A Tour of Lacan's Graph of Desire

In this video, we're going to go on a tour of Lacan's graph of desire. We'll check in at each of its points, explain what all this algebra means, and go through the concepts behind it. We throw in plenty of real-life examples, so if you're not familiar with Lacan already, or if, like me, you're turned off by Lacanian jargon, it'll still make sense. I'll also be putting all the quotations from Lacan on screen as we go through, so you can see what Lacan himself said about the graph of desire, and so that more hardcore Lacanians can follow up the references. Oh, and hit subscribe to see new videos as they're released and check out more about Jacques Lacan and psychoanalysis on LacanOnline.com.

So, background in history first off: almost everything from Lacan comes from his seminar, the collective name for the roughly twenty-seven or so year-long series of courses he did from 1952 to 1980. Each seminar is devoted to a different topic, and what you have in the Écrits is basically a 900-page condensation of all this material at around the midway point of Lacan's work, in 1966. Now, Lacan developed his graph of desire throughout Seminar V, from 1957 to 1958, which is on what he calls the "formations of the unconscious." Why "formations"? What are they? Formations, he says, are forms. Forms have relations to each other, and when we put them together, they comprise a topology. That's not exactly what we get in the graph of desire, but this is what Lacan tells his audience when he's wrapping up that seminar. And he says he didn't want to scare people away by talking about it at the start. When the graph of desire gets condensed for publication into the Écrits, it's the paper "The Subversion of the Subject and the Dialectic of Desire" where we find its most succinct elaboration. That's what most people use when they reference the graph. So it's with that text that we'll explore it here. That said, if you want a crystal-clear walkthrough by Lacan himself of the graph, head to Seminar V, specifically the later part of that seminar, to get your head around it, and then maybe come back to "Subversion of the Subject."

Now, the first thing to say about the graph of desire itself is that Lacan doesn't refer to it as a "graph of desire" anywhere in the Écrits or in Seminar V, when he spends months explaining it. He just calls it "his graph." It was Žižek, in particular, who popularized the idea of a "graph of desire" with his short commentary that we find at the end of the Écrits. So if it's not a "graph of desire," what is it a graph *of*? Well, in the first place, Lacan says it's a graph of what psychoanalysis shows us: the practical structure of the data of analytic experience. But it is about desire insofar as Lacan says it shows where desire is situated in relation to a subject defined on the basis of his articulation by the signifier. More on that in a moment. Second thing to say is that, as Miller correctly notes, there are graphs, not just one graph—four, to be exact—and we'll walk through each of them. While the later forms are extensions of the earlier ones, Lacan uses them to elaborate different ideas. So we'll treat them like a ladder, the comparison that Žižek uses, and take them step by step.

So this is what Lacan calls the elementary cell of the graph of desire: Graph 1. And we have four points. Our starting point is this little triangle here, and the trajectory takes us through to the barred S, Lacan's symbol for the subject. The subject is not the individual, not the person or the ego, but it is human subjectivity. And we should hear, in this term "subject," the implication "subject to." This is why Lacan describes the subject as a function. Lacan makes it clear that we're not talking about the subject of psychology. Lacan takes a pretty dim view of psychology, calling psychologists "Philistines," referring to its lowly purpose of social exploitation, and most cuttingly saying that psychologists just do a "judicial astrology." What's wrong with psychology is its criterion as the unity of the subject, he says. Hence why the subject here, S, has a bar for it. Lacan's dismal view of psychology is repeated throughout his work, and on LacanOnline.com you can read more in my article "What Does Psychoanalysis Have to Do With Psychology?"

Here, in "Subversion of the Subject," alongside criticisms of psychology, Lacan levels criticisms of the reduction of subjectivity to consciousness, or states of consciousness—even if there are higher forms of consciousness, like the degrees of Samadhi in Buddhism, the trips and highs of psychoactive drugs, or the states of enthusiasm described by Plato. Lacan's point, in short, is that no matter how much you meditate, you're still going to be a divided subject—what are you? In short, divided by the effect of the signifier, denoted here by S'. If you want to know more about the effect of the signifier, check out my videos on "What's So Unconscious About the Unconscious" and my series on repression. Here, I'm going to flash up some quotations from Lacan for those who appreciate the references, to illustrate how fundamental the effect of the signifier is in the construction of human subjectivity. But in short, we can say that a signifier is a linguistic unit, a fragment of language. A signifier could be a word or part of a word, but one which is unhinged from any particular meaning, any fixed representational reference, and which thereby refers only to other signifiers, denoted here by S', rather than to a particular meaning or signification. This assemblage of signifiers, taken together as a structure, is a key component in language—language as a formal structure rather than any particular language like English or French—as a whole. This is sometimes loosely referred to as the symbolic, the symbolic register, or the symbolic order. Lacan is saying that from the very start of our lives, indeed even before our births, we are [ __ ] by the symbolic, and once you're [ __ ], you can't get un[ __ ].

