Deleuze/Guattari have developed a concept of the abstract machine in which the machines appear neither as universals nor as ideals; rather, they are to be understood in terms of the assembly, transformation, and combination of connections on a plane of consistency (non-formalized functions and non-formed matter) that traverse the abstract machines. They play a pilot role only insofar as they neither precede nor represent concrete reality, but are enveloped by it, and have a function that deconstructs reality. Deleuze/Guattari write, “An abstract machine in itself is not physical or corporeal, nor semiotic, it is diagrammatic […]. It acts by matter and not by substance, by function and not by form. […] An abstract machine is the pure matter-function-the diagram, independent of forms and substances, of expressions and contents that it will disseminate” (Deleuze/Guattari 1992: 195). At the level of consistency of the abstract machine, it is about the real combinatorics (deterritorialization) of non-formalized functions and non-formed matter-energies; it possesses the function of operating directly at the level of the material. However, there is no question, especially in view of a vitalist-inspired materialism debate of which Deleuze/Guattari are supposed to be the founders, that the two authors also relate their concept of matter and function back to socio-economic and political processes, to concrete propositional structures and real machines. Guattari writes: “‘At the beginning’ of propositional assemblages one finds neither the word nor the subject nor the system nor the syntax […], but one finds elements of semiotization, subjectivation, production of consciousness, of diagrammatism and abstract machines” (Guattari 1979: 43). The notion of the diagram cannot be separated at all from the notion of the abstract machine, the effects of which Deleuze described as follows: “(It) incessantly whirls the matters and the functions in such a way that incessant changes occur” (Deleuze 1987: 53). Accordingly, abstract machines are more than just operative, virtualized and virtualizing models that can always be updated in concrete machine structures and constitute the respective relations, components and parts of concrete machines and their temporal processes. The rotations of the flows and vortices, their turbulences has here the absolute of an intensive quality as reality. From the outset, as Hans-Dieter Bahr has also shown, such machines do not allow any unifying descriptions that could point to a naive causality and a unified interaction of the machines, even taking into account the four causalities according to Aristotle (materialis, formalis, finalis and efficiens). At the same time, the abstract machines are always enveloped by concrete structures. “For a proper abstract machine refers to the whole structure: it can be defined as a diagram of the structure. It is not linguistic, but diagrammatic and supralinear. The content is not a signifier and the expression is not a signified, but both are variables of the structure” (Deleuze/Guattari 1992:127
On the one hand, the abstract machine has a structuring effect as a diagram; on the other hand, the abstract machine breaks through structuring and stratification. In one direction, the abstract machine as diagram forms the pattern of envelopment and unfolding in a concept; in the other direction, it forms the pattern of a dissolution or stabilization of loose connections. The diagram possesses neither substance nor form and neither content nor expression have, It is a form of expression, thus the principle of the production and dissolution of form.
If now several such abstract machines interlock or translate each other, then a kind of plan is mostly contained in it, which however does not hold hypothetical, but always factual possibilities ready, which can condense themselves under circumstances to algorithmic functions. On the level of the machine, the diagram designates the way in which machines are ordered, rhythmized and organized, in order to subsequently couple themselves to other machines and thus produce consistency themselves, this e.g. in the sense of the mathematical group theory conceived by Abel and Galois, a configuration of fields by means of successive adjunction of symmetrical objects, which thus arises from a linkage given by the temporal successive executions of symmetries. (Cf. Deleuze 1992a: 231) Nevertheless, it would be wrong to conceive of the diagram merely as a drawing, plan, or as a (problematic) structure; rather, it already contains in its germ a (material) arrangement of structurality, e.g. directional vectors, which are able to set in motion a rhythmic development, namely that of the unfolding/folding of a machine itself, which moves through time as (event): the vector space becoming of the machine and its singularities within a differential topological field, where the field of directional vectors as well as the attractors define the “virtual” trajectories (of curves), of which never all are actualized. Thus, in order to construct the diagram of a machine, it is necessary to take into account the factual possibilities of how, when and where a machine performs its transformations and modulations, writing each of its components as a mathematical variable: The dimensions (attractors, vectors, trajectories) of a purely topologically constructed space in which each singular point (points by which curves change direction) is “defined” by dimensions (of average points, objective zones of indeterminacy) representing a particular or possible stage of the machine; empirical studies in this context might serve to determine the various trajectories of a system corresponding to a particular path in topological phase or vector space. Diagrams would thus be understood in this sense as topological vector spaces, to which always belong specific problematics and potentials, which in turn may be influenced by certain dimensions (attractors, trajectors, bifurcation) in a singular situation. The results of non-linear processes, when summarized in a diagram, are not written as straight lines, but as curves, which again refers to non-causal relationships. On the other hand, today just a multitude of current, numerical and hyperstable machines, which are dominated by powerful attractors, seem to constantly tend to form cruel mechanisms of solidification in order to mitigate any disturbances or irritations, so that one would probably have to say that the diagram always possesses aleatory and determinative structures at the same time, such as that of a Markov chain. This serves Deleuze/Guattari to describe a relation of two chains characterized by a common organization, without demanding a unitary or governing principle that ensures systematic commonality.
