ΦFTU, or how the Given is Given

This time I’ll taking a closer look at Félix Guattari’s ‘Schizoanalytic Cartographies’. Why? Well, if you are familiar with his takes on Louis Hjelmslev, alone and/or together with Gilles Deleuze, you are in for a treat.

To be honest, it is a very difficult book. It’s also very technical with a lot of tables and figures, so you really need to enjoy his work to get through it. This is one of those cases where I’d say that more is just more and less is just less, by which I mean that you probably wish that he’d be like he is with Deleuze in ‘Anti-Oedipus: Capitalism and Schizophrenia’ or in ‘A Thousand Plateaus: Capitalism and Schizophrenia’, letting it all sink in, as opposed to relying on this kind of bewilderingly meticulous presentation.

Even his (xv) translator, Andrew Goffey, points out that this book is really difficult. To clear, Guattari’s works are fairly difficult, but I’d say that this book is, at times, next level difficult. It pushes his thinking to its limits, taking some of his ideas further than he does in other books, which is why it is, at times, so difficult to read, as acknowledge by Goffey (xvi). In this book you’ll find Guattari giving “the Spinozist Semiotics of Hjelmslev” a new spin, to use Goffey’s (xvi) expression. Well, I guess I shouldn’t say new, because it’s not like he doesn’t cover that in his other publications. It’s rather that he takes another look at that, which is exactly what attracted me to this book.

If you think that his other takes on Hjelmslev are difficult to understand, this is going to be even more difficult. Goffey puts it quite well when he (xvi) states that reading the book will lead to experiencing all kinds of feelings, including but not limited to “bewilderment, surprise, amusement, frustration and perhaps irration at its exorbitantly baroque qualities” and I think that will also be the case with this essay. I don’t think it is a secret that my style can be exorbitant or baroque, i.e., happily all over the place, without much care for the readers.

I think I need to point out that I don’t write the way I do, exorbitantly or in baroque fashion, just to fuck with my readers. No, no. It’s just what I do. It’s just how I roll. It’s just how I write. I can write in other styles, very conventionally, following a certain structure, but the thing is that I’m quite unconventional and I like to keep it that way, if possible, because it helps me to keep things open-ended. It leaves room for creativity. It leads me to all kinds of encounters that give me new ideas. Mix it up! Don’t be afraid to mix it up!

Goffey (xviii) points out that Guattari gets a lot of hate for his style. He (xviii) reckons that it is, at times, labeled as having “a peculiarly Gallic taste for rebarbative abstruseness”, which is a nice way of saying that it comes across as fucking irritating, being written in a way that is unnecessarily difficult for the reader. He (xviii) also remarks how Guattari’s work is, at times, derided for being overly theoretical, which is another way of saying that it is elitist and out of touch with reality, or, even worse, for just consisting of “fashionable nonsense”, as if he didn’t know what he was on about, even though he, if anyone, knew what’s what. The thing is that his style is what it is because it challenges us to think, for ourselves, as opposed to slavishly adhering to conventions. He has this “insouciance with regard to explicit or tacit norms of langauge use” precisely because he is against “tired rituals and institutionalized fictions of intellectual endeavour”, as Goffey (xviii) points out.

Goffey (xviii) makes a really good point here when he compares the criticism of jargon with the criticism of sophistry. It’s not really about style. It’s about who gets to speak and doesn’t, or a “regulatory zeal”, as he (xviii) puts it. He (xviii) summarizes this quite neatly:

“Whilst it is often tempting to consider the awkward or abstruse vocabulary of jargon as exemplifying the conceptual weaknesses or semantic difficulties of fashionable nonsense, or the protective defensiveness of sects and secret societies, a point of view that doesn’t presuppose some tacit linguistic normativity is obliged to read such asperities differently.”

Indeed. It’s like the two ways of reading a book Deleuze (7-8) explains in ‘Letter to a Harsh Critic’. Either you obsess about it, trying to understand it, what it contains, what it truly means, or you just take what comes through in the process of reading, a bit of this, perhaps a bit of that, or maybe nothing, that can also happen. Deleuze and Guattari work in this second way, and so do I, nonchalantly, unapologetically.

Anyway, I won’t go through all of ‘Schizoanalytic Cartographies’. It’ll be a pick and mix, which, I’m sure you’ll hate if you want it all, but, hey, this my essay and I get to do whatever I want with it. Plus, I don’t think it’s worth covering it all. As interesting as it may be, there are also some parts that aren’t really that well connected to what I’ll be dealing with. What’s that then? Well, in short, once more, I’ll be looking at how the given is given or, the giving of the given, to put it in another way.

But how is this relevant to landscape and discourse? Well, as tricky as Guattari’s diagrams tend to be, I reckon they get the job done. They also help us to better understand how landscapes pertain to concrete assemblages and abstract machines.

The functors and the domains

Right, he has this two-dimensional thing going on in the book. He (57) reckons that it would be better to present it all three dimensionally, but, you know, that is quite the challenge when you are working with printed pages. Anyway, let’s jump right into it, starting from something, in the middle, if you will.

He (28) presents this two-by-two matrix, which I have edited a bit (I):

	Actual	Virtual
Possible	Actual possible	Virtual possible
Real	Actual real	Virtual real

Before I explain that, it’s worth pointing out that you can find Deleuze explain this ‘Bergsonism’. He (96-97) notes that actual and virtual should not be confused with possible and real. He (96) specifies this:

“We must take this terminology seriously: The possible has no reality (although it may have an actuality)[.]”

Yes, note how Guattari (28) indicates that this is indeed the case. The possible may have actuality but it cannot be real, as otherwise it wouldn’t be, merely, possible. Deleuze (96) continues:

“[C]onversely, the virtual is not actual, but as such possesses a reality[.]”

Again, this is what Guattari (28) also points out. Now, to be true to this, he refers to the actual possible as the phylum of actual possibility (marked in the text as ϕ for phi, probably because it’s about the phi-lum), the actual real as the flux of actual real (marked as F for flux in the text), virtual possible as the universe of virtual possibility (marked as U for universe) and virtual real as the territories of virtual real (marked as T for territories). So, in short, we get this (II):

	Actual	Virtual
Possible	ϕ	U
Real	F	T

If we look at how he and Deleuze explain this in ‘A Thousand Plateaus’, they (88) note that an assemblage has two axes: horizontal and vertical. The horizontal axis has to do with the segments of the assemblage, content and expression, of which content is always actual and the expression is always virtual. This has to do with what Louis Hjelmslev (30) states in ‘Prolegomena to a Theory of Language’:

“[T]here can be no content without an expression, or expressionless content; neither can there be an expression without a content, or content[]less expression.”

It is specified in his notes (271) that the possible, both actual and virtual, the ϕ and the U, pertains to Hjelmslev’s forms, i.e., the forms of content (actual possible) and forms of expression (virtual possible), whereas the real, the F and the T, pertain to Hjelmslev’s substances, i.e., substances of content (actual real) and substances of expression (virtual real). In addition, to explain the links between the possible and the real, both actual and virtual, it is noted (271) that, the F and the T are manifestations of the ϕ and the U, as for Hjelmslev substance is formed matter, i.e., how form manifests itself in matter.

