‘Concrete Rules and Abstract Machines’ (some notes & comments on Brassier’s talk at the ‘A Thousand Plateaus and Philosophy’ London Workshop)


[What follows is a summary of, and some comments on, Ray Brassier’s talk regarding the final chapter of A Thousand Plateaus. Delivered in London, 2015, at the A Thousand Plateaus and Philosophy Workshop]

At the very least one can confidently say that the reputation of A Thousand Plateaus precedes itself. At times, its reputation even precedes a reader’s first encounter with the text itself. And in light of ATP‘s repute, one of the features of this text that is known by all is that its authors have written the book in such a way that a reader can skip ahead or begin from the middle of whatever plateau grabs their interest. We are told that ATP is a book written to liberate its audience and to affect us so that we feel free to pick and choose where the story begins and ends. As Massumi himself notes in his translator’s forward, reading ATP is best done in the same way one listens to a record:

“When you buy a record there are always cuts that leave you cold. You skip them. You don’t approach a record as a closed book that you have to take or leave. Other cuts you may listen to over and over again. They follow you. You find yourself humming them under your breath as you go about your daily business. A Thousand Plateaus is conceived as an open system…The author’s hope…is that elements of it will stay with a certain number of its readers and will weave into the melody of their everyday lives” (ATP, xiv).

Despite the kernel of truth in Massumi’s record metaphor (the element of truth being that it is the case that throughout the chapters of ATP Deleuze and Guattari remain consistent in their use of specific terms and concepts and thus develop a unifying thread throughout all the plateaus that renders a one’s decision of abrupt beginnings and endings of little consequence), to overemphasize this staggered and haphazard approach to ATP is to elide one of it’s most fundamental features; a feature that Brassier will seek to highlight in his reading of the final chapter, ‘Concrete Rules and Abstract Machines.’

For Brassier, there is in fact a fundamental or privileged plateau: namely, the chapter on the Geology of Morals. Why? Because when Deleuze and Guattari conclude their text with a set of concrete rules for effectuating specific abstract machines, they base this final chapter on the very logic of double articulation develop in the Geology of Morals plateau. For Brassier, what’s striking when one reads ATP is the consistency with which Deleuze and Guattari use their vocabulary. Thus, despite the appearance of a proliferation of concepts tied to particular sets of practices (art, science, philosophy, literature, psychoanalysis, etc.), the concepts developed throughout ATP in fact constitute a unified logical system. Thus, says Brassier, it is the logical and conceptual relationship between double articulation and the final chapter that gives the lie to the kinds of readings of this text that fall in line with Massumi’s prescribed approach. However, before directly engaging with the relationship between double articulation and the final chapter of ATP, Brassier spends some time clarifying Deleuze and Guattari’s text in relation to other philosophical positions, and specifically in relation to those philosophies that lay claim to the title of materialism.

I). What is it that makes rules ‘concrete’ and machines ‘abstract’?

For Brassier, Deleuze and Guattari’s materialism is neither a contemplative representation of a pre-existing material reality, nor a series of practical imperatives that presupposes and yet disavows a theoretical representation of the world. For all its idiosyncrasy, ATP is a very classical work – where ontology is at one with ethics. This is not to say that it is a conservative work. Rather, it is a contemporary reactivation of the classical task of philosophizing: a fusion of understanding what there is and how to live (what we should do). The title of the last chapter, ‘Concrete Rules and Abstract Machines,’ gives Brassier a hint at how Deleuze and Guattari reconceive of this classical aim of philosophizing. Namely, by developing what Brassier terms an ‘abstract materialism’ (unformed matter) in tandem with a ‘concrete ethics’ (practical prescriptions for action selected independently of universal law). Thus, the question Brassier aims to clarify and explain is this: how can concrete practices engage formless matter? This is another way of asking about the relation between the ABSTRACT (machine) and the CONCRETE (actions); or, in Deleuze and Guattari’s language, between the UNFORMED (i.e., matters/flows that characterizes the plane of consistency) and the EFFECTUATED (i.e., how concrete rules develop the abstract machine enveloped in the strata/stratification).

