Chromatic Aberrations

Back to Deleuze and Guattari. Two more postulates to go, one after this. Like the last time, I’ll be looking at the fourth chapter or plateau in ‘A Thousand Plateaus: Capitalism and Schizophrenia’. With regards to the previous postulate it was established that while content and expression are not opposed to one another on their own, but they are once formalized. Moreover, while they retain their independence, they still feed into each other. Most importantly, the postulate also helped to define machinic assemblages and collective assemblages of enunciation, as well as the abstract machine and how it is and is not a diagram.

Like last time, the relevant part of the book is titled ‘November 20, 1923 – Postulates of Linguistics’ and this time I’ll be covering the third of these postulates, titled by the two (92):

“III. ‘There Are Constants or Universals of Language That Enable Us to Define It as a Homogeneous System’”

Once again, in case you don’t feel like reading further, their reply to this is, in short, simply no. Anyway, judging by the postulate alone it shouldn’t take much to figure out that this postulate has a lot to do with structuralism. Deleuze and Guattari (92) kick off by stating that:

“The question of structural invariants—and the very idea of structure is inseparable from invariants, whether atomic or relational—is essential to linguistics.”

Okay, but what’s the deal? They (92) explain:

“It is what allows linguistics to claim a basis in pure scientificity, to be nothing but science … safe from any supposedly external or pragmatic factor.”

As pointed out in the plateau thus far, for them language doesn’t stand outside people, hence the point out external or pragmatic factor reiterated here. They (92) elaborate that the role invariants lead to six related assumptions:

One, it is assumed that there phonological, syntactical and sematic constants (92):

“[T]he constants of a language (phonological, by commutativity; syntactical, by transformativity; semantic, by generativity)[.]”

Two, it is assumed that these constants are decomposable (92):

“[T]he universals of language (by decomposition of the phoneme into distinctive features; of syntax into fundamental constituents; of signification into minimal semantic elements)[.]”

Three, these constants can be hierarchized (92):

[T]rees linking constants to one another, with binary relations between trees (see [Noam] Chomsky’s linear arborescent method)[.]”

Four, there is an idealized capacity to produce utterances, “the speaker-hearer’s knowledge of his [or her] language”, which, famously, according to Chomsky (4) is competence, as distinguished from performance, which is the actual production of utterances in “concrete situations” that is judged according to the ideal capacity, as explained in ‘Aspects of the Theory of Syntax’. In Deleuze and Guattari’s words (92):

“[C]ompetence, in principle coextensive with language and defined by judgments of grammaticality[.]”

Five, homogeneity is all-encompassing (92):

“[H]omogeneity, bearing on elements and relations as well as intuitive judgments[.]”

Six, while, I’d say that, this does not happen by necessity, there is this temptation to give primacy to synchrony, i.e., dealing with all there is at a give point in time (think of it as like a slice of a dice) instead of as a thinking of it all as a temporal continuum, which is diachrony (think of all the slices that make the dice, but without distinguishing between the slices as they are what is sliced from the dice and not what make the dice). This results in treating certain states of affairs as a constant, as assessed at some point in time, as something beyond itself, as what just is and ought to be, as transcendent or universal, according to which everything is then to be judged. In their (92) words:

“[S]ynchrony, which erects an ‘in-itself’ and a ‘for-itself’ of language, perpetually moving from the objective system to the subjective consciousness that apprehends its principle (that of the linguist himself or herself)[.]”

I’m not going to paraphrase these six assumptions beyond what I just did as I take it that the reader is familiar enough with linguistics. Also, the assumptions listed by the two are actually surprisingly self-explanatory, for once. Back to the problem for the two, they (92) argue:

“One can juggle all of these factors, subtract some or even add new ones. They go together, however, because the essentials of all of them are present on the level of any one.”

So, in other words, as pointed out already, a closed system is neat in the sense that it is a closed system. Its internal mechanisms explain it. There is no external influence to it. Therefore it remains the same, or constant, homogeneous and universal. They (92) provide an example:

“[T]he distinction between speech and language is recapitulated in the distinction between competence and performance, but at the level of grammaticality.”

