thus Deleuze’s insistence that A Thousand Plateaus is a work of ‘[p]hilosophy, nothing but philosophy . . .’ (Deleuze 1980a: 99). 2. ‘Every undertaking of destratification (for example, going beyond the organism, plunging into a becoming) must therefore observe concrete rules of extreme caution’ (ATP 503). See also ATP 171–83. 3. See especially ATP 281–4. Miguel de Beistegui has convincingly argued that Deleuze

co n c re te rules a nd a bstract mach in es | 279 and Guattari contrast the plane of transcendence, or development, which maintains a classical hierarchical distinction between (transcendental) condition and (empirical) conditioned, albeit in the form of unconscious virtuality and conscious actuality, to the plane of immanence, or consistency, where the difference between stratificatory and destratificatory processes is unfolded on a single level, such that the principle of perceptibility cannot but be perceived together with that which it renders perceptible. See Beistegui 2010: 47–76. 4. E.g. ‘There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome. These lines always tie back to one another. That is why one can never posit a dualism or a dichotomy, even in the rudimentary form of the good and the bad’ (ATP 9). 5. ‘[W]hat is primary is an absolute deterritorialisation, an absolute line of flight, however complex or multiple – that of the plane of consistency or body without organs (the Earth, the absolutely deterritorialised). This absolute deterritorialisation becomes relative only after stratification occurs on that plane or body: It is the strata that are always residue, not the opposite’ (ATP 56). 6. Nevertheless, the parochialism of this list should give us pause: all French, all writing in the 1970s. Can a theory so ambitious afford so narrow an evidential base? The other chief inspiration is, of course, the Danish linguist Louis Hjelmslev, originator of the distinction between content and expression.