The kinds of rules or the practical injunctions that Deleuze and Guattari are interested in are not simply rules understood as a set of prescriptions to be carried out upon pre-existing matter. As Brassier notes, Deleuze and Guattari aim to develop a set of rules for both thinking and acting in the world the essence of which are not simply the genesis of true as opposed to false representations of reality. Thus, action cannot merely rely on a true representation of reality just as thinking cannot simply rely on actualized praxis. For D&G, thinking is not to be confused with the function of representation but rather is the activity of diagramming a plane of consistency from within stratified existence. For Brassier, thought does not give us the world as it is but constructs a map of singular and ordinary points that define our specific strata. Likewise, action doesn’t simply carry out an idea or program but aims at freeing elements from its strata, since it aims at all the terms found in ATP that begin with the prefix de– (-territorialization, -stratification, -coding). It is for this reason that Brassier goes on to say that the kinds of rules we get from the final chapter of ATP “are concrete to the extent that they effectuate the abstract”; to the extent that they destratify, deterritorialize, and decode, what is stratified, territorialized, and overcoded/captured. In Brassier’s own terms, what is at stake in understanding the relation between the abstract and the concrete are the freeing up  of what is implicit in stratification toward the aim of putting what is fixed, coded, and rigid, into continuous variation (deterritorialization) and in order to repurpose it for an altogether different functioning on an altogether different plane (of consistency). In a key passage from the Geology of Morals plateau Deleuze and Guattari write, “The plane of consistency is always immanent to the strata; the two states of the abstract machine always coexist as two different states of intensities” (ATP, 57). Thus, if the task of this “diagrammatics” of thought and practice is to liberate formless matter and non-formal functions from stratification, and if this freeing up of unformed matter and non-formal functions take place by means of an absolute deterritorialization, then the subsequent question is one of determining, in concrete terms, the actuality of formless matter and non-formal functions. In other words, what is retained from the strata in the process of deterritorialization?

It is at this point that Brassier offers the following hypothesis: What would be retained from stratified function on the plane of consistency is the torsion of destratified intensities, particles, signs and flows. That is, what one is left with regarding a destratified intensity are the traits or components of the plane of consistency. However, says Brassier, the point of torsion is indiscernible from the vantage point of anyone invested in the distinction between self and non-self, personal and impersonal, and hence this approach to composing the plane of consistency requires caution. “Caution is required for the composition of the plane of consistency.”

II). Absolute and Relative Deterritorialization & The Principle of Immanence

It is at this point where concrete rules become relevant since we have to understand how the composition of consistency requires deformalizing stratified functions and subjecting them to the torsion of absolute movement. For Brassier, a concrete rule is concrete and practical insofar as it affects a stratum with this “torsion of absolute movement.” What is important in Brassier’s formulation here (and is crucial for his whole interpretation of this final chapter), is the following: the mechanism by which stratified functions and formed matter are transformed into destratified functions and unformed matter is this “torsion of absolute movement.” For Brassier, just as important as the role played by absolute deterritorialization in the formula is the idea of torsion as a form of measurement. Torsion = measure of absolute movement. What effects the liberation of particles, signs, and flows from their strata is this process of torsion, or, absolute movement. Absolute movement, in other words, is identical to the process-of-torsion, while torsion-as-category-of-diagramming the world is that which allows us to discriminate between possible points in striated space whereby absolute and relative movements can be catalyzed.

 We can simplify all of this and say that destratification exists whenever absolute movement serves as the determining element in a stratified relation. When absolute movement determines, affects, conditions, and guides the relative movements of stratification and striated space what is effected is precisely the ‘freeing up’ effect Brassier mentioned earlier regarding the relation between the abstract and the concrete. When absolute movement determines the relative functioning of striation/stratification, what is produced are a set of decoded flows, lines of flight; or what amounts to the same, the liberation of previously formed-matter and bodies with assigned functions. At this point Brassier quotes from section D in 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. A movement is relative, whatever its quantity and speed, when it relates a body considered as One to a striated space through which it moves, and which it measures with straight lines, if only virtual…D is absolute when it…brings about the creation of a new earth, in other words, when it connects lines of flight, raises them to the power of an abstract vital line, or draws a plane of consistency. Now what complicates everything is that this absolute D necessarily proceeds by way of relative D, precisely because it is not transcendent” (ATP, 509-10).