To be a bit nitpicky here, the F and the T are manifestees, and the ϕ and the U are the manifestants, and their relations are the manifestations, as explained by Hjelmslev (186) in ‘La stratification du langage’. Anyway, if flip we the table (pun intended), we see how this works in relation to Hjelmslev’s work (III):

	Real	Possible
Actual	F	ϕ
Virtual	T	U

Now, why would you do that? Well, it’s because that’s how Hjelmslev’s net is typically presented (IV):

	Substance	Form
Content	Substance of content	Form of content
Expression	Substance of expression	Form of expression

And, to clarify that, combining the two (V):

	Substance (Real)	Form (Possible)
Content (Actual)	Substance of content (F)	Form of content (ϕ)
Expression (Virtual)	Substance of expression (T)	Form of expression (U)

To further clarify that, to add the missing terms, matter, function and manifestation (VI):

		Substance (Real)		Form (Possible)
Content (Actual)	Matter	Substance of content (F)	Manifestation	Form of content (ϕ)
				Function
Expression (Virtual)	Matter	Substance of expression (T)	Manifestation	Form of expression (U)

I will shuffle back and forth between these two presentations, Guattari’s (26) four functors and corresponding domains, tipping it all to its side where I find it useful, in hope of getting more out of it. The four functors are the F, the ϕ, the T and the U, which he (26-28, 56-57) further specifies as:

• F = material/energetic and signaletic Flows (Actual, Real) = entities arranged in Complexions
• Φ = abstract machinic Phyla (Actual, Possible) = entities arranged in Rhizomes
• T = existential Territories (Virtual, Real) = entities arranged in Cutouts
• U = incorporeal Universes (Virtual, Possible) = entities arranged in Constellations

At this point, it is worth noting that he seems to have flattened Hjelmslev’s bi-plane configuration (two planes, content and expression) to a monoplane configuration (one plane), considering that the Flows (F), pertains not only to material flows, but also signaletic (a-signifying / non-signifying semiotic) flows, and how they include libido (material), capital (material), labor (material) and signifier (semeiologic, signifying semiotic), as he (26-27) points out. I’ll return to this issue later on.

I think it’s also worth adding here, harking back to an earlier essay that deals mostly with Hjelmslev, that, for Deleuze and Guattari, Hjelmslev’s substance is their flow and form is their code, as mentioned by Guattari (202) in ‘Hjelmslev and Immanence’. He (203) further elaborates their take of the two, noting that Hjelmslev gives too much credit to substance (flow) when he treats it as that what animates and fecundates an eternal form, which I take to be a criticism of mixing it up with matter, sort of like giving the two transcendent status, hence his remark about being haunted by Saussure, even though that makes no sense in this configuration. His (203) take is that:

“[Form is] a productive machine, a code in decompensation, a code in productive position, emitting flow.”

In other words, it is the form (code) that regulates the flow, in a positive sense, making it go here and/or there, not in a negative sense, blocking the flow. He (203) continues:

“Its substance, its ‘matter,’ are anti-production.”

Now, you need to know what he means not only by production, but also by anti-production, which is something that he and Deleuze cover in ‘Anti-Oedipus’. In short, as explained by them (235), it has to do with how all that production has to deal with anti-production, which sets limits to the production, conditioning it. They (235) exemplify anti-production with the state, the police and the army.

So, as substances (flows) are what’s real, not merely possible, as that’s exactly what appears to us, they are what sets limits to form (code). This means that form (code) doesn’t merely impose itself upon unformed matter, thus forming matter, producing substance as formed matter, as if it came out of nowhere, as if there was nothing before it. The substances (flows, formed matters) also simultaneously limit or condition the forms which are not real but possible. This is why they (235) state that anti-production is within production itself. Of course, it’s not a fixed thing, so that wherever you have production, you also have this or that much anti-production, as they (235) point out.

For them (235), different setups have different substances (flows, formed matters) and forms (codes), which define how it all works and what are the limits or the conditions of production, i.e., what can and cannot be produced under those circumstances. They (235) compare despotism with capitalism, noting that despotism relies on transcendence, which, in short, means that it is the despot or despot-god, serving as god, in the absence of god, is that substance that acts as the anti-production, defining what can and cannot be produced, whereas capitalism is much more regulatory and effusing instead of prohibitive or limiting as its guiding principle is to latch on to anything, whatever, it doesn’t matter what it is, in order to get something out of it, a surplus. They (235) further elaborate this with the capitalist system:

“On the one hand, it alone is capable of realizing capitalism’s supreme goal, which is to produce lack in the large aggregates, to introduce lack where there is always too much, by effecting the absorption of overabundant resources.”

To which they (235-236) add that:

“On the other hand, it alone doubles the capital and the flow of knowledge with a capital and an equivalent flow of stupidity that also effects an absorption and a realization, and that ensures the integration of groups and individuals into the system.”

In other words, if you don’t know how capitalism works, the idea is to provide you with something, but not just something, some thing among other things, but something that you appear to lack. Note how the production of that something is accompanied by its very own anti-production. There’s all this, whatever it is, but, alas, you don’t have it, unless, unless you spend some of that capital to get it. They (236) are very clear on this, noting how ironic it is that people can very knowledgeable, have all the information and the training they need to succeed in life, which means they probably make a good living from applying all that so that, you know, it’s smiles and all that, yet, somehow, they can be made stupid, obedient, repressive and repressed, even self-repressive, just by having them watch television or, I guess, nowadays browse the internet.

If you, my dear reader, probably an academic, think that you are somehow above this, by default, just because you are an academic, note how they (236) are actually talking of you here. They (236) exemplify this with the career of Gregory Bateson, who, to his credit, studied all kinds of things, fair play to him, only to end up working for the Office of Strategic Services, which was a World War II era precursor to the Central Intelligence Agency. Yeah, that went well. Now, to my understanding, they are not ridiculing him for that, but rather use him as an example of what can and does happen to people, even to the best of us, or so to speak.

So, following that tangent, back to Guattari (204) who reiterates that Hjelmslev had this thing for Saussure, which pushed him to retain “a taste of eternity” when it came to the forms and “a taste of transcendence” when it came to the substances, only to finally detach himself from “Papa Saussure” by the time he started to write his text on the stratification of language ‘La stratification du langage’. According to him (205) that’s all well and good, like finally, but, as much as he (205) likes Hjelmslev’s net, that 2×2 panel or 2×3 panel configuration, if you include matter in it like he (73) does in ‘The Role of Signifier in the Institution’, the split into two planes, content and expression, still bothers him. In his (205) words:

“Very well! These are panels of consistency strata that are dependent on planes. But what’s annoying, as far as I’m concerned, is that there are planes and not a plane, a pure plane of consistency, of the filiation of deterritorialized machinic inscriptions[.]”

He (207) reiterates that it would be better to simply have a single plane, a single plane of consistency or a plane of machinic filiation, and n-strata. This would be great in his (207) view, because:

“All of Hjelmslev’s epistemological hopes would be realized and all of linguistics would topple over! Because wouldn’t it be even better to say that there are as many ‘semiotic’ functions as there are machines!”

This is interesting as the text was written sometime between 1969 and 1972, when he and Deleuze were working on ‘Anti-Oedipus’, some eight years before ‘A Thousand Plateaus’ was published, as noted by the editor, Nadaud (23). That said, I don’t see how him doing this by himself or with Deleuze, except, perhaps, in ‘Schizoanalytic Cartographies’.

I’m tempted to think that he simply focuses on language and semiotics in ‘Schizoanalytic Cartographies’, which would then explain why, later on, he (54) invokes discursivity in his diagrams. After all, this is pretty basic stuff in linguistics, the figurae (figures) being morphemes on the content side and phonemes on the expression side, as Hjelmslev (31-34, 44-45) points out in ‘Prolegomena’. André Martinet agrees. He (22-26), in turn, points out in ‘A Functional View of Language’ that the first articulation (content) pertains to monemes (an umbrella term he prefers to use instead of morphemes) and the second articulation (expression) pertains to phonemes. In writing those figurae (figures) would, of course, be graphemes.

Then again, I’m not buying this explanation, considering that, for him (26-27), flows are both material and signaletic. So, in other words, it appears that instead of placing all that’s material on the content plane and all that’s semiotic on the expression plane (the expression plane being itself semiotic or, rather a semiotic system), like in a connotative semiotic, which is how he and Deleuze approach this issue in their other words, he opts to place them on a single plane. This means that he looks at this in an entirely different way, which is not the Hjelmslevian way that he and Deleuze rely on in their other works, ‘A Thousand Plateaus’ being the prime example.

The material, the semiotic and the pragmatic

To make more sense of this rearrangement, which, to be honest, doesn’t mean that this it works any better than the Hjelmslevian arrangement that I’m more familiar with, we need to look at how he (58-59) sets this up in this book. In short, there are three levels of unconscious, i.e., something that we don’t have conscious access to. The first level is the level of the referent, what, I guess, we could also call the level of the indexical or denotative. This is the material level. The second level is the level of the semiotic, which, I guess, we could also call the level of the symbolic or connotative. Unlike the first level, which is all about the denotatum, this extends it to designatum. The third level is the level of the pragmatic and subjective. The gist of this is that the first level supports the second level and the third level, whereas the second level supports the third level.