They (92) note that this may lead to objection, linguists pointing out that there is room for improvement and the willingness to do so, by, for example, including pragmatics in the mix. That said, they (92) argue that the problem would still persist as it would, in the case of pragmatics, result in adding yet another factor that relies on constants or universals, hence the earlier point on juggling the factors, adding and/or removing them. In other words, it would still remain a closed system. Pragmatics then remains as either what is beyond language, out there, not, strictly speaking, language, or as something that is subordinated to language. The gist of this is that they are not buying this. They call shenanigans. Using the example of the arborescent model, they (92) continue:

“[W]hen efforts are made to make Chomsky’s trees bud and to shatter linear order, as long as the pragmatic components marking the ruptures are placed above the tree or effaced from the derivation nothing has really been accomplished, one has failed to constitute a rhizome.”

If you have no idea what a rhizome is, well, you are, once more, out of luck because this is how Deleuze and Guattari chose to write the book, in non-linear a-centered fashion, as a rhizome. So, there you go, you are welcome. The problem for them (92) is that if you fix things, then indeed you fix things. It was elaborated in quite the detail in the previous essay covering the second postulate that the abstract machine is not static, hence the moniker machine. So, they (92-93) argue:

“[T]here 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 built around variables and variations.”

This might seem a bit far off, a stretch if you will, but in the past I’ve argued in my essays that attempting to fix the issues related to categorization, say, binaries, with more categorization is hardly an answer. Why? Well, it’s because it results in just more of the same. Something is added, removed and/or altered, but the system remains the same. You address the symptoms, not the cause of the symptoms. So, as pointed out above, dividing an entity results in a dividual. A binary would be the result of the first cut, this part and that part, the one and the other part, the right and the wrong and so on. Attempting to fix the split, the resulting dividual, with more splitting doesn’t fundamentally change anything. It only increases the number of parts, hence the irony of, for example, calling oneself an individual yet putting labels on oneself. Back to Deleuze and Guattari, they (93) exemplify this, in reference to Chomsky and William Labov, by stating that:

“Every language is an essentially heterogeneous reality; linguists know this and say so.”

Well, yes, but do go on (93):

“But this is a factual remark. Chomsky asks only that one carve from this aggregate a homogeneous or standard system as a basis for abstraction or idealization, making possible a scientific study of principles.”

Aha, right, reducing heterogeneity to homogeneity is the issue? Well, they (93) add:

“Limiting oneself to standard English is thus not the issue, for even a linguist who studies Black English or the English of the ghettos is obliged to extract a standard system guaranteeing the constancy and homogeneity of the object under study (no science can operate any other way, they say).”

So, no. That’s not really the issue. Coming up with parallels, well, comes up with just that, parallels. What’s worth paying attention here is how a standard is always abstract as abstracted from something concrete. The problem that comes with this is that this applies not only to standards, but also to the so called non-standards. How so? Well, that’s because the non-standards also appear to us as standards, of sorts. They are like the standards of what is considered non-standard, for example Black English, when contrasted with the standard, for example American English. What you have instead is variation, which is then thought to consist of varieties, which, in turn, are like synchronous snapshots of how certain groups of people speak. Anyway, I’ll let Deleuze and Guattari (93) continue:

“Thus Chomsky pretends to believe that by asserting his interest in the variable features of language, Labov is situating himself in a de facto pragmatics external to linguistics.”

They are having none of this, nor is Labov in their view, so they (93) argue that:

“When [Labov] brings to light lines of inherent variation, he does not see them simply as ‘free variants’ pertaining to pronunciation, style, or nonpertinent features that lie outside the system and leave the homogeneity of the system intact; neither does he see them as a de facto mix between two systems, each homogeneous in its own right, as if the speaker moved from one to the other.”

Instead, they (93) add:

“[Labov] refuses the alternative linguistics set up for itself: assigning variants to different systems, or relegating them to a place outside the structure. It is the variation itself that is systematic[.]”

So, as I pointed out earlier, what may have seemed to bear no relevance, addressing a split with further splits doesn’t resolve the split. That’s just more splits. Approving of Labov, they (93) assert:

“[He] sees variation as a de jure component affecting each system from within, sending it cascading or leaping on its own power and forbidding one to close it off, to make it homogeneous in principle.”