Let us go into more detail in the context of an essay by Ray Brassier. In Deleuze/Guattari, Brassier assumes, as far as the writing of A Thousand Plateaus is concerned, a new determination of the abstract, which would consist in the fact that, in the course of a new concept of praxis, one could speak of the abstract being enveloped by the concrete and requiring concrete rules, in order to arrive at the abstract, at an unformed and destratified, which, however, could certainly be determined positively and was characterized by the features of a plane of consistency (sign-particles, intensity-continuums, and deterritorialized currents are distributed on it). (Brassier 2022: 81) Brassier speaks, with regard to the real process of the abstract machine by which consistency is established, of a mapping that unites saying and doing; in the interplay of theory and practice, this level is established by means of very concrete rules that set the abstract in motion. What is at stake here is a performative, experimental, and machinic practice by which the level of traditional representation is abandoned and the real of the level of consistency is re-mapped in the production process without any teleological aspect and precisely not copied. (Ibid.: 83) The concrete layers and assemblages that must be assumed, since they envelop the abstract machines, must be simultaneously de-organized, de-stratified, and de-subjectified by them. The level of consistency then still retains enough of the layers when it wrests variables from them, which in turn operate on the level as functions of their own, as a torsion of the above-mentioned elements of the level of consistency. (Deleuze/Guattari 1992: 98) The stratified functions of the layers must thus be deformalized and fed to the torsion of an absolute, whirling movement (deterritorialization) in a smooth space. (Brassier 2022: 86) By means of the operation or processes of deformalization, then, the continuity of intensities, the emission of sign-particles, and the conjunction of flows are ensured at the level of consistency.
In his book on Foucault, Deleuze has already suggested that implicit in the production of the real is a specific relationship between saying and doing, which Brassier takes up to emphasize the importance of doing in particular when it comes to the production of the level of consistency. In this context, the destratifying practice of the abstract machine is always situated in the midst of an organized, stratified, and subjectified environment of concrete assemblages, which it is precisely from these points of view (organization, stratification, and subjectification) that it is necessary to deconstruct. The level of consistency thus wrests certain variables from the layers and assemblages in order to let them operate as destratified particles, flows, signs, and intensities, whereby this can only happen by means of concrete rules with which stratified functions can be deformalized in each case and exposed to absolute movement/deteritorialization. (Ibid.: 86) In these movements, bodies connect and differentiate in a smooth space of the plane of consistency. Abstract matter is therefore always unformed and destratified.
For Brassier, the ontological theory of stratification (which is twisted with the destratification of abstract machines) is central to Thousand Plateaus as the theory of a self-organization of matter, where this self-organization is to be understood as the real autoproduction of reality (including its representations), and this beyond Deleuze’s otherwise preferred split between virtual and actual. In doing so, Brassier resorts to the double division of content and expression that conditions every stratification, every order and structure. Content (matter) and expression (language) each possess a form and a substance, thus each has its own determination of form and substance; from this point of view, they are to be regarded as independent of each other and heterogeneous. Thus, an expression cannot be a representation of a content, and its function is not simply to describe a content.
At the physical level, the content is characterized by the sequences of molecular units that are formally coordinated. The expression has as its content compact-functional structures and molar compositions formalized by the structures superimposed on them, substance and form of the expression. Brassier summarizes, “Stratified content is formed matter; stratified expression is structured function” (ibid.: 89). The two disaggregated segments of content and expression are the origin of real physical, biological, and socio-economic strata and structures. In these strata, matter is always ascribed a determinate function in terms of its three formations, while function is ascribed a determinable form in terms of its molecular and semiotic substances. The respective strata, moreover, split and link their segments, make incisions and reconnect, and are each already related to the original abstract machines that establish an isomorphism between intelligible expression and sensuous content in the real (not in thought) in their destratifying ways. Concrete structures, in turn, stratify by structuring functions and shaping matters, and thus always envelop an abstract machine in each case.