To connect this to Hjelmslev’s work, it is added in the notes (271) that the second level of unconscious, i.e., the semiotic level, “corresponds to the Hjelmslevian function of solidarity” that, according to Hjelmslev (30, 35-36) in ‘Prolegomena’, is contracted by the two functives, form of content and form of expression. This simply means that this arrangement has three levels, one, two, three, of which level two is Hjelmslevian semiotics. It is also stated in the notes (271) that levels one and three pertains to what Hjelmslev calls manifestation, so that in each case the substance, substance of content and substance of expression, is the manifestee, as manifested according to the forms, which are the manifestants, as explained by Hjelmslev (166-167, 170, 186) in ‘La stratification du langage’.

In other words, Guattari seems to have reworked, not the assemblages, as such, but the way he presents them. Instead of presenting the material aspect of them and the semiotic aspect of them, side by side, like having two sides, faces or heads, like he and Deleuze (70, 291) refer to them in ‘A Thousand Plateaus’, he presents them as superimposed. You have level one, laid over by by levels two and three, so they appear to us as superimposed, as one level. While this way of going about it is, I’d say, certainly more complicated and thus more difficult to comprehend, at least at first, it doesn’t have that awkwardness of talking about the material and the semiotic side by side, as if they were, somehow, next to each other.

I acknowledge that a part of the difficulty of comprehending it all might be attributable to me. I’ve worked with the Hjelmslevian take, mixed a bit of Martinet, as presented by Deleuze and/or Guattari, and I was bewildered, if not annoyed by this change in presentation. But I see now what he’s trying to do here, so fair play to him. He (57) briefly comments on this, noting that it’d be better to illustrate what he has to say three dimensionally, but that’s not something that he can afford as it has to presented on a two-dimensional plane, it all being explained on paper.

In the past I’ve mentioned this issue, noting how difficult it is to present something on one plane, two-dimensionally. When you have something like Hjelmslev’s net, how do you look at it? Are you looking at it from above, like a map, treating it as one plane, split into two planes, or are you, perhaps, looking at it top to bottom, so that the content plane is above the expression plane?

If you ask me, there’s no right or wrong way to look at it. To me, what matters is that you have all that’s material or corporeal, all those bodies, in the broadest sense of the word, and all that immaterial or incorporeal, all those signs, and in between them is the interesting part, how they come together, what I’d call the interface. As long as you get that, you’re good.

There is, however, a certain advantage when it’s all presented as levels. He (59) presents it as a triangle, but I think it’s more apt to present the levels as layers (VII):

Now, I think this is, however, missing the point. I’d rather think of levels aligning on top of one another, so that the semiotic level is superimposed on the material level and the pragmatic level is superimposed on the semiotic level. The result is like what you get with an overhead projector, kind of like what you get when you stack transparencies on top of one another. But first, let’s imagine they all have something on them (VIII):

Here you have three levels. The bottom level has a horizontal pattern, the mid-level has a vertical pattern, and the top level has a dotted grid pattern. Now, they are not neatly aligned like transparencies on an overhead projector, but you should get the point. When they are neatly aligned as a stack, what you get is a flattened projection where all the levels are flatted to one level (IX):

This is basically what Guattari has done in ‘Schizoanalytic Cartographies’. It’s just a different way of looking at it all. This makes a lot of sense when you think of that overhead projector example. It’s also how we encounter just about everything. I mean, it’s not like there are two separate realities out there, one that’s the material reality and another that’s the semiotic reality. We are tempted to think otherwise, to look at the world as if we were outside of it and to think that there is a beginning and an end, but we are always in the thick of it, in the middle of things, here and now, as Deleuze and Guattari (23, 25) point out in ‘A Thousand Plateaus’.

In fact, they (7, 22-23, 37) also keep reminding us of that reciprocity, how you can’t have one without the other, how there can be no content without expression nor vice versa, and how the collective assemblages of enunciation are inseparable from the machinic assemblages of desire. They (37) provide a particularly apt summary of how it all comes together:

“Every statement is the product of a machinic assemblage, in other words, of collective agents of enunciation[.]”

It’s clear that, for them, statements are part of the collective assemblages of enunciation, not of the machinic assemblages of desire, but, be that as it may, you can’t have collective assemblages of enunciation, nor any statements without the machinic assemblages of desire. It would be tempting to conclude that this simply means that all that’s material comes before all that’s semiotic, and, in a way that’s true, as acknowledged by Guattari (58) in ‘Schizoanalytic Cartographies’, but you also have to keep in mind that all of this, all of that’s material, is nonsensical without all that’s semiotic. So, as I pointed out, and, as pointed out by Hjelmslev (30) in ‘Prolegomena’, you can’t have one without the other, really, as you need that reciprocity of the content and expression, their solidarity, which ties them together as a function.

Before I move on, I think it’s also worth clarifying here that what they (37) call collective agents of enunciation is just another label for the collective assemblages of enunciation. The agents here do not refer to “peoples or societies but multiplicities”, nor to individuals as even individuals are multiplicities, all of that pervades them, all of that makes them who they are, at any given moment. This has to do with the proper sense of what an individual is, someone or something that cannot be divided. For them (37) this means that a proper name is truly the mark of an individual. It’s just all there, already, at any given moment. No need to explain it.

The virtual and the actual

I don’t think explained the actual and the virtual that well, so I’ll return to it now. Right, what I find interesting in Guattari’s (28) formulations is that it explains how you can’t have something virtual without something actual, and, oddly enough, neither can you have something actual without something virtual. This is why the double articulation goes (if considered in isolation), or, rather, appears to go (if this is not considered in isolation from other articulations that have occurred and/or occur simultaneously) from substance to form and then, again, from form to substance, as explained by Deleuze and Guattari (40-41) in ‘A Thousand Plateaus’.

This only makes sense. You have to have some content, something actual that could have any form, yes, but it has this and/or that form, thus appearing to us as certain substance (formed matter), for that expression, which then becomes part of content after the expression as there can be no content that hasn’t been expressed.

Anyway, so, why the fuss over these terms? Wouldn’t we be just fine without them? Deleuze (208) explains this quite well in ‘Difference and Repetition’:

“The virtual is opposed not to the real but to the actual. The virtual is fully real in so far as it is virtual.”

In other words, the virtual is always real, just as the actual is always real, unless one of them or both are merely possible, which is the opposite of real. He (208-209) continues:

“Indeed, the virtual must be defined as strictly a part of the real object – as thought the object had one part itself in the virtual into which it plunged as thought into an objective dimension.”

To which he (209) adds that:

“The reality of the virtual is structure. We must avoid giving the elements and relations which form a structure an actuality which they do not have, and withdrawing from them a reality which they have.”

I still want to further clarify the actual and the virtual before I move on. Charles Sanders Peirce (763) provides an excellent definition of this in ‘Virtual’:

“A virtual X (where X is a common noun) is something, not an X, which has the efficiency (virtus) of an X.”

Which he (763) then exemplifies with:

“So virtual representation was the non-representation of the American colonies in the British Parliament, which was supposed to be replaced by something.”

To explain this in common parlance, which will only make sense, believe me, something virtual is the equivalent of something that is actual, but without being actual. For example, when I say something like ‘those things are virtually indistinguishable’ I’m claiming that I cannot distinguish them from one another, that might as well be actually the same, but I’m not saying that they are actually the same. I might also say something like ‘that’s virtually impossible’, which means that it’s not actually impossible, but it might as well be. It is as if was, without being so. That’s what he (763) means by efficiency (virtus).

He (763) wants us to remember that virtual should never be mixed up with potential or, as already mentioned as discussed by Deleuze and Guattari, with possibility:

“[Virtual] has been seriously confounded with ‘potential,’ which is almost its contrary.”

How so? How is potential (or possibility) not correct here? He (763) explains this:

“For the potential X is of the nature of X, but is without actual efficiency.”

Note how potential is always tied to something, whereas virtuality pertains to something that is not tied to it. Instead, it has its efficiency (virtus). He (763) exemplifies this:

“A virtual velocity is something not a velocity, but a displacement; but equivalent to a velocity I the formula, ‘what is gained in velocity is lost in power.’”