It’s not worth quoting everything Deleuze and Guattari have to say on Labov in this regard, so I’ll do it in my own words instead. The point is that variation is within the system. It is an infinite continuum, not a finite set of things. In other words, as they (93) discuss, a speaker of a supposed non-standard doesn’t pass from one system to another, but rather within one system, that is of language. Oh, and, yes, I know, heresy! We can have none of such! Heresy! Vile heresy! Why? Well, on one hand one can concede that standardization has its benefits, you know it’s convenient, productive and efficient when there is little time wasted on having to clarify things, back on forth, but on the other hand, if there is no (one) standard to be juxtaposed with another (the other) non-standard, then how on earth can one assert a standard? Indeed, that’s a good question, but also sort of the whole point. Standards, as handy as they are, can function as a medium. If you fail to meet the standard, you know as scientifically proven to be so, then well, too bad for you. Learn the language! Get with the program! So, instead reiterating things a bit here, Deleuze and Guattari (93-94) argue:

“Must it not be admitted that every system is in variation and is defined not by its constants and homogeneity but on the contrary by a variability whose characteristics are immanent, continuous, andregulated in a very specific mode (variable or optional rules)?”

In other words, the system is not defined by homogeneity but by heterogeneity, not by constants but by variation. The system is not static but dynamic. Examining it as a system with constants ignores how it keeps changing, becoming, inasmuch as it does, of course. Anyway, moving on, Deleuze and Guattari (94) challenge what a language is:

“In the course of a single day, an individual repeatedly passes from language to language. He successively speaks as ‘father to son’ and as a boss; to his lover, he speaks an infantilized language; while sleeping he is plunged into an oniric discourse, then abruptly returns to a professional language when the telephone rings.”

Before explaining this further, they (94) note that some will object, claiming that it’s the same language, but the variations have to do with extrinsic factors. They (94) object to such objections, arguing that in that case the question is prejudged:

“First, it is not certain that the phonology is the same, nor the syntax, nor the semantics. Second, the whole question is whether this supposedly identical language is defined by invariants or, on the contrary, by the line of continuous variation running through it. Some linguists have suggested that linguistic change occurs less by systemic rupture than by a gradual modification of frequency, by a coexistence and continuity of different usages.”

They (94) provide “I swear!” as an example and argue, as listed above, that it depends on the assemblage, i..e, who says it and to whom. They then (94) emphasize that:

“[T]here is no reason to say that the variables are merely situational, and that the statement remains constant in principle.”

Instead, they (94) argue that:

“Not only are there as many statements as there are effectuations, but all of the statements are present in the effectuation of one among them, so that the line of variation is virtual[.]”

Unless I’m mistaken, this is the point I made in a previous essay about direct discourse building on indirect discourse. Clarifying this, they (94) rephrase:

“[I]n other words, [it is] real without being actual, and consequently continuous regardless of the leaps the statement makes.”

What results from this, they (94) characterize as:

“To place the statement in continuous variation is to send it through all the prosodic, semantic, syntactical, and phonological variables that can affect it in the shortest moment of time (the smallest interval). Build the continuum of ‘I swear!’ with the corresponding transformations.”

Summarizing this, they (94) argue that to them this is pragmatics, that is a pragmatics internal and immanent to language, not external to it. They (94) specify that taking the situation into account does not mean that the difference is to be explained by the context, by which they mean reducing it to a matter of content as it results in “extracting a pseudoconstant of content[.]” That is why I used the word assemblage earlier on, instead of context or situation, as I take it that you, the reader, have already parsed together what an assemblage is. This reduction may seem confusing, so in their (94) words:

“Everything is explained by the situation of the child in relation to its father, or of the man in relation to castration, or of the citizen in relation to the law.”

Instead, they (94) propose:

“Placing-in-variation allows us to avoid these dangers, because it builds a continuum or medium without beginning or end.”

So, from finity to infinity. They (94-95) elaborate what it entails and what it doesn’t:

“Continuous variation should not be confused with the continuous or discontinuous character of the variable itself: the order-word, a continuous variation for a discontinuous variable.”

Again, from finity to infinity, no beginning, no end. To be more specific, they (95) add:

“A variable can be continuous over a portion of its trajectory, then leap or skip, without that affecting its continuous variation; what this does is impose an absent development as an ‘alternative continuity’ that is virtual yet real.”

Clarifying their view on constants, they (95) characterize them as:

“A constant or invariant is defined less by its permanence and duration than by its function as a center, if only relative.”