Of interest here is not simply the relation of the absolute to the relative (a relation of determining factor and determined element), but the necessity that pertains to the absolute. Absolute deterritorialization by necessity proceeds by means of relative deterritorialization. And this necessity of absolute movement to proceed by means of relative movement is grounded in the principle of immanence. It is this link between Absolute Deterritorialization, Relative Deterritorialization, and the criteria of immanence that guides Brassier’s critique and analysis of ATP’s final chapter.

While Brassier does not go into the details of how these three terms relate to one another despite the crucial role these terms play in his critique, we can roughly sketch out the argument he has in mind based on the passage previously cited. In the passage above, a specific set of propositions are offered to the reader regarding the relationship between the absolute, the relative, and their immanence:

i). The absolute is not relative to anything but itself, thus maintaining its status as truly absolute – (“…what is primary is an absolute deterritorialization an absolute line of flight, however complex or multiple…This absolute deter becomes relative only after stratification occurs on that plane or body: It is the strata that are always the residue, not the opposite” (ATP, 56)).

ii). The relative is relative to what is absolute, thus maintaining its status as truly relative to something other than itself – (“A movement is relative, whatever its quantity and speed, when it relates a body considered as One to a striated space through which it moves…” (ATP, 509)).

iii). Despite the Absolute being independent from anything other than itself, Absolute Deterritorialization remains tied to the relative territorializations, stratifications, and striations of the relative movement of deterritorialization – (“Now what complicates everything is that this absolute D necessarily proceeds by way of relative D, precisely because it is not transcendent” (ATP, 510)).

iv). D&G argue for this relation of the Absolute as existing by way of Relative movements in order to ensure that their version of the Absolute is also one in which what is Absolute is also immanent to the reality of things – (“There is a perpetual immanence of absolute deterritorialization within relative deterritorialization; and the machinic assemblages between strata that regulate the differential relations and relative movements also have cutting edges of deterritorialization oriented toward the absolute. The plane of consistency is always immanent to the strata…” (ATP, 56-7)).

v). However, as Brassier will point out, rendering the Absolute as immanent to the world is tantamount to making the Absolute depend upon, and thus relative to, its relative movements of deterritorialization for its reality.

vi). Thus, it would seem that what was initially said to be Absolute (since, in the last instance, this process exists in such a way as to be independent from everything other than itself) is revealed to be, in actual fact, dependent upon something other than itself (Relative Deterritorialization) for its reality. In other words, what makes the Absolute “real” is the fact that it exists as, or inheres within, relative movement as such.

One main consequence Brassier will draw out from these propositions on the nature of absolute movement is that D&G‘s position appears to subscribe to the view that if one wants to judge whether a process is of an absolute or relative nature, this judgment remains wholly depend upon the strata within which one resides. If this is the case, then it would be possible for there to be a situation where certain traits or functions can appear to be destratifying and absolute (absolute movement) from one perspective while appearing to be destratifying but relative (relative movement) from another. As Brassier formulates it: “The more you enforce on the immanence of the criteria of evaluation … the more it becomes difficult to say whose going to tell you whether or not something is deterritorializing, intensificatory.”

It is for these reasons that Brassier asks at the end of his lecture whether or not we have simply relativized the absolute? In other words, does machinic pragmatism lapse back into liberal pragmatism? The question for D&G, as Brassier points out, is the following: how can I act in such a way as to facilitate the construction of the plane of consistency? How can I recognize those traits that are decoding but in a way that facilitates the consolidation of consistency? Brassier’s problem, then, is that the concrete rules developed by D&G seem to ultimately reside within a perspectivalist framework. Certain traits or function, while being destratifying from one perspective, may turn out to be stratifying, constraining, and deadening from an other perspective. This, then, is the suspicion that what D&G have done is simply relativize the absolute, where the absolute would be the seat of justifiable appraisal of becomings, by locating the grounds for the appraisal of becoming within each and every perspective one may take on becoming itself.

