This talk is an examination of the final, and I think still the shortest plateau in A Thousand Plateaus, but in a way what I'm going to try to do here is to try to use it as an optic through which to get a handle on what this book is trying to do. Because it's a pretty extraordinary work. and understanding exactly that it mixes remarkably sophisticated conceptual abstraction with a series of what seem to be practical, ethical and aesthetic imperatives. I want to try to understand the articulation of these two dimensions of the book. And I think this articulation is explicitly stated in the title of this final plateau, Concrete Rules and Abstract Machines.
So what relation between the abstract and the concrete is at issue here? In other words, how do rules relate to machines? And the term rule is unusual, especially for Deleuze and Guattari, given their antipathy to any kind of Kantianism and to any kind of rationalist universalism. So the word rule here is being used in a very peculiar sense. And I'm going to try to hopefully elucidate that sense. in order to understand the relationship between rules concrete rules and abstract machines we need to clarify the parameters within which this work operates and the key to do this is to understand that Deleuze and Guattari's materialism is neither a contemplative representation of an objectively existing
material reality nor on the other hand a series of practical imperatives that presupposes yet disavows a theoretical representation of material reality. In other words, when you're conjuring prescriptions about what to do or how you should act, it seems that there's often a surreptitious invocation of theory. There's some kind of conceptual theorization which is implicit. And it seems to me that those in Glutari want to be explicit about the articulation of both dimensions. So for all us, you know, idiosyncrasy, ATP, conforms to a classical model of philosophy. It's a very classical word. When ontology, understood as the account of what there is,
is at one with ethics, understood as a practice or art of living. And Deleuze's work on Spinoza, you know, I'm sure everyone is familiar with the proper Deleuzean understanding of ethics, as opposed to any kind of Kantian moral philosophy. but this is not to say that it's a traditional or conservative work it's a contemporary reactivation of the classical task of philosophizing which is the fusion of understanding what there is what exists in the world and how to live what we should do what are the stakes of this reactivation it fuses an abstract materialism wherein matter is conceived independently of form with a concrete ethics, where action is selected independently of universal law.
But how can concrete practices engage formless matter? I'll hopefully try to explain what this formlessness, why abstract matter is necessarily formless in the Los Angeles Society. This is another way of asking about the nature of the distinction between the abstract and the concrete. Abstract, as I'll try to show, means unformed. but the unformed is endowed with positive traits of its own. So abstract matter is described as constituting a plane of consistency characterized by continuums of intensities, particle signs, and de-territorialized flows. And this vocabulary is very precise. And actually, rereading this book, I'm struck by its precision.
It's a book that seems intimidatingly dense and complex, and there's a profusion of concepts and distinctions. But what's striking when one rereads the book is the consistency and precision with which Daudon Guattari uses vocabulary. They use these terms in a very, very precise and consistent way from beginning to end. Finally, the plane of consistency must be made. It's not given. And all the injunctions about, from the very beginning of the rhizome plateau, the multiple must be made. It's not given. But consistency is not attained through abstraction,
by abstracting from the inconsistent, or empirical multiplicity, but by diagramming what is most concrete in both thinking and doing. So concrete means practical. That's one sense in which I think concrete rules must be understood here. Recognizing and releasing the positive traits characteristics of the unform is a practical matter and one that is moreover constrained by certain rules. What sorts of rules? Because real or abstract matter cannot be represented within material reality the rules or practical injunctions governing the constructions of the real the plane of consistency cannot be read off some pre-existing reality. So these rules will be concrete precisely to the extent that they effectuate the abstract.