They (95) elaborate this through music, arguing that in the tonal system of music there are laws of resonance and attraction that determine stable and attractive centers, functioning to organize forms. What results from this, they (95) argue, is the major mode, “a linear, codified, centered system of the arborescent type.” They (95) then characterize the atonal, the minor mode as decentered, fleeting, unstable, or, well, less stable, and irreducible to tonality, always on the move, developing, dissolving and transforming itself to an extent that form itself is dissolved, undistinct. I don’t think I’m competent enough in all things music to explain this properly, but at least I tried. I acknowledge that I might be off, so there’s that. It’s always better reading yourself anyway. In summary, Deleuze and Guattari (95) argue:

“By placing all its components in continuous variation, music itself becomes a superlinear system, a rhizome instead of a tree, and enters the service of a virtual cosmic continuum of which even holes, silences, ruptures, and breaks are a part.”

Therefore they (95) argue that:

“[T]he important thing is certainly not to establish a pseudobreak between the tonal system and atonal music; the latter, on the contrary, in breaking away from the tonal system, only carried temperament to its ultimate conclusion[.]”

I take it that the point is not to juxtapose the two, set them as a binary pair, the one and the other. Instead, they (95) argue for going the exact other way:

“[T]he ferment in the tonal system itself … that dissolved temperament and widened chromaticism while preserving a relative tonality, which reinvented new modalities, brought a new amalgamation of major and minor, and in each instance conquered realms of continuous variation for this variable or that.”

Pay attention to the word ferment, a process of bringing about change, as in fermenting sugars into alcohol. Anyway, I’ll let them (96) finish this line of thinking:

“This ferment came to the forefront and made itself heard in its own right; and, through the molecular material thus wrought, it made audible the nonsonorous forces of the cosmos that have always agitated music[.]”

They (96) end their detour into music in this postulate by stating that:

“Music is not alone in being art as cosmos and in drawing the virtual lines of an infinite variation.”

The key here is, I believe, the part on infinite variation. Moving on and returning to linguistics, they (96) acknowledge that linguists might object to their inclusion of music into the discussion of language. They (96) concede that indeed music is not language as there is no correspondence, but also point out that they are not suggesting that. Instead they (96) ask to reject the presupposition of the distinctiveness of language and speech, as well as to reject what such distinction entails, relegation of certain features outside language. Those of you interested in what they call the voice-music relation, how voice is separated from music in the sense that music accompanies voice, can take a closer look at this page (96). I think I’d only muddle it here as I don’t think I’m qualified to say much about music. It’s just not my forte. I’d love to learn more, of course, but it is what it is. Anyway, the point here is, I think, that voice and music are considered separate, albeit this is not a necessity rather than something that has come to be. They (96) make note of speaking in tongues as an examplary exception, fusing or blurring voice and instrument, making them no longer merely speak or play.

Taking cues from music, Deleuze and Guattari (97) characterize linguistics and juxtapose it with language:

“Linguistics in general is still in a kind of major mode, still has a sort of diatonic scale and a strange taste for dominants, constants, and universals. All languages, in the meantime, are in immanent continuous variation: neither synchrony nor diachrony, but asynchrony, chromaticism as a variable and continuous state of language.”

What they (97) suggest instead of the type of linguistics they refer to is what they call “chromatic linguistics”. The emphasis is on internal pragmatics, intensities and values. Moving on, they (97) jump to discuss language and linguistics, as juxtaposed with style and stylistics. They (97) begin by characterizing style as:

“What is called a style can be the most natural thing in the world; it is nothing other than the procedure of a continuous variation.”

The irony that follows, in just a moment, is that what they here call style is probably what I’d call freestyle. So, they (97) state that style, as it is understood in linguistics, is problematic:

“Of the dualisms established by linguistics, there are few with a more shaky foundation than the separation between linguistics and stylistics[.]”

Bold statement, but I’ll let them (97) finish:

“[A] style is not an individual psychological creation but an assemblage of enunciation, it unavoidably produces a language within a language.”

This touches one of my previous essays, how style affects writing. That’s why I just noted that going astray from it, intentionally, is rather freestyling. As examples of this, that is contrary to how it is defined in linguistics, they (97-98) list a number authors who are in what they call a bilingual situation: Franz Kafka, Samuel Beckett, Gherasim Luca and Jean-Luc Godard. Skipping bits here, Deleuze and Guattari (98) argue that:

“[T]he essential thing is that each of these authors has his own procedure of variation, his own widened chromaticism, his own mad production of speeds and intervals.”