III). ‘It’s not clear what a pure abstract machine could be’ – Brassier

If one agrees with Brassier’s position, that D&G effectively relativize the absolute; that D&G consequently divest themselves of the means to discriminate between relative and absolute movement since the measure of absolute deterritorialization is perspectival; a few consequences follow regarding the relationship between the rules for effectuating the abstract machines that are ostensibly buried within strata themselves. Given that one of the principle tasks D&G set for ATP as a whole is that of constructing various diagrams in order to liberate the elements of various strata in the world (formed matters and bodies with assigned functions), and in light of Brassier’s comments, a few problems arise for the relationship between concrete rules and abstract machines as conceived by D&G.

To briefly recapitulate what has been said: concrete rules are fabricated in order to “develop the abstract machines enveloped in the strata.” If these concrete rules are successful in constructing their plane of consistency, they then effectuate the abstract machine which ,”cuts across all stratifications, develops alone and in its own right on the plane of consistency whose diagram it constitutes … piloting flows of absolute deterritorialization (in no sense, of course, is unformed matter chaos of any kind)” (ATP, 56). This general movement of developing the abstract machines enveloped in the strata, then, is how one goes from the relative to the absolute. As D&G remark, one does not achieve this passage

“simply by acceleration […] What qualifies a deterritorialization is not its speed…but its nature, whether it constitutes epistrata and parastrata and proceeds by articulate segments…or, on the contrary, jumps from one singularity to another following a nondecomposable, nonsegmentary line drawing a metastratum of the plane of consistency” (ATP, 56).

However, in order to fabricate concrete rules one requires some degree of knowledge regarding what is relative and what is absolute in any given strata. In order to fabricate concrete rules that are effective one needs to know how to measure degrees of deterritorialization (as Brassier notes, caution is required in the construction of the plane of consistency and is watchword of ATP as a whole). How does one measure degrees of deterritorialization? The answer given by D&G and emphasized by Brassier is the following: “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).

It is this ‘presumably pure abstract machine’ that is supposed to serve as the measure of degrees of deterritorialization from the vantage point of stratified existence. In other words and despite the fact that we always find ourselves caught in the middle; that we always must begin in the middle of things; this ‘presumably pure abstract machine’ is the means by which we can create concrete rules that will effectuate a deterritorialization and destratification; those practical rules that will effectively usher in a qualitative transformation of strata themselves. Brassier concludes on two points of tension with this final chapter of ATP.

First, a pure abstract machine would be an abstract machine that is entirely developed. An abstract machine that was in reality ‘pure’ would be one that is no longer tethered to the relative movements of stratification and would no longer be “compromised by envelopment by a strata.” The idea of a entirely developed abstract machine in all its purity would seem to go against D&G’s various claims throughout ATP that what we must always be privy to is the coexistence of intensities as opposed to searching for their sequential, causal, or evolutionary, linkages. This is most clearly seen in their treatment of how best to account for the historical emergence of the State relative to non-State societies. As they write, “everything coexists, in perpetual interaction […] The nomad exists only in becoming, and in interaction; the same goes for the primitive. All history does is to translate a coexistence of becomings into a succession” (ATP, 430, my emphasis). At the very least there appears to be, on Brassier’s reading, an unresolved tension between this pure abstract machine which is no longer compromised by envelopment (i.e., it is entirely developed and free to relative movement) and D&G’s commitment to privileging the coexistence of intensities over and against orders of succession and evolution.

Second, and as we have already seen, Brassier ends by explicitly dealing with his claim that D&G have relativized the Absolute as opposed to their claim to have absolutized relativity. Brassier’s problem regarding the relationship between Absolute deterritorialization, relative deterritorialization, and the principle of their mutual immanence,  is that concrete rules themselves are wholly dependent on the strata within which they reside. Without a means of measuring degrees of deterritorialization in spite of one’s strata (while still acknowledging one’s stratified preconditions) we end up in a situation whereby what appears as absolute movement within one strata can appear as a relative or regressive movement from another. Hence the claim that D&G have simply relativized the absolute – where the absolute would be the seat of justifiable appraisal of becomings – by locating the grounds for the appraisal of becoming within each and every perspective one may take on becoming itself.


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