Neat, eh? This solves the problem with having to rely on the opposition of possible and real or what one could also call the realization of the possible. Now, you might be wondering what’s the problem with that? Isn’t that the same? Well, no. I’ll explain why.

The axes

Deleuze and Guattari (88) state in ‘A Thousand Plateaus’ that the vertical axis of an assemblage has to do with territoriality, so that one end pertains to territoriality or (re)territorialization, whereas the other side pertains to cutting edges of deterritorialization or just, more simply put, deterritorialization. When we combine the two axes and the functors/domains, we get something like this (X):

I’ve changed the terms in that diagram. The original looks something like this (XI):

Here Guattari (54) refers to the infinite and finite as pertaining to deterritorialization and the plural and unary as pertaining to discursivity. Okay, I need to break this down.

Okay, on the left-hand side we have the actual, and, on the right-hand side we have the virtual. He (58) also refers to the actual as the given and the virtual as the giving, because, on this horizontal discursive axis, you have start from something, from some given, but then you also must be able to explain the giving, i.e., how that given is given. In other words, it’s like when you plan a research question, you are typically pushed to think of a how question, as opposed to a what question. This makes sense because the how is usually much more interesting than the what, and may help us to understand why, but you can’t examine how something is given, without acknowledging it first as a given. That’s why I find it a bit silly when, for example, students are mocked for asking those what questions. I mean, okay, if that’s the only thing, fair enough, not that interesting, but you can’t ask the more interesting questions pertaining to giving without confronting the given. I mean, duh?

I’m not entirely happy with him using discursivity for the horizontal axis, mainly because it’s just confusing, but, okay, I’ll go with that. It’s his thing, so, yeah.

Anyway, he (58-59) refers to the actual or the given as plural and the virtual or the giving as unary, but I won’t get into more detail why he has chosen to use those instead of the given and the giving, which he’ll then keep on mentioning. The short answer to that is, I believe, that the given is always plural, either a multiplicity on the deterritorialized or infinite side, or multiple on the (re)territorialized or finite side, whereas the giving is always something that involves one, a single element drawn from the plural.

Unary is an odd term, I’ll give you that, but a dictionary, in this case the Oxford English Dictionary (OED, s.v. “unary”, adj.), will help us to understand the choice:

“Composed of a single item or element.”

And, in mathematics, logic and linguistics (OED, s.v. “unary”, adj.):

“Of an operator, operation, or transformation: involving or operating on a single element.”

As well as in chemistry (OED, s.v. “unary”, adj.):

“Of a chemical system: consisting of a single component.”

So, the point here is that unary is one (element, component, or the like), binary is two, ternary is three, quaternary is four, quinary is five, etc., as a dictionary will tell you. Now, this is not to say that giving will only involve one element, component, or the like in each case, but, to my understanding, it’s unary in comparison to the given, which is plural, which is, in turn, simply plural in comparison to the unary, which is giving.

Plurality also pertains to continuity and fusion of elements, whereas unary pertains to discontinuity and mixing of elements, as he (61) points out. Another way of expressing is to state that the content is more plural than the expression, which, is, in turn, more unary than the content, as, in this configuration, content is on the left-hand side and expression is on the right-hand side.

Moving on! On top we have the possible and at the bottom we have the real. This vertical axis of deterritorialization indicates how on the top you have infinity and at the bottom you finity. Another way of expressing this is to indicate that on top you have deterritorialization, to the point that it’s irreversible, and at the bottom you have (re)territorialization, so that any deterritorialization in this end remains reversible, as explained by him (61). This also means that high deterritorialization results in everything being far from equilibrium and, conversely, low deterritorialization is close to equilibrium, as he (61) also points out.

Mapping the entities and the tensors

If you think what’s been covered so far is complex, perhaps even unnecessarily complex, well, you are in for a treat. He (60) throws this at you (XII):

Now, I’ve taken some liberties with this “[m]ap of entities and tensors”, as he (60) calls it. To make sense of this, I’ve retained the two axes, so that the horizontal axis is the axis of discursivity and the vertical axis is the axis of deterritorialization. The gist of this still is that, on the top everything is highly deterritorialized, to the point of infinity, whereas everything is highly (re)territorialized, so that you get finity. What’s on the left, the content, is the given, highly plural, and what’s on the right, the expression, is the giving, highly unary. In the middle you have the solidary function.

I’ve retained most of the terms used by him (60). If they don’t seem to make sense, it’s because they’ve been abbreviated from the French original, hence some of the mismatches. I’ll list them, instead of having them in the running text as otherwise it’s a pain to unpack that diagram.

I’ll start with the entities listed as entities of pragmatic manifestation. These entities are synapses, which are located on the left-hand side and the right-hand side, where the triangles meet, at the edge of the circles.

• S = synapses

• Se = synapses of Effect, pragmatic synapses (Effects on the left)
• Sa = synapses of Affect, subjective synapses (Affects on the right)

These pragmatic entities pertain to the pragmatic level, which is the third level of the unconscious, as he (64) points out. Their job is to “‘adjust’ the three types of quantum configuration of non-separability, separation and quantification”, which I’ll get to soon enough. He (64) elaborates what this means:

“[T]he past potentialities of the Systems and Structures of level I and the surplus values of possibility of the semiotic concatenations of level II, bearing the future, find themselves capitalized, put into action, rendered present.”

So, that’s why you need the synapses, i.e., the pragmatic entities that constitute level III. They are, in the present, here and now, but they are, of course, linked to the past and the future, as he (64) points out here. Anyway, He (64-65) continues:

“The actualization of Effects and the virtualization of Affects cannot be assimilated to mechanical causation or dialectical implication, because their occurrences are indissolubly linked to the contingent, singular character of the Assemblages that effectuate it.”

At this point you might be scratching your head, thinking that weren’t we going from level I to level II and from level II to level III. Well, yes, but once we get to the pragmatic entities, we still have those pragmatic tensors that lead back to those level I material entities, as level III is always linked to the other levels, as he (65) goes on to point out. Again, that’s the here and now, being in the middle of it all, in the making. There is not a distinct first move (material), followed by a distinct second move (semiotic) and a distinct third move (pragmatic).

To be clear, we most certainly don’t start with the subject or consciousness, as the whole idea here is to understand how subjectivity or consciousness is produced. In his (65) words:

“The ‘present’ of schizoanalytics pragmatics doesn’t imply any primacy of a clear, distinct, continuous, rational, capitalistic and symbolically castrated consciousness.”

What have instead is, as he (65) puts it:

“The temporal schizzes and dyschronies generated by fragmented becomings are inscribed in its register in their own right.”

Anyway, it’s time to move on. In each corner, by the functors ϕ, F, T, and U, we have the entities of intrinsic reference. The codes and systems are on the left, and the ordination and structures are on the right.

• Rm = machinic Rhizomes
• Mc = matters of Content
• Me = existential Matrices
• ΣU = constellations of Universes

Tensors, what’s discussed in the previous essay, are marked by the arrows. There are two kinds of tensors: tensors of intrinsic reference and semiotic tensors. The former pertains to the first level of unconscious, the material level, whereas the latter pertains to the second level of unconscious, the semiotic level, as he (62) points out.

Tensors of intrinsic reference are marked by the arrows that point to both directions, by what he (62) refers to as “bijective couples”. This means that these tensors are reversible, as he (62) points out. They operate between the entities of intrinsic reference on each side. He (62) notes that there are systemic tensors situated in between the machinic rhizomes and the matters of content. He also (62) notes that there are structural tensors situated between the constellations of universes and existential matrices.

• Yt = Systemic tensors (Y because St was already in use)
• Ut = Structural tensors (U because St was already in use and Tt just didn’t work for me)

In addition to these two tensors, there are also two other tensors that he (65) refers to as efferent tensors. I’ll return to these later on:

• Et = Synaptic tensors of Effect
• At = Synaptic tensors of Affect

I also abbreviated these two in the diagram, because it’s pretty crowded otherwise.

He (60) indicates these material tensors in text in his own diagram, but I abbreviated them because, firstly, they don’t fit neatly, and, secondly, his way of presenting them is a bit confusing. It is also worth noting here that as this pertains to the first level of unconscious, its inner workings are inaccessible to us as our understanding of it is mediated through the second and third levels of the unconscious, as emphasized by him (62). This is just a fancy way of saying that we don’t direct access to this level, to all that that has to do with regimes of bodies, because we make sense of the world, pragmatically, through regimes of signs. This is pragmatics 101.