They (98) characterize this as stammering, no, not stammering as such, this is not to make fun of people who do, but making the language itself stammer. They (98) use the example of being, to be, and and, the conjunction. In French they are est and et, but they are identical in pronunciation, so they (98) exemplify this movement as the redundancy of “AND … AND … AND …”. That’s why I just made a mess of a previous sentence, making the automatic language checking tool object to my writing by placing and and and one and after another and. Haha, get it? They (98) further characterize making language stammer as:

“To be a foreigner, but in one’s own tongue, not only when speaking a language other than one’s own. To be bilingual, multilingual, but in one and the same language, without even a dialect or patois. To be a bastard, a half-breed, but through a purification of race. That is when style becomes a language. That is when language becomes intensive, a pure continuum of values and intensities. That is when all of language becomes secret, yet has nothing to hide, as opposed to when one carves out a secret subsystem within language.”

I think it’s worth emphasizing that it is a movement of from style to language, not from language to style, hence the point by the two about not creating a mysterious subsystem to language. In a previous essay I focused exactly on a what is, arguably, a secret subsystem of language, held as such for no apparent reason by priests who oppose sorcery. Yeah, we can have none of that!

If you fail to understand that, the thing with style is that you are, in fact, freestyling. It’s improvised, experimental. Simply put, in their view, language is style. Inasmuch as you make sense, you can’t fuck it up. As long as someone gets it, which is not the same as everyone getting it, you are doing it right. If someone says that you aren’t doing it right, according to some made-up standard, some abstraction that is abstracted from something concrete, from some actual state of affairs defined by some who happen to be in the privileged position to do so (cough, cough, priests), you can tell them to fuck themselves. If someone tells you that you aren’t, let’s say, formal enough, that you are all over the place or that you are, how to put it nicely, frothy or airy-fairy, they are really just trying to discipline you, to normalize you, to make you conform to whatever style they uphold as the standard. That’s power relations for you.

Now, the point of that is not to copy someone else’s style, attempting to be like that person. Why? Well, because that’s just like treating style as a standard, something that you need to adhere to. Are we in the habit of writing like the people we read? I’d say yes. Is it a problem then? I’d say yes and no. If you just imitate others, for the sake of imitating them, for the glory, if you will, then yes, that’s a problem. But if you cannot help it, if it just happens, if it is just like it passes through you, like it’s speaking in tongues, then no. There’s no way you can come up with your own style that’s unlike other styles because it’s not like all direct discourse isn’t based on indirect discourse, as discussed in a previous essay.

After making the point on stammering, Deleuze and Guattari (99) further characterize chromatic linguistics:

“We are no longer in the situation of linguists who expect the constants of language to experience a kind of mutation or undergo the effects of changes accumulated in speech alone. Lines of change or creation are fully and directly a part of the abstract machine.”

Deleuze and Guattari are not linguists and they are fully aware of this. They don’t claim to be either. So, if you’ve been wondering who they build on in linguistics, then, well, it is revealed in this postulate. They (99) continue:

“[Louis] Hjelmslev remarked that a language necessarily includes unexploited possibilities or potentialities and that the abstract machine must include these possibilities or potentialities.”

That may seem surprising, but it’s not particularly surprising for them to work on Hjelmslev. After all, open endedness, possibilities and potential is recurring theme in ‘A Thousand Plateaus’, if you haven’t noticed. In the notes (526) it’s pointed out that the oeuvre in question is Hjelmslev’s ‘Language: An Introduction’. Anyway, Deleuze and Guattari (99) explain their interest:

“’Potential’ and ‘virtual’ are not at all in opposition to ‘real’; on the contrary, the reality of the creative, or the placing-in-continuous variation of variables, is in opposition only to the actual determination of their constant relations.”

I believe I may have mentioned this earlier already, also in another essay or other essays, but it’s worth reiterating and emphasizing that the virtual is not opposed to the real. In ‘Difference and Repetition’, Deleuze (208-209) states:

“The virtual is opposed not to the real but to the actual. The virtual is fully real in so far as it is virtual. … [T]he virtual must be defined as strictly a part of the real object – as though the object had one part of itself in the virtual into which it plunged as though into an objective dimension. … The reality of the virtual consists of the differential elements and relations along with the singular points which correspond to them.”