So notice it in the graph: this elementary cell of the graph. We begin with the barred subject. There is no entry point into language; you are already conditioned by language. Notice also here how the barred subject sits between two signifiers, in effect suspended in the gap between these S and S'. This is why Lacan says that the subject represents a subject for another signifier, in the same way that a lawyer represents her client for another lawyer, or an ambassador represents her country for another ambassador. Lacan's suggestion is that Freud had some intuition about this when he described how the unconscious worked before the arrival of modern linguistic theory. Freud talked about a primary psychical process which was characterized by two mechanisms: condensation and displacement. Lacan aligns these two with linguistic mechanisms: metaphor and metonymy. In other words, he says the effect of the substitution and combination of signifiers in the synchronic and diachronic dimensions respectively, in which they appear in discourse. The lesson to be drawn from the book-length studies that Freud wrote on dreams, slips of the tongue, and jokes is that these all show how unconscious processes are at work, which exhibit these same essentially linguistic mechanisms. Hence Lacan's most well-known maxim: "The unconscious is structured like a language." The unconscious is therefore a totally different form of psychical reality to consciousness. The unconscious is not a non-consciousness, not the negation of consciousness, as he refers to it here. Consciousness, he says, is obsolete to us.

In grounding the unconscious, what kind of subject do we mean then by "subject of a linguistic unconscious"? Lacan makes a distinction here between the subject of the statement and the subject of the enunciation. What do I mean when I say "I"? "I" by itself makes no sense. I have to follow it up with something: "I am happy," "I am tired," "I am a man," etc. And here we have the deferral of signification along a chain—more on that later. But what about a sentence like "I am lying"? Is the speaker lying, or is he telling the truth? Lacan uses this example because he says we can only understand it as non-paradoxical if we split the sentence into "I" and "am lying," and make a distinction between the subject of the statement and the subject of the enunciation. So is the subject lying, or is he telling the truth? Lacan's answer is that he is telling the truth via his lie. At the level of the subject of the statement, he is lying; at the level of the subject of the enunciation, he's telling the truth about that lie. The subject of the enunciation can be understood as the subject of the unconscious. It's a subject that emerges from within our speech, through our signifiers, and which differs from or contradicts the "I" of the statement. Lacan calls the subject of the enunciation the subject, not insofar as it produces discourse, but insofar as it is produced, cornered even, by discourse. What Lacan is getting at is the fact that the subject is not quite the agent of what he says as much as he speaks: he is spoken. The words that he uses carry a meaning which exceeds the one he hoped to convey when he opened his mouth, and it's through the act of enunciation that we have access to the unconscious in the psychoanalytic sense. This is why Lacan says that the presence of the unconscious, being situated in the locus of the Other, can be found in every discourse in its enunciation. Separating out these two subjects in speech can also help us understand how Lacan's famous maxim that "the signifier represents a subject for another signifier" refers to exactly this split between the speaking subject that enunciates words or signifiers and the "I" of the subject of the statement. As Lacan says, "What the unconscious brings back to our attention is the law by which enunciation can never be reduced to what is enunciated" in any discourse. In other words, an unconscious production is one in which you don't recognize yourself and what you've actually said. This is an exposé well known to anyone who's undertaking a psychoanalysis.

But let's take a more everyday example: advice. What's going on when people give advice? Salesmen are in a bar discussing work and the deals that they're expecting to close in the coming weeks. One boasts to the other that he's very confident on sealing a deal in the near future, and he's planning to commit to his boss that he will get it signed before the end of the month. His colleague jumps in with words of advice, given in the strongest possible terms: "Never commit, never commit," he says. These words might be taken as nothing more than sage advice. Were the men not at this particular bar, on this particular evening, to celebrate the colleague's engagement to his fiancée, with words "never commit," we can wonder what commitment was being warned against, and therefore who the advice was aimed at. What Lacan says in his Seminar IX on identification can tell us what's going on here. By this very fact in the enunciated, Lacan says, he—the colleague in our example—alights something which is properly speaking what he cannot know, namely the name of what he is. The enunciated subject, in the act of enunciated, there is this latent nomination. We never find the unconscious expressed with the first-person pronoun. While their unconscious thoughts, desires, and fantasies are often voiced through an enunciation which is ostensibly intended for someone else. So when we receive advice, we should always ask: who is this more relevant to—me or the person giving it? This is what Lacan calls the inter-dit, which in French is also a homonym of "forbidden." It is the very place at which the transparency of the classical subject divides, he says, and this is one of the reasons he calls the title of this paper in the Écrits "The Subversion of the Subject."