The semiotic tensors are marked by arrows, or “projective vectors” as he (62) calls them, shooting from each entity, crossing over where the two functives, content and expression meet in the middle, in that solidary function. He (62) adds that these semiotic tensors are irreversible, which simply means that they go one way, you know, like an arrow that’s been shot.

• t = tensors

There are two tensors of persistence (from systems to structures; actualization)

• Nt = noematic tensors
• St = sensible tensors

There are also two tensors of transistence (from structures to systems; virtualization)

• Mt = machinic tensors
• Dt = diagrammatic tensors

He (60) has also indicated these semiotic tensors in text in his own diagram, but I thought it would make sense to do what he has done with the other terms.

To make sense of what he (54-55) by structures and systems, they are “two configurations of intrinsic deterritorialization” that, by all logic, pertain to the first level of the unconscious (the referent, the material level), as they are intrinsic. Systems are on the left and structures are on the right in the diagram.

To make more sense of that, he (55) adds that content and expression are two configurations of extrinsic deterritorialization. This means that, by all logic, they pertain to the second level of the unconscious (the semiotic level), as they are extrinsic. Content is on the left and expression is on the right in the diagram.

This double take, calling what’s on the left systems on the material level and content on the semiotic level and what’s on the right structures on the material level and expression on the semiotic level, is, perhaps a bit misleading, if your starting point is how he and Deleuze discuss this in ‘A Thousand Plateaus’ as they use content and expression for just about anything, material or semiotic. Then again, I see what he is doing here. Fair enough. Point taken.

Where those semiotic tensors arrive, where those arrows land, mark the semiotic entities. On the left are the diagrams and machinic propositions, the semiotic entities of expression (crossing over from expression). On the right are the sensible territories and the noema, the semiotic entities of content (crossing over from content).

• Pm = machinic Propositions (abstract machinic Rhizomes)
• Dg = Diagrams (energetico-signaletic Complexions)
• Ts = sensible Territories (existential Cutouts)
• N = Noema (incorporeal noematic Constellations)

Starting from the top, he (64) states Pm are capable of overtaking their matters of expression (coming from the expression side to the content side) that operate as their messengers (being the material, the medium of expression), which results in us having this sense of it always having been that way, and, I would add, always going to be in that way. He (64) uses the example of faciality, how it involves an incorporeal transformation of the corporeal world, a projection of a face of the Christ like standard onto a capitalistic machinic Phyla (Φ). This is also how landscapity works.

In his (64) words, this happens when we go from the material entities ΣU, in the domain of U, to the domain of Φ, carried by the semiotic tensors Mt that “actualize an abstract propositional expression”, resulting in Pm:

“From … to … ‘without guarantee’, charged with a potential for possibilities, dependent on a temporization that ceases to impose on the entities that fall within their jurisdiction the need to maintain a speed less than that of the relative threshold of the speed of light.”

Next up, he (63-64) refers to semiotic entities Dg as the signaletic matter, at domain F, to which we get from the material entities Me, in the domain of T, as the semiotic tensors Dt that “actualize a diagrammatic Expression” carry them there:

“From … to … ‘without guarantee’, that are charged with a potential for possibilities, dependent on a relative temporization and whose entities are obliged to respect the celebrated law which states that physical particles have speed that are less than or equal to that of light.”

He (64) exemplifies this with how “the signaletic matter of a credit card” is “able to trigger an ATM, depending on whether or not its PIN corresponds to what is typed into the machine, whether or not the card or machine is damaged”, “whether or not one is in [at home] or abroad” or something along those lines, anything that has to with how that all works. Of course, we have less use for ATMs these days, but credit and debit cards are everywhere, working exactly like this, having all these algorithmic features (e.g. when you are using the contactless payment, for example) and what not.

Moving on to Ts, in the domain of T, to which we from the material entities MC, in the domain of F, as carried by the semiotic tensors St that “virtualize sensible contents”, as noted by him (63):

“From … to … ‘without guarantee’ that are charged with a possibility-potential and are dependent on a duration with neither subject nor object, a pure existential turning-over, the entities which have null speed[.]”

He (63) exemplifies this with a totemic icon (in an anthropological assemblage), with a territorialization refrain (in an ethological assemblage) and with an imago (in a phantasmatic assemblage). The idea here is that you have this flow (F), which then results in a sensible territory, a cutout, something (unary) cut out from something (plural).

Then we have the semiotic entities N, in the domain of U, that we get to from the material entities Rm, in the domain of Φ, once the semiotic tensors Nt carry them there and “virtualize noematic contents”, as he (63) points out:

“From … to … ‘without guarantee’, charged with potential for possibility dependent on an infinitely fragmented, ‘multiplicious’ duration, the entities of which have an absolute speed, that is to say, a speed that cannot be related to EST coordinates[.]”

He (63) exemplifies this with “the Cheshire cat’s smile, which Whitehead tells us is encountered at all points in space without it being possible to localize it at any point in particular.” So, if his (63) explanation seems a bit difficult, the example ought to help you understand how these entities of absolute speed cannot be localized, as such, but rather appear everywhere, like that smile.

It is worth noting that you get from an entity of intrinsic reference, from what I like to call a material entity (because it’s just shorter), to a semiotic entity through one of the semiotic tensors, as emphasized by him (62). That said, it is the tensor that does the work in each case, that marks these entities as semiotic entities, not the entities at their point of origin, as they are material entities, as he (62) goes on to add. This is particularly important for him (62) because, on the third level, on the pragmatic level, “these semiotic entities are bearers of a surplus value of possibility susceptible of being actualized at the pragmatic level.”

The points he wants to make is also particularly important because he is stating that, oddly enough, you get from nowhere to somewhere, from something really basic, from some material entities to semiotic entities. It’s miraculous, really. This is something you can find in Hjelmslev’s work already, so the credit goes to him, which, I’m sure, Guattari would be willing to acknowledge.

Entities are important whenever we deal with quantification, which, according to him (55-56) pertains to inter-entiterian relations (as in between entities, from one to the other), as established between non-separability and separation. I’m gonna start with these two: non-separability and separation, before I continue explaining his definition of quantification.

He (54) explains that non-separability has to do with “the synchronic correlations at a distance that guarantees modes of compossibility between diverse entity states” and it has the status of intrinsic reference, which, in turn, means that it has to do with the first level of unconscious (the referent, the material level). If I get this right, he is talking about the entities, how they combine and recombine (or compose/decompose), so that we have all that there is, like this, or like that, at any given time. In terms of tensors, he (54) adds, this pertains to the vertical axis of deterritorialization and, it appears, that he is talking about the systemic and structural tensors.

He (55) also explains that separation has to do with “the diachronic inter-entiterian transformations on the basis of which the components of semiotization are established.” So, separation has to do with the second level of unconscious (the semiotic level) and, more importantly, how we get there from the first level, from the material entities to the semiotic entities. This is why he (55) states that it pertains to the other axis, that horizontal axis of discursivity, and to “vectorized tensors”, what he also refers to as tensors of separation. Those tensors consist of the four semiotic tensors (Nt, St, Mt, Dt), and four other tensors, what he calls the tensors of surplus value of the possible (ΔF, ΔT, Δϕ, ΔU; in short, surplus tensors) that “have the capacity to relay the sites of sense and to transfer them towards pragmatic Effects and Subjective affects”, as explained by him (55). He (65) refers to them as afferent tensors. At this point, when we cross over to Effects and Affects, we are already dealing with the third level of the unconscious (the pragmatic and subjective, what I like to just call the pragmatic level or the level of pragmatics).

So, in summary, there are the semiotic tensors (Nt, St, Mt, Dt) that result in the creation of what he (55) here calls sense entities, i.e., those semiotic entities (Pm, Dg, Ts, N), which, in turn, can get carried away by the tensors of surplus value of the possible (ΔF, ΔT, Δϕ, ΔU) to the pragmatic Effects and subjective Affects, by what I believe he (60) means the synapses of effect (left side) and affect (right side) that are also known as the entities of pragmatic manifestation.