That might only confuse the reader, so I think it’s helpful to take a look at what Brian Massumi (36-37), has to say about the virtual and the actual in ‘A User’s Guide to Capitalism and Schizophrenia: Deviations from Deleuze and Guattari’:

“The virtual is the future-past of the present: a thing’s destiny and condition of existence[.] … To avoid philosophical baggage, they are more likely to say that a thing is ‘actual’ than that it ‘exists.’ [A]ctuality is dynamic they use the word ‘becoming’ in place of ‘being.’ A thing’s actuality is its duration as a process – of genesis and annihilation, of movement across thresholds and toward the limit. The virtual is real and in reciprocal presupposition with the actual, but does not exist even to the extent that the actual could be said to exist. It subsists in the actual or is immanent to it.”

I think Massumi does a very good job explaining virtual and actual, virtuality and actuality. Deleuze and Guattari tend to use rather uncommon vocabulary and that has to do with certain baggage that comes certain words, as noted by Massumi. He (37) clarifies this further:

“The element of immanence – thought-matter – could be called eternal, but not without introducing an unwelcome religious or Platonic tinge.”

Indeed, there is that problem with working on existing concepts. So, in summary, it was established that the virtual is not in opposition to the real. It is, in fact, real, well, inasmuch as it is. Once actualized, it still subsists in the actual, as clarified by him (37). Moreover, actuality has to do with crossing the threshold to being actual, followed by no longer being actual, as also clarified by him(37). Where was I on the postulates? Right, back to Deleuze and Guattari on Hjelmslev. They (99) state:

“Each time we draw a line of variation, the variables are of a particular nature (phonological, syntactical or grammatical, semantic, and so on), but the line itself is apertinent, asyntactic or agrammatical, asemantic.”

Okay, do elaborate (99):

“Agrammaticality, for example, is no longer a contingent characteristic of speech opposed to the grammaticality of language; rather, it is the ideal characteristic of a line placing grammatical variables in a state of continuous variation.”

In other words, it’s not longer a matter of correct vs. incorrect, but about a continuum, variables in variation. They (99) go on to provide examples of incorrect or agrammatical uses of language, which can be then reconstituted as grammatical in order to figure out the agrammatical came to be. However, they (99) object to this:

“[W]e should avoid taking the view that the atypical expression is produced by the successive correct forms. It is instead the atypical expression that produces the placing-in-variation of the correct forms, uprooting them from their state as constants.”

We are tempted to do the exact opposite that they promote, to declare something as incorrect and reformulate it into its proper form by working our way back. In other words, there is this urge to set boundaries and fix things accordingly in case something is off. However, that misses the mark for Deleuze and Guattari. They (99) argue that:

“The atypical expression constitutes a cutting edge of deterritorialization of language, it plays the role of tensor; in other words, it causes language to tend toward the limit of its elements, forms, or notions, toward a near side or a beyond of language. The tensor effects a kind of transitivization of the phrase, causing the last term to react upon the preceding term, back through the entire chain. It assures an intensive and chromatic treatment of language.”

So, if we fix language withing certain limits, it stays within those limits. More specifically it is confined to those limits, preventing the actualization of the virtual. In other words, assuming boundaries limits the potential by assuming that the boundaries cannot be pushed or crossed. Once you mark the boundaries as fixed and transgression as simply incorrect or agrammatical, it’s the end of play. Going back to the earlier point on stammering, they (99) add that:

“An expression as simple as AND … can play the role of tensor for all of language. In this sense, AND is less a conjunction than the atypical expression of all of the possible conjunctions it places in continuous variation.”

As a result then, they (99) argue that:

“The tensor, therefore, is not reducible either to a constant or a variable, but assures the variation of the variable by subtracting in each instance the value of the constant (n – 1).”

If you are wondering what in the world is a tensor, well, it’s a concept borrowed from mathematics. According to the Oxford English Dictionary, it (OED, s.v. “tensor”, n.) is:

“[A] quantity expressing the ratio in which the length of a vector is increased.”


“An abstract entity represented by an array of components that are functions of co-ordinates such that, under a transformation of co-ordinates, the new components are related to the transformation and to the original components in a definite way.”