So practice and theory realize one another. Theoretical concepts are effectuated in practice. Practical imperatives are formulated in theory. So this project then can be understood as a radicalization of philosophical pragmatic. Indeed, it characterizes philosophy as a whole. Pragmatics is one of their terms for describing what it is they're doing. but it's a pragmatics where neither the agents nor the function of practices can be taken for granted the reference of the communal we constantly invoked both by traditional pragmatists and neo-pragmatists 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 And by the same token, the habitual functions and goals established around this existing we, the goals and purposes that we prescribe for ourselves, according to our current understanding of the word, need to be suspended. Normal functioning and established finalities need to be disrupted. But this disruption cannot be immediately achieved. Since we always start in the middle, we start stratified, organized, subjectified. Thus a practical challenge is to understand how we can destratify, disorganise and desubjectify without lapsing into religious self-abnegation. Or to quote a dozen-glethora, 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. 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. It's not a point of this blank identity, the white knight or the black knight. Something must be retained, something of the subject, something of the sign, something of the organism. This is a quote. That which races or dances upon the plane of consistency thus carries with it the aura of its stratum, an undulation, a memory, or a 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. So, what I'm going to propose, or my hypothesis, is that what will be retained from stratified function on the plane of consistency is the torsion of destratified intensities, particles, signs, and flows, the traits, the components of the plane of consistency. But because the point of torsion is indiscernible from the vantage of anyone invested in the importance of a distinction between self and non-self, or personal and impersonal, its approach requires caution. Caution is required for
the composition of the plane of consistency, and it's obviously one of the watchwords of a thousand plateaus. So this is the point at which concrete rules for the composition of consistency become relevant. To understand how concrete rules are articulated with abstract machines, we have to understand how the composition of consistency, according to rules, requires deformalizing stratified functions and subjecting them to the torsion of absolute movement. And this is a quote from the concrete rules plateau. 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. and I think this vortex here is crucial they mean torsion is a measure of torque actually is a measure of this movement this twisting movement that tornadoes exhibit for instance and it seems that this is what deformalization or destratification on the plane of consistency does, it twists elements from stratified functions from the three fundamental strata, physical, chemical, biological, and anthropomorphic.
So absolute movement then is attained through the deformalization of stratified function. Deformalization ensures the continuity of insensities, the emission of particle signs, and the combination or conjunctions of deterritorialized flows on the plane of consistency. Once again, continuity, intensive continuity, emission, particle emission, and combination of flows are consistent. These are the terms they use over and over again for these constructions of absolute movement. So abstract then means de- or unformed, which ultimately means de-stratified. and I think stratification
is the source of all formalization so this is why I think the geology of morals plateau the third plateau is absolutely crucial to understanding the whole book and I think it gives a lie to the claim that the plateaus can be read in any order that's not true if you don't read if you haven't understood the plateau, the geology of Morrill's plateau, as I learned in my course, you literally, it's very hard to understand what they mean in the other plateaus. So I think that stratification is absolutely crucial to understanding decoding and detortualization, precisely as these operations already presuppose stratification.
Stratic synthesis is absolutely primary. What is stratification? okay so this is it's a forbidding it's one of the most complicated and demanding sections of the entire book but i'll try to give a kind of a very quick gloss on it stratification is the double articulation of content and expression i'm sure you all know so 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. And I'll just use the kind of physical stratum as an example of this double articulation. At the elementary physical level, content is articulated by splitting material flows
into successively coordinated molecular units so that molecular substance is formally coordinated. So this is the substance and form of content. content has a form and a substance expression on the other hand is articulated by establishing functional compact stable structures and by constructing molar compounds onto which these structures are superimposed so molar compounds are formally structured this is the substance and form of expression so this is just beginning at the physical, chemical level. It gets, the plateau then moves on to characterize
the procedures of stratification, first of all, in the biological domain, and then ultimately in the anthropomorphic realm. Now, stratified content is formed matter, and stratified expression is structured function. So all stratification is the articulation of formed matter and structured function. In other words, you form a matter and you make it do something. Stratification is materialization or substantialization if you want and then the functionalization, the physical or organic or linguistic functionalization
of that form matter. Both articulations are segmented and the bi-univocal relations between segments of content or formed matters and segments of expression or structured functions are the source of every real structure, whether physical, biological or sociopolitical. So material reality comprises three fundamental types of strata. Physical, chemical, biological and anthropomorphic or, as those in the contrary reputed allomorphic. Allomorphic because anthropomorphic strata have the power to colonize all the others. Only the first strata, the physical chemical, gives molar expression to molecular content. Biological and allomorphic contents are not necessarily molecular, nor are their expressions necessarily moral.
This is something they insist upon. now you have to see I think here in reference to the debates about what kind of philosophical work A Thousand Classes is, I think the answer to the question about whether this is some kind of extension of some critical transcendental project, in other words whether it's some kind of eccentric transcendental phenomenology or whether it is in fact a work of metaphysics is the latter. The answer is if you understand that stratification is a real process. In fact, reality as such is constituted through stratification.