Back to quantification, by which he (55) simply means “the establishing of the sites of entities”, i.e., where and at what level they will or won’t “come to be grafted instances that will be specified energetically from a thermodynamic, physico-chemical, biological, etc. angle.” In other words, quantification has to do with how we get from entities to other entities through these tensors, what we might also call vectors, and how they are mapped in relation to one another, i.e., where this and/or that takes place (at the material level, at the semiotic level, at the pragmatic level), inasmuch as it does (as there’s no guarantee that something will take place; maybe, maybe not).

If that’s difficult to grasp, which I don’t think it is, once you do all the necessary work to make sense of his diagram, what he (60) calls his “[m]ap of entities and tensors”, he (56) also calls quantification the “taking consistency of Flows”. He (56) also warns us not think of any agency, of any kind of action, reaction or interaction, prior understanding how this all works (quantification, non–separability, separation). This is why he and Deleuze (22) state in ‘A Thousand Plateaus’ that “all we know are assemblages”, the “machinic assemblages of desire and collective assemblages of enunciation.”

In this context Guattari (56) emphasizes the importance of the latter, what in this book he calls the “Assemblages of enunciation”, noting that they need to be taken into consideration, “in so far as [they] have been constructed and in such a way that they have effectively become producers of quantification, that is to say, have acquired a sectorial ‘point of view’, a ‘reading capacity’, the state of entities as an economy of energetico-spatio-temporalized Flows.” To be clear, I don’t think he is ignoring the machinic assemblages of desire, all that that is on the material level. I think he is rather emphasizing the collective assemblages of enunciation here because it is necessary for the world, i.e., all those things, all that there is, materially speaking, to appear to us in this or that way, as a certain order of things, as he (56) points out. In his (56) words:

“This paradoxical dimension of a quantification proper to the ‘order of things’, the fact of considering a ‘point of view’ as an energy charge rests on the same kind of petition of principle as those that inspire our whole ‘metapsychology’.”

To which he (56) adds that:

“Here it leads us to postulate that if, at a molar level, there is numbered and numbering striation, grasped at the nth degree of redundancy of entity sites, this is because such a problematic was already posed at the most molecular levels.”

The way I see it, what he does here is to explain how the molar, what we consider these things, like this keyboard or this mouse, are not the only things that can be quantified. We could break both things to their component parts, and the break those components down to their component parts, and so on and so forth, until we are at what he calls the molecular level, which, to be clear, is not to simply decomposable to the level of molecules. Instead, the idea is that you can always compose something out of something else and decompose something into something else.

It’s also worth noting here how quantification pertains to the material level, marked de– and reterritorialization, and the semiotic level, marked by discursivity, or, as he (56) puts it, its role is to articulate two quantum configurations. There is this double articulation. He (56) further clarifies this:

“[It] also [has] as its mission the retroactive and prospective projection onto the Plane of Consistency of the potentiality for the discernibilization of: 1) quanta of deterritorialization within non-separability; 2) quanta of discursivity within separation.”

To go back a bit, just for a moment, note how the material level deals with what cannot be separated, which only makes sense, considering that you can’t separate it in order to move it somewhere else, to some other level. It’s always there, in this this or that composition. It’s at the semiotic level where you have that separation, albeit it is not material that separates, so that you get this extra, on top of what’s there. This make sense, considering that he and Deleuze (81) insist in ‘A Thousand Plateaus’ that expressions are attributable to bodies, and that they transform the bodies incorporeally, never corporeally as only bodies can alter other bodies corporeally.

This leads us quite nicely to a point that Guattari (56) wants to emphasize, to how there’s nothing hidden. There’s nothing waiting for us to uncover. Everything therefore becomes a matter of production. In his (56) words:

“It will be noted that this retroaction differs from the previously refused postulation of hidden semiotic parameters, to the extent that for these parameters there is no longer any possibility of an articulation that can do without this third level of quantification.”

Unless I’m mistaken, the third level here is the pragmatic level. At this point, he (56) also warns us not to think of the pragmatic level as a superstructure to the semiotic level and the semiotic level as a superstructure for the material level. There is no subordination between the levels of the unconscious, which he (56) also calls the quantum configurations, nor any kind of “mimetic tracing”, “duplication or dialectical synthesis.”

This leads us to the two tensors that I mentioned but so far haven’t explained, the synaptic tensors of Effect (Et) and Affect (At). They extend the tensors of surplus value of the possible (ΔF, ΔT, Δϕ, ΔU) by carrying the pragmatic and subjective entities, the synapses of Effect and Affect, towards the material entities of Systems (on the left: Rm of ϕ and Mc of F) and Structures (on the right: ΣU of U and Me of T), aggregating them at the systemic and structural sites of material level, as he (65) goes on to point out.

Unless I have missed something, this completes the diagram, so that all the entities and tensors listed by him should now be covered, so that the flow of quanta, from entities to entities, within each level, marked by the material tensors that pertain to their composition, deterritorialized/reterritorialized, semiotic tensors, running from the material entities to establish semiotic entities, surplus tensors that carry the semiotic entities to the synapses of affect and effect, from which it flows back to the material entities.

To make more sense of that, here is the diagram again, with color coding (XIII):

As you can see, I’ve indicated all that pertains to level one (material entities and tensors) in blue, to level two (semiotic entities and tensors) in red and to level three (pragmatic entities and tensors) in purple. It’s worth noting that, as done by Guattari (60), I haven’t marked the surplus tensors, nor the synaptic tensors with arrows. You can, however, see them in purple, and how they are between the semiotic entities and the pragmatic entities (synapses) and between the pragmatic entities (synapses) and the material entities, marked in dash.

To go back a bit, you can also see how all this operates on a single plane, on what he (56) calls the plane of consistency, which is divided into four domains of consistency (Φ, F, U and T), as already discussed. If we flip this to its side, we get can see how this aligns with Hjelmslev’s net (XIV):

So, in Hjelmslevian terms, as discussed in the notes (271), on top we have content, which is split into substance of content (F = material/energetic-signaletic Flows) and form of content (Φ = abstract machinic Phyla), and at the bottom we have expression, which is split to substance of expression (T = existential Territories) and form of expression (U = incorporeal Universes).

The axis of deterritorialization, the tensor marked in blue but now horizontal after the flip, is what Hjelmslev would call manifestation, how “substance is the manifestation of form in matter”, as explained in the notes (271). This means that F is the manifestee of the manifestant Φ and T is the manifestee of manifestant U, as also explained in the notes (271). The sign-function, i.e., the solidarity of content and expression is marked by the overlapping of the circles. As it’s a matter of semiotics, it functions only on the semiotic level, as it is also pointed out in the notes (271) and as you can see the tensors marked in red crossing over, whereas the tensors marked in blue and purple do not cross over.

I think there is a small gaffe in his notes (271). I just pointed out how manifestation is the relation between substance and form, which is how you get formed matter (substance) out of matter. It is true that “substance is the manifestation of form in matter”, with emphasis on it being a manifestation of rather than just about manifestation, like in general. Agreed, but I don’t fully agree with how he states in his notes (271) that while “the level of the secondary unconscious corresponds to the Hjelmslevian function of solidarity”, “the conjunction of tertiary and primary levels corresponds to that of manifestation.” Why? Well, while I agree that solidarity, i.e., the sign-function, has to do with the second level (semiotic level) and that manifestation has to do with the conjunction of the third level (pragmatic level) and the first level (material level), I’d say that it can also take place on the first level (material level), simply because, for Hjelmslev, the relation between substance and form is that of manifestation, the former being the manifestee (the manifested), the latter being the manifestant (what manifests), as I pointed out early on. Then there’s also the thing with how solidarity is between the form of content (material) and the form of expression (semiotic), so I think that it is a bit misleading to simply state that the second level (semiotic level) corresponds with solidarity. I mean yes, you need that second level (semiotic level), but, at least for Hjelmslev, you also need to first level (material level) as well.

Now, to be fair, Guattari does imply this in the notes (271), as he does clearly explain that manifestation is the relation between substance and form. I also do have to acknowledge that from the viewpoint of the third level, i.e., from a pragmatic perspective, we can only make sense of the first level through the second level, so, yes, that’s how manifestation appears to us, as this relation between the third and the first levels. That makes sense.