On the one hand, the abstract machine is enveloped by a stratum (e.g. the technosphere) whose composition it helps to define; on the other hand, it possesses its own level of consistency, which it constantly destratifies. Stratification is associated with formed matter and structured functions, but when the abstract machine destratifies, the expressive functions and expressed matter are decoupled or deformed so that there are only pure functions and matter. Thus, in the real processes of the abstract machine, stratification (unity of composition) and destratification (deformation of matter and function) are not separate; rather, they are mutually dependent. Destratification here implies the articulation of non-formalized functions with a formless matter on a level of consistency, and this is done by means of asignified signs (expression) and heterogeneous intensities (content), the former employing tensors of strata to express different degrees of intensity qualities, while the latter indicate them as speed, conductivity, resistance, etc. Abstract machines compose a continuum of variation in which discontinuous differences and degrees of heterogeneous qualities are distributed and can lead to certain singular phenomena. Abstract here is to be understood as a function of variables, where quantifications by tensors entail a manifold of non-metric measures, i. e. not numbers as units, but heterogeneous intensities such as speed.
Brassier speaks of a novel synthesis of non-formalized functions and unformed matters, when a kind of diagrammatization takes place, by which signs, flows and particles are constructed and conjugated on a plane of consistency quite real qua deformalization. The diagram drives expression and content into the strongest deterritorialization, so that forms disappear on the consistency level and only functions remain. [1] For this practical (non-cognitive) composition of consistency, the diagrammitization of unformed matter and non-formal functions by means of tensors, the operators of the swirling of signs and flows, rules, which here have an optional character, are again necessary to wrest deformalized functions from the strata – they are planifications, concrete movements of the abstract that cut through all strata and recompose unformed matter, non-human becoming, and inorganic life again and again. (Ibid.: 96) This destratification in no way eliminates the difference between performance (doing) and competence (saying), which at the same time remain connected. At the same time, the rules necessary for the production of consistency remain optional (neither attached to a purpose nor contingent) and playful, that is, each move changes the rules; with rules one chooses and they are formulated as questions rather than providing immediate answers. Then, when choices are made, they provide answers to the specificity of the concrete structure and its territoriality, on the one hand, and to the actions of abstract machines and their degree of deterritorialization, on the other.
However, it is not only destratifying practices that open up potentialities, but always the asubjective concrete assemblages that even act (practice here possesses material and cognitive operators), by means of pre-individual collectivities (including the human component) that employ signs, flows, and codes to achieve various degrees of territorialization. However, these constraining conditions simultaneously empower actors to destratify. The more connections, differentiations, and dimensions of consistency are established by means of rules that allow for differentiations in terms of connections and dimensions, the more successful the level, which is the selective mode in which new connections, differences, and thresholds take place purely within the level in the first place. Here it becomes apparent that differences do not stand in a fundamental opposition to connections, but are formed by means of them, just as vice versa, so that Deleuze/Guattari can speak of transversal connections that arise between differences. By no means is it a matter of producing ideal only-differences. If the relations between differences do without conceptual mediation, then the essential is relocated to circumstances that are not characterized by EST, but ET. The ET here refers to connective syntheses and the concatenation of differences that transcend parts and have no predetermined totality.
The plane itself connects the dimensions by which it is also composed. The machine diagrammatics simultaneously connects unformed function and unformed matter by means of the plane of consistency in a real process of saying-doing, leading to a real of consistency that is in turn enveloped by concrete realities, by assemblages that are necessary to compose the plane and are therefore inseparable from it. However, it is not only the cognitive diagrammatics of us that selects, but also the level of the abstract machine itself that selects by means of rules and thus consolidates. If destratification is to occur, it cannot occur without stratification. The assemblages of the stratified and the abstract machines of the destratified now seem to be in a reciprocal process of interchangeability. The assemblages decide, just as they are decided by the abstract machines and the level of consistency.
[1] With respect to form, Deleuze makes two divisions: In the first outline, content concerns metastable entities that are selected as substance and put into a statistical order of connections and sequences that constitutes form. It is a content substance and a content form. The second division indicates the expression, where the form precedes the substance: Here the form consists in the construction of solid or molar structures. Here we are dealing with a form of expression and a substance of expression. While the first outline negotiates probabilities, the second outline is about structures. One encounters Deleuze’s notion of a genesis of structure, which transcends the formed structure to genetic conditions, with which a kind of indeterminate form or formless form becomes conceivable
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