I’m hardly a mathematician, so I’ll leave it up to someone else explain this. Commenting on this, in ‘An Aesthesia of Networks: Conjunctive Experience in Art and Technology’, published in 2013, Anna Munster (28) states that as having to do with Riemannian geometry:

“A tensor describe the relation between vectors; for example, a stress tensor is the relation between the directional input of stress deforming along a surface and the eventual directional output of the stress. Whereas input and output are vectorial and are coordinate dependent, the tensor is relational and coordinate independent.”

In other words, as Munster (28) explains, a tensor only has function, “its function is to generate relationality.” So, as in the second dictionary definition provided here, Munster (28) states that it can only be inferred, not sensed, as in the case of a coordinate system.

Getting back on track here, Deleuze and Guattari (100) note that it’s not uncommon to relegate creative uses of language poetry, childishness and madness. However, they (100) argue that this only applies if the abstract machine is defined by constants and relegating change to “a cumulative effect or syntagmatic mutation.” Contrary to such formulation, they (100) argue that:

“[T]he abstract machine of language is not universal, or even general, but singular; it is not actual, but virtual-real; it has, not invariable or obligatory rules, but optional rules that ceaselessly vary with the variation itself, as in a game in which each move changes the rules.”

I particularly like their definition of it as a game that keeps changing as it is played. It is in constant variation, well, inasmuch as it is, that is. I’m fully aware that it makes language a nightmare to represent, but I think that is the point, because it is, as they (100) argue:

“That is why abstract machines and assemblages of enunciation are complementary, and present in each other.”

In summary then, they (100) characterize the abstract machine and the diagram:

“The abstract machine is like the diagram of an assemblage. It draws lines of continuous variation, while the concrete assemblage treats variables and organized their highly diverse relations as a function of those lines. The assemblage negotiates variables at this or that level of variation, according to this or that degree of deterritorialization, and determines which variables will enter into constant relations or obey obligatory rules and which will serve instead as a fluid matter for variation.”

If you think that, well, geez, that’s a nightmare to represent it’s because it is. However, as they (100) point out, it’s not that there aren’t obligatory rules and certain constant relations. It’s not an incomprehensible flux either, otherwise we wouldn’t be making any sense of anything at all, ever. It’s just dynamic, far more dynamic than we like to think. As they (100) point out:

“There is indeed braking and resistance at a certain level, but at another level of the assemblage there is nothing but a come-and-go between different types of variables, and corridors of passage traveled in both directions: the variables effectuate the machine in unison, in the sum of their relations.”

This is the end of the third postulate. In the final bits Deleuze and Guattari (100) reiterate that language does not exist outside people; “the assemblage of enunciation is always collective[.]” They (100) also point out that “[t]here is no primacy of the individual” and that, instead, there is only singular abstract and collective concrete. So, connecting the abstract machine to the assemblages, they (100) argue that it, the abstract machine, depends on the assemblages, as elaborated in the previous postulate, and vice versa. There’s more to say on the topic, especially with regards to the role of style in language (this has been covered to some extent in a previous essay), but everything in due time. The following postulate looks at language in major, as a standard, but that’s something for the next essay. I probably left the reader hanging, here and there, but, well, I guess it comes with the territory.


  • Chomsky, N. (1965). Aspects of the Theory of Syntax. Cambridge, MA: The MIT Press.
  • Deleuze, G. ([1968] 1994). Difference and Repetition (P. Patton, Trans.). New York, NY: Columbia University Press.
  • Deleuze, G., and F. Guattari ([1980] 1987). A Thousand Plateaus: Capitalism and Schizophrenia (B. Massumi, Trans.). Minneapolis, MN: University of Minnesota Press.
  • Hjelmlev, L. ([1963] 1970). Language: An Introduction (F. J. Whitfield, Trans.). Madison, WI: University of Wisconsin Press.
  • Massumi, B. (1992). A User’s Guide to Capitalism and Schizophrenia: Deviations from Deleuze and Guattari. Cambridge, MA: The MIT Press.
  • Munster, A. (2013). An Aesthesia of Networks: Conjunctive Experience in Art and Technology. Cambridge, MA: The MIT Press.
  • Oxford English Dictionary Online (n. d.). Oxford, United Kingdom: Oxford University Press.