As a side note, I think it would also be apt to refer to manifestation as materialization, as I’ve done in the past in my research when I’ve talked about materialization of discourse (or as materialized discourse or discourse materialized), considering that there is that conjunction of the third level (pragmatic level) and the first level (material level), that we get to once we move from the second level (semiotic level) to the third level (pragmatic level). As explained by Richard Schein (663) in his outstanding article ‘The Place of Landscape: A Conceptual Framework for Interpreting an American Scene’:

“Each seemingly individual decision behind any particular … landscape is embedded within a discourse. When the action results in a tangible landscape element, or total ensemble, the cultural landscape becomes the discourse materialized.”

While he is using discourse here, it works as the expression plane is the discursive plane, if we opt to use Foucauldian terms. Anyway, he (663) exemplifies this:

“Examples of such discourses might include zoning theory and practice, architectural design trends, economic consumption patterns, and others.”

He (663) finishes off this by explaining the manifestation, what he calls materialization:

“As a material component of a particular discourse or set of intersecting discourses, ‘the cultural landscape’ at once captures the intent and ideology of the discourse as a whole and is a constitutive part of its ongoing development and reinforcement.”

In other words, there’s that move from the second level (semiotic level) to the first level (material level) through the third level (pragmatic level), that manifestation or materialization, whatever you want to call it (what matters is that you get the point). You can’t have something that we deem semiotic without the material. How so? Well, let’s take something like speech, which is, of course, spoken. That requires a speaker (material) who uses parts of body (material) to modulate the passage of air (material) from lungs (material). It’s the same if we (material) put up a road sign (material), by the side of a road (material). You need that materialization, that manifestation. Now, of course, none of that makes any sense (what is speech besides modulation of the passage of air to make sounds? what is a road sign besides something made out of metal with some paint or tape on it?) unless we take the semiotic side into account. We need to understand a lot more behind it, what has been said and done before, the semiotic side of it, to make sense of any of it, but that doesn’t negate the importance of the material side of it.

Guattari provides us another good word that also conveys what we are here. In his book ‘Lines of Flight: For Another World of Possibilities’, he (18) calls it incarnation. He (17-18) uses it in a regilious context, when explaining how the role of Christianity, namely Catholicism, shifted from how it was when the Roman Empire existed to how it was in the Middle Ages. He (17-18) notes how during the Roman times Christian places of worship were these dark candlelight lit unground places where people could barely see anything, whereas in the Middle Ages these grand cathedrals were constructed, with light beaming in, glistening metals and jewels, iconographic stained glass and impressive liturgies, and the like. The point he (18) wants to get across is that not only was the world constructed differently (materially), but it was also understood differently (semiotically) in different eras. In addition, the constructions (material) played a role in shifting that understanding of the world (semiotic), as Christianity could not appear to people in the same way in these two very different settings (material). In his (17-18) words:

“[T]he abbey at Saint-Denis, for example, … assembles [agence] a collective semiotisation, an incarnation … of the relation of God to men and to royalty.”

In other words, Christianity is not and was not this abstract thing that remained fixed. It’s also not like it just happened to be case that people had these different places of worship at different times. Yes, people probably did initially gather in those dark places because that was their only option and then moved into better venues, those well lit cathedrals, when they had the opportunity to do so. Now, of course, those buildings weren’t there already, just waiting to be moved into. Plus, it’s not either the case that people just suddenly opted to build such grand buildings. Instead, you have that constant interplay of the two, the material and the semiotic. There’s that, sure, but that’s not exactly what here is after here. His point is that Christianity itself transformed (semiotically) as it was incarnated in the grand architecture (materially).

In any case, if you know your Hjelmslev, you might object to Guattari’s mapping of his net, because it appears that you no longer need to go from substance of content to form of content in order to get to form of expression, which allows access to the substance of expression. It’s clear that you can go from substance to form, yes, and, in reverse, from form to substance, inasmuch as we think it all happens simultaneously, immanently, as opposed to there being this one initial move or articulation, followed by another, and so on and so forth (the material tensors marked in blue would be otherwise indicated as going from F to Φ and U to T, in sequence, which would then make sense, fair enough, if you think of it that way), but the semiotic tensors marked in red may fool you to think that you can go from substance of content (F) to substance (T) and/or form of expression (U) without passing through the form of content (Φ). However, that’s not possible, as explained by Guattari in ‘Schizoanalytic Cartographies’ (58):

“[A] principle of exclusion that forbids direct tensorial relations between, on the one hand, the consistencies of F and U and, on the other hand, the consistencies T and Φ.”

What’s still different from Hjelmslev is that it is or at least it appears that you can go from one substance to the other, considering that this constraint only applies to directly crossing over from substance of content (F) to form of expression (U) and from substance of expression (T) to form of content (Φ). In a sense, that is true, but when you get into the details, when you look at the entities and the tensors, you’ll notice that you can cross over from content to expression through the sign-function (the overlapping area) through the semiotic tensors (marked in red), and to get to one or the other, the form of content or the form of expression, you’ll need to go from the semiotic entities to the pragmatic entities (synapses) through the pragmatic tensors (marked in purple). That’s the only way you’ll get back to the material entities, through those pragmatic entities. This is the point he (60, 62) makes about the first level being inaccessible to us. What happens on that level is always merely mediated to us.

You might also be tempted to point out that you can’t go from expression to content, and I would agree. That said, that only applies if we look at one instance, where you have some content for some expression. We also need to consider how an expression can function as content to another expression. His (60) map takes that into account, so, yeah, you can do that, as he (59) points out. It makes sense. This has to do with how the content is deemed to pertain to the given and the expression to the giving, as he explained by him (58-60).

I’ve reworked his (60) mappings a bit here (XV), combining the one where he maps the entities and the tensors with the one where he indicates that there is an intrinsic systemic referent that corresponds to the given (the circle first from the left), and an intrinsic structural referent that corresponds to the giving (the circle first from the right). I wanted to combine the two mappings here because I think it helps to understand how, for him (59-60), the given is always given, how it always involves giving, which, in turn, always involves something that’s given. In other words, to understand the first level, you need to understand the second level and the third level, or, as he (60) puts it, you need to realize that systems and structures only make sense to us inasmuch as they are “mediatized by tensors of discursivity” (semiotic tensors) or “by Assemblage synapses” (pragmatic entities).

This way of mapping the process is pretty difficult, which is certainly a disadvantage, aye, but it does have advantages over the presenting it as a net. While the net is simplistic and gives a good idea of how it all comes together, it may come across as very linear, going from one thing to another and that’s it. Of course, if you know that a content is, in itself, an expression, and that an expression can be content for another expression, you’ll get the point. No problem. That said, if you don’t know that, you may miss the point.

Guattari (57) comments on this difficulty, noting that, on one hand, you have these three levels of unconscious that are distinct and autonomous, and, on the other hand, the entities presuppose one another, operating through one another and even transforming one another, albeit, I guess, indirectly, at arm’s length, because, well, they do remain distinct and autonomous.

In my opinion, the major advantage is presenting it all on one plane, whereas presenting it as the net, so that you have the content plane and the expression plane, tempts you to think that there are two planes. It is certainly bewildering at first, before you read the text, again and again, to make sense of it, bit by bit, but once you understand it all, all those terms he uses, entities, tensors, and what not, you learn to appreciate it. I did, anyway.

Sure, good luck trying to use that presentation in an article, hahahaha, because there simply isn’t going to be the space for you to explain how it works. More is more, more complexity involves more complexity. This is why a net like presentation might work better in certain contexts. Then again, I might be wrong about that. I mean, Hjelmslev’s net does its job, aight, but it does require considerable familiarity with his work or with someone else’s takes of it.

Anyway, to add a further layer of complexity to this, it’s time to move on to valence. Guattari (65-66) states that there are bivalent codings and orderings, trivalent synapses and tetravalent synapses.