Reality in the sense of the reality investigated by representable reality, the reality that is cognizably tractable, as opposed to the real understood as the plane of consistency. So stratification is a process of division, such as strata shatter the continuums of intensity, introducing breaks between different strata and within each strata. But this division is real, not ideal. It's not dialectical. It's not inner head. It's not a function of representation. The strata are real. Strata split and segments, but they also conjoin and connect. So D&G time and again insist on the real as opposed to the formal distinction between content and expression.
They use real in a scholastic sense. A real distinction is a distinction in existence. When you distinguish two independently existing things. Whereas a formal distinction is a merely conceptual distinction. so stratification then is a real synthesis establishing a common route for expressive form and expressed content so there's an isomorphism between content and expression again, it's another quote their independence does not preclude isomorphism in other words, the existence of the same kind of constant relations constant relations between segments of content and segments of expression on both sides.
This isomorphism makes of stratification an instance of divine judgment. And when they say divine judgment, they mean divine as opposed to human judgment or cognitive judgment. When they say that strata are judgments of God, they mean judgments of God in the absolute sense. sense, as if God's thinking makes the world, God's judgment, his articulations of subjects and predicates, constitutes cognizable reality. So what they're saying is that synthesis, it's not a function of transcendental subjectivity, it's not a function of a human, of some kind of not human but kind of impersonal transcendental subject or thinker synthesis is actually
deployed through matter is self-synthesizing so that's why it has an ontological as opposed to cognitive significance and this is another quote indeed the significance of the doctrine of synthetic judgment by which I think they mean Kant is to have demonstrated that there is an a priori link or isomorphism between sentence and figure or linguistic expression and form bodies, a form of expression and a form of content. So, real distinction, reciprocal presupposition, and isomorphy are the characteristics of stratic synthesis.
So, stratification is both something that splits and separates, but it also joins and unites. And that's what double articulation does. You divide, but then you connect at the same time. The alternative to stratic synthesis is not analysis, the formal disintegration of the abstract and the concrete, but another kind of synthesis, which is to say an alternative intrication of the abstract and the concrete, or form and matter, if you want. This synthesis is not cognitive but practical. And it unfolds as what Dewey Zingotori called the diagramming of the junction between non-formal functions and unformed matters.
Here's another quote from the final plateau. Abstract machines consist of unformed matters and non-formal functions. Every abstract machine is a consolidated aggregate of matters, functions, phylum and diagram. machinic phylum and rhizomatic diagram. This is evident on a technological plane. Such a plane is not made up simply of formed substances, aluminium, plastic, electric wire, etc., or organising forms, programme, prototypes, etc., but of a composite of unformed matters exhibiting only degrees of intensity, resistance, conductivity, heating, stretching,
speed or delay, induction, transduction, and diagrammatic functions exhibiting only differential equations or more generally tensors. So in a way what they mean by a non-formal function is something like a machine diagram or a wiring diagram, where a wiring diagram is a kind of connects elements material elements, but the way in which those elements are connected, in other words the engineering of these elements, their consolidation, doesn't have a logical structure, it's not a purely kind of, it's not logically formalizable, but nor is it simply empirical, it's not simply a series of connections between empirically
empirically tractable properties or things like behavioral dispositions. So, tensors then are the operators of torsion through which deformalization composes intensities, sine particles and flows on the plane of consistency. What does this mean? It simply means that deformalization diagrams this kind of relationship between these elements of an assemblage, but liberates them from their stratic articulation. It disarticulates them to construct the diagram, but a diagram which is functional but non-formalizable.
So diagrammatic composition is the identification of these points of torsion. but this composition requires concrete rules again there are rules rules of planning or of diagramming as we will later see or elsewhere the abstract machine is not random the continuities of intentities, emissions of particles and combinations of flows do not occur in just any fashion so it's the rules of the French would be planification assuming it has planing actually if you think of it like a carpenter planes a surface that's what it means to create a plane of consistency
it's the planing which generates a surface that ensure consistency these rules ensure consistency not decoding deterritorialization or restratification this is very important decoding deterritorialization and destratification are not simply, it's not stuff that is just going on, it's stuff that is going on around us all the time. But what they're saying is that the kind of destratification that they're interested in, the kind of destratification that has to be effected, is rule government. So they're saying that there is something to be done. This is why the practical dimension is,
and the point is that once you recognize when you're diagramming an assemblage you're supposed to identify you have to do something when you're diagramming it in order to understand what you can then do to push this configuration this machinic assemblage into another state so these rules extract deformalized functions from strata quote again The plane of consistency is occupied, drawn by the abstract machine. The abstract machine exists simultaneously developed on the destratified plane it draws and enveloped in each stratum whose unity of composition it defines.