So back to Graph 1, the elementary cell. Think of it as like a button tie. Lacan says, beginning on the left, we have two signifiers, S and S', which represents the signifying chain. The signifier, Lacan says, stops the indefinite sliding of signification. What does this mean? Take the example of the phrase "The weed is..." How we finish this sentence with a further signifier will determine retroactively its signification. "The weed is getting me high" produces a different meaning-effect than "getting too high." One might refer to smoking a joint; the other to gardening. One refers to me; the other refers to a plant. How we end the sentence determines how we understand its beginning and how we position ourselves relative to it. Lacan's most famous illustration of this is with the bathroom doors analogy. From "The Instance of the Letter": two identical bathroom doors, behind which are presumably two identical bathrooms. The only thing that determines their difference is the signifiers "Gentlemen," "Ladies" above them. The point Lacan is making is that the difference lies not in the thing, the signified, but in the signifier—"Ladies" and "Gentlemen." The signified is totally out of play. In Lacan's model, we know that young children have grasped this when they start making signifying substitutions in their use of language. The example Lacan gives here is when a child says that the cat goes "woof woof" and the dog goes "meow," referring to the properties of things in a way that presents them as exchangeable—the one thing can stand for another, and these two things are not inherently fixed to a given reference. Graph 1 presents the subject as caught in the loop of the signifier's passage. As we said earlier, the little triangle at the bottom right is the starting point of our journey through this graph. Or, as Pontelise calls it in his write-up of Lacan's Seminar V, "that by which the human subject, in his essence as problematic subject, is situated in a certain relationship with the signifier." What does this mean? Let's take another example: a man complains of two problems. First, he thinks he's too skinny, and so he eats large portions of high-calorie food in an attempt, he says, to gain weight. Second, he suffers from insomnia. When I ask what it is that keeps him awake, he says, "Some things in my life have a lot of weight." The same signifier in different contexts. When we say someone is unconscious of something, we should think that they've repressed it, in the sense of pushed it down into the unconscious. It's simply that they don't see the link between two things in different contexts. In our example, the connection between the man's eating habits and his insomnia. Remember that when we ask someone to describe some aspect of their life, they could say whatever they liked. That they used the same term to describe two things which then have no connection indicates to us that there may indeed be a link, and that this link is worth exploring. But why does this vector run backwards, in a negatively oriented direction, with the signifier's vector, as Lacan puts it? Exactly because of the retroactive effect of signification that we saw earlier with the "weed" example. What works here is what Freud calls the "effect of Nachträglichkeit," translated by Žižek as "peh-chu," and translated better by Laplanche and Pontalis afterwards as "afterwardsness." It's a crucial concept in psychoanalysis that Lacan pulled out of Freud, and which Laplanche built pretty much an entire career around. Unfortunately, in Strachey's translation at the Standard Edition, its German is rendered as "deferred action," which doesn't quite capture the subtleties of "afterwardsness." In English, we can also read this negatively oriented direction to refer to the way that the subject receives his message back from the Other in inverted form. More on that later.

And so on to the second version of the graph, where Lacan introduces a new set of terms. Let's start with A and S(A). Here, A is the Other, with a capital O—the so-called "big Other"—because it's not an Other like another person, but instead what he calls the locus of the treasure trove of signifiers. One way to think of the Other is like a switch point in a network. In any network, it's not the input that matters, but the passage—it's just such a junction. In the same way that a train station is indifferent to the trains that pass through it, so the Other has no subjectivity or intentionality in its own right. It's like the pure subject of modern game strategy, Lacan says—the preliminary site of the pure subject of the signifier, like the traffic flowing through a junction at any one point. Lacan describes the Other as the inscription of a combinatorial—combinations may be exhaustively enumerated. It's the Other of language, or the Other of language in its entirety. So it's not the place where everything gets a meaning, like the key to the code—even if we might appeal to the Other in order to find meaning. It's rather the space where speech and language are constituted, because language, the words we use, can be distant or alien to us even as we speak them. Even if we speak a particular language very well, we can think of the Other as the site where language as a purely differential structure comes together—a network of signifiers that only makes sense collectively, founded on binary opposition to each other, like night and day, Adam and Eve, or ladies and gentlemen, in Lacan's analogy. Now, this only makes sense when we look to the left, S(A), and we see punctuation. Lacan says the effect of punctuation on a signifying chain, just as we saw in the elementary cell with the "weed" example. As Lacan says, "One is a locus, a place rather than a space; the other is a moment, a punctuation rather than a narrative."

So let's trace this line that runs from the signifier on the left to the voice on the right by thinking about how the infant negotiates his entrance into this symbolic order. The child is born into a signifying universe that precedes him and which divides him—a world of signifiers which, in their brute, roaring materiality, are absolutely meaningless. The significations that are communicated to the child by the Other—let's say, from the caregivers—incarnated for the child, the Other, are denoted by s(A). But to the mother or caregiver, these significations are themselves alien, because their signifiers will always carry a signification of which they are unaware. This Otherness is an aspect we see in the voice, which can be thought of as this signifying chain—the effect of meaning, as Miller puts it. There's a great example of this trajectory in action in Freud's case history of little Hans, real name Herbert Graf. This young child, four and a half years old, has just taken a bath and notices that when his mother dries and powders him, she takes care to avoid one special part of his body. Hans finds this odd and asks his mother why she won't touch it. "Because that'd be piggish," his mother replies. "What's that—piggish?" Hans retorts. "Because it's not proper," she snaps back. Notice how we have two signifiers that made no sense to Hans—"piggish" and "proper"—and they're given that signification by the mother, even though she herself doesn't know where they come from or what they really mean. They are, in Freud's excellent term, "pre-sexual," but it's great fun. The Hans case demonstrates how the register of language can be used as both the condition and prohibition of enjoyment.

So let's trace the line that runs from the barred subject up over the