• Bivalent codings and orderings = conjunction of two (afferent) surplus tensors

• Effect of extrinsic coding (left side) = ΔT and ΔU, having the consistency of F and Φ respectively as they are in these domains
• Affect of extrinsic ordering (right side) = ΔF and Δϕ, having the consistency of T and U respectively as they are in these domains

He (65) exemplifies the Effects of extrinsic coding with “a ‘groundless’ perception of the order of delirium or hallucination” and the Affects of extrinsic ordering with “a ‘lived impression’ on an aesthetic, oneiric or mystical plane”. In any case, what’s worth noting here is that these codings (left side) and orderings (right side) are bivalent, which is a fancy way of saying that they are combinations of two elements. No more, no less.

• Trivalent synapses = conjunction of two (afferent) surplus tensors (ΔT and ΔU or ΔF and Δϕ) and one (efferent) synaptic tensor (Et or At)

• Systemically closed Effect (left side) = efferent synaptic tensor (Et) has the consistency of F
• Systemically open Effect (left side) = efferent synaptic tensor (Et) has the consistency of Φ
• Structurally closed Affect (right side) = efferent synaptic tensor (At) has the consistency of T
• Structurally open Affect (right side) = efferent synaptic tensor (At) has the consistency of U

He (65) specifies the first two, noting that a systematically closed Effect is “an effect of enslavement in the cybernetic sense”, such as “a conditioned reflect system”, and that a systematically open Effect is “a system far from equilibrium”, such as a “micro-social system[] in which family therapy and network practices endeavor to intervene”.

He (65-66) also specifies the latter two, adding that a structurally closed Affect is, “for example, an ego, superego or ego ideal function” and that a structurally open Affect is, “for example, a ‘becoming’ animal, child, vegetable, cosmos” or the like.

If you are familiar with his work, with or without Deleuze, he is in favor of those open Effects and Affects. Why? Well, because they are, indeed, open, as in open-ended. He is certainly for the rhizome (abstract machines, Phylas) and becoming (nomadic subjectivity) and against machinic enslavement (continuous de/reterritorialization; the hallmark of capitalism) and being (social subjection).

• Tetravalent synapses = intrinsic coding effects and systemic synapses, both open and closed, or extrinsic ordering Affects and structural synapses, both open and closed

To make more sense of this, when you combine something that is bivalent (two elements combined) with two synapses (one that is open and one that is closed, one plus one), you get tetravalence (four elements combined).

To summary this “game of taking consistency”, as he (66) calls it, you have all these entities, tensors and synapses, material, semiotic and pragmatic, that explain what an assemblage is or, rather, how it works. He (66) also notes that an assemblage can be polarized, either favoring persistence (from left to right), the virtualization of an Affect or transistence (from right to left), the actualization of an Effect.

• Persistence = persistential virtual implosion (from plural to unary)
• Transistence = transistential actual expansion (from unary to plural)

It’s worth adding here that while an assemblage can be highly polarized, it can never result in the removal of Affect or Effect, as pointed out by him (66). It’s like with Hjelmslev, how content and expression can never collapse into one another.

When it comes to taking consistency (of F, Φ, U or T), going from plural to unary, “[t]he more (intrinsic or acquired) consistency an Affect possesses at the degree zero of discursivity”, going from unary to plural, “the more consistency the differentiated Effect, with which it is assembled, is in position to acquire”, as explained by him (66). In other words, the more the consistency you have as a given, the more consistency the giving can have. So, yeah, more can get you more than less, and, conversely, less can get you less than more, as he (66) also points out.

He (67) calls this crossing over both ways, from content to expression and back, from the given to giving and back to given, the double movement of the affectation and effectuation of consistencies, which, I reckon, is his more sophisticated take on double articulation. You will like it if you want something better than Hjelmslev’s net, something that doesn’t appear to stop, but you’ll hate it if you think that this just adds unnecessary complexity.

What else is there

I was quite doubtful of this, how it’ll pan out, not to mention whether I can make sense of it, which I think I now can, but, yeah, I reckon it did pan out alright. It does question what we are used to, hierarchical and linear models, which is what he wants to accomplish with it, as he (67) points out.

I think I have to emphasize how reluctant I was to go through this. I mean, it is a very difficult book. That said, challenging myself, immersing myself in his jargon, turned out to be very productive. Not only did it help me to better understand his and Deleuze’s take on Hjelmslev, it also led to read and write on all kinds of interesting things that would never end up being published in anything ‘proper’, even though I kept this pretty clean. I mean, I was going go with ‘Axes, bloody axes!’ as one of the headings, but I went with something more ‘proper’ instead, just so that you who quit reading this essay, ages ago, never even getting to this point, being, you know, all ‘proper’, could continue reading, not having your feelings hurt by such impropriety.

His discussion of quantification was something that I particularly liked, because, like Baruch Spinoza, he gives it an interesting spin. I love how he is full on quantitative, and all nonchalant about it, which, I’m sure, angers a lot of people in the social sciences. The thing is, however, that he gives it the life it needs, which is exactly why I appreciate it. His discussion of the unconscious is also a highlight for me, because, like in his other works, he shifts our attention away from the subject, which would be the starting point in much of what it considered qualitative, to the production of subjectivity, which is, in his account, firmly quantitative, because it involves all those entities, material, semiotic and pragmatic, that are carried and transformed by the tensors. To combine those two, I just love the way he isn’t content with taking something as a given, but instead works his way, both vigorously and rigorously, to explain how the given is given, while also explaining how the given keeps on giving.

I may end up writing more on this book, but we’ll see what I get out of it. Maybe something, maybe nothing. We’ll see. In the meanwhile, I’ll try to go through this again, to fix some typos and other small blunders that I’m sure plague my essays. I don’t have a lot of time for such, but I try my best to fix those little things wherever I encounter them in these essays, in case you’ve ever wondered how a typo from 2020 has been fixed. It’s likely that I checked some reference, these being kind of like my own notes, only notice a small typo, so I’ve fixed it on the fly.

References

• Deleuze, G. ([1966] 1988). Bergsonism. New York, NY: Zone Books.
• Deleuze, G. ([1968] 1994). Difference and Repetition (P. Patton, Trans.). New York, NY: Columbia University Press.
• Deleuze, G. ([1990] 1995). Letter to a Harsh Critic. In G. Deleuze, Negotiations, 1972–1990 (M. Joughin, Trans.) (pp. 4–12). New York, NY: Columbia University Press.
• Deleuze, G., and F. Guattari ([1972] 1983). Anti-Oedipus: Capitalism and Schizophrenia (R. Hurley, M. Seem and H. R. Lane, Trans.). Minneapolis, MN: University of Minnesota Press.
• Deleuze, G., and F. Guattari ([1980] 1987). A Thousand Plateaus: Capitalism and Schizophrenia (B. Massumi, Trans.). Minneapolis, MN: University of Minnesota Press.
• Guattari, F. ([1972/1977] 1984). The Role of the Signifier in the Institution. In F. Guattari, Molecular Revolution: Psychiatry and Politics (R. Sheed, Trans.) (pp. 73–81). Harmondsworth, United Kingdom: Penguin Books.
• Guattari, F. (2006). Hjelmslev and Immanence. In F. Guattari, The Anti-Œdipus Papers (S. Nadaud, Ed., K. Gotman, Trans.) (pp. 201–223). New York, NY: Semiotext(e).
• Guattari, F. ([1989] 2013). Schizoanalytic Cartographies (A. Goffey, Trans.). London, United Kingdom: Bloomsbury.
• Guattari, F. ([2011] 2016). Lines of Flight: For Another World of Possibilities (A. Goffey, Trans.). London, United Kingdom: Bloomsbury.
• Hjelmslev, L. ([1943] 1953). Prolegomena to a Theory of Language (F. J. Whitfield). Baltimore, MD: Waverly Press.
• Hjelmslev, L. (1954). La stratification du langage. WORD, 10 (2–3), 163–188.
• Martinet, A. (1962). A Functional View of Language. Oxford, United Kingdom: Clarendon Press.
• Oxford English Dictionary Online (n. d.). Oxford, United Kingdom: Oxford University Press.
• Peirce, C. S. (1902). Virtual. In J. M. Baldwin (Ed.), Dictionary of Philosophy and Psychology, Vol. II (pp. 763–764). New York, NY: The Macmillan Company.
• Schein, R. H. (1997). The Place of Landscape: A Conceptual Framework for Interpreting an American Scene. Annals of the Association of American Geographers, 87 (4), 660–680.