This distinction between development and envelopment is also, I think, crucial. So it's concrete rules then that effectuate the abstract. this is the claim I'm making in other words this is why this is why they're not simply kind of describing the world they're not describing the functioning or the kind of the coordination of reality they're diagramming it and these diagrams are designed to give you a point of traction they're supposed to allow you to do something in the world that's what concrete rules are for and what these concrete rules do is that they develop the abstract machines
enveloped in the strata this development hinges upon the distinction between stratification and assemblage agencement because stratification is the precondition for every machinic assemblage and assemblages are at once territorial and de-territorializing assemblage then is a practical condition for the development of the abstract. And this is obvious in French. Agencé is a verb. It means to assemble. So concrete assemblages develop abstract machines. And 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 becomeings. So then the suggestion is that rules of destratification just means rules of planification which just means the development of the enveloped. So now the second relevant factor to understand how this development, this practical development of the abstract can be brought about is by understanding the relationship between abstraction and variation. Abstraction is a function of variation.
Here's another quote. Abstract does not mean universal, ideal or eternal. It is a function of variation. Quote, there is no reason to tie the abstract to the universal or the constant or to face the singularity of abstract machines insofar as they are constructed around variables and variations. That's why abstract machines are functions of variation. So concrete rules then are tensors of continuous variations. A concrete rule allows you to put something to a state of continuous variation. Quote again. 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 obligatory rules distinguish between constants and variables and in fact the kind of moral universalism or practical practices that Dozen Gotari are attacking think it's always possible to identify an invariant, a formal invariant, across a variety of different empirical circumstances. This is another kind of residue of hylomorphism.
The idea that you can have invariant form and variable content. so obligatory rules presuppose this they presuppose the distinction between variable and invariant whereas optional rules concern the construction of a continuum of variations that's why concrete rules must be optional so now Deleuze and Guattari give at least two hints at how two ways in which these concrete rules can be kind of delineated or kind of characterized. First of all,
it's a question of understanding the way in which an assemblage is a conjoining of a saying and a doing. A machinic assemblage conjoins saying and doing. a regime of enunciation and form bodies. So the first axis is a first axis in terms of which one can characterize rules of assemblage, concrete rules of assemblage. And by asking the questions, which content and which expression? What kind of content is developed here and what kind of expression? Which regime of signs? Which system of bodies? So in each case, it's necessary to ascertain both what is said and what is done.
That's the first axis of evaluation for concrete rules. The second axis is asked, what are the cutting edges of deterritorialization? What abstract machines do they effectuate? Here's a quote. 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 deterritorialization and what abstract machines do they effectuate? So diagramming lets us see to what extent a line of flight is destratificatory or liberatory.
but this diagramming or this assessment is going to be for us. The point, look at the questions you're asking when you're diagramming an assemblage. What is the territoriality of the assemblage? What is the regime of science in the pragmatic system? What are the cutting edges of deterritorialization and what abstract machines do they effectuate? so the question it's not clear at least whether this the answers to these questions these questions are well I mean they're explicitly perspectival how you answer these questions will depend on what kind of body you have
what kind of assemblages you are you know connected with or participating in so in effect that's why there's no kind of value, absolutes or neutral standpoints for this work of diagramming according to rules. So in effect, consistency proceeding by consolidation acts necessarily in the middle, by the middle, and stands opposed to all planes of principle or finality. In other words, The ways in which the concrete rules are put into practice, identified and put into practice,
depends upon variable circumstances. Because you're always acting in a, you know, well, I was going to say, it's tempting to use the language of particularity here, particularity or contingency. But of course, this is the very vocabulary that becomes redundant in Deleuze and Guattari's framework. You can no longer oppose the necessary and the contingent, or the universal and the particular. Now, I'm not going to read the whole of this quote, but once again, I want to point, I've just highlighted the two crucial sections
where they emphasize the way in which concrete rules are rules of selection, rules of discrimination, if you want. The plane of consistency is like Masumi has Roe. The French is Enfilade. Enfilade, I learned recently, it's like in 18th century houses, 18th century houses of the French aristocracy, you'd have one door a series of rooms that were connected by doors and they weren't joined by any kind of corridor there's a door that leads you from one room straight into another room so an amphialade of doors is a series of chambers that are serially connected to one another
and that's how we're to envisage the articulation of the plane of consistency These are thresholds, intensive thresholds. But the concrete rules for the construction of the plane obtain to the extent that they exercise a selective role. And I'm just going to skip to the last sentence. So what is selective? What is retained and preserved and 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 nature or enter into a larger composition without requiring a new criterion
of comparison. So the key thing is that the link between selection, okay, you're selecting those elements which increase the number of connections at each level of division. So, and again, thus there's a whole process of selection of assemblages according to their ability to draw a plane of consistency with an increasing number of connections. This is why 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.
Now, this second, it's this actually kind of second clause which I think is curious or becomes perplexing, because the rules of selection are always articulated on the anthropomorphic or alloplastic strata, which, as Nkothari said, are particularly propitious for the assemblages. And again, I won't read the whole of the quote, I'll just read the final sentence. On the one hand, the anthropomorphic strata are propitious to machinic assemblages, and there seem to be, you know, they insist that there are greater, again, I can't use the word possibility, there are greater kind of, I don't know,
capacities for deterritorialization in the anamorphic strata than in the physical, chemical, or even biological strata. But at the same time, they want to say this, but Dostoyan Guattari disavow what they call any ridiculous cosmic evolutionism. It's not even, you know, well, it's against a bad interpretation of Bergson, where you would have something like a cosmic evolution, a kind of an ascent of stages, an increased complexification, intensification, etc., let alone something like the Scharding Omega part. So on the other hand, they want to disavow any kind of convergence. There's no convergence. There's no final destination for becoming.
Yet at the same time, the anamorphic strata are particularly propitious for the assemblages. They allow a greater degree of deterritorialization. So the question is, how do you measure degrees of deterritorialization? Well, you measure them with regard to a presumably pure abstract machine. And what is a presumably pure abstract machine? Well, it's only comprehensible if you take the theory of stratification absolutely seriously. The only way in which it's possible to identify the pure abstract machine,
the pure abstract machine is that which is entirely developed, which is somehow not compromised by envelopments in a stratum, no longer provides a kind of a center of unity. Now, I think there's a tension here between these two claims. it's not clear what a pure abstract machine could be if the selection of destratified traits intensities, particle signs, flows operates according to criteria discernible only from within the anthropomorphic strata in other words, if it's only from the anthropomorphic strata that you can measure the degrees of proximity
to the pure abstract machine has our composition of consistency not re-enveloped the abstract in the concrete have we not absolutely relativized the absolute we're supposed to absolutize relativity according to Deleuze but it's not clear in which this articulation of relative and absolute or in fact the identification of something like absolute movement on the plane of consistency which is a necessary component for destratification is strictly kind of available to those in Guattari given the terms given the pragmatic remits
which they set themselves and then I'm just going to end here, so then the question is does machinic pragmatism if this is the case then, does machinic pragmatism not risk lapsing into its more prosaic cousin, liberal prism. The question then is, if the question of machining prism is also how to you know, how can I act in such a way as to facilitate degrees, you know, the construction of planar consistency. How can I recognize those machining traits which are de-territorializing, decoding, intensificatory,
but in a way which is, which facilitates the consolidation of consistency. The question is, the role of concrete rules makes the evaluation of the consolidation of consistency relative to, well, to who? to who because we're always stratified subjectified territorialized okay and we're trying to identify those points that are you know at which we can kind of de-territorialize but in a cautious creative constructive way okay but then the kind of the um you know by enforcing the more you
enforce the imminence of the criteria of evaluation, or the more you insist on the necessary concretion of the rules, then the more it becomes difficult to say, well, who's going to tell you whether or not something is deterritorializing, intensificatory, destratificatory? Who gets to say? Okay, that's it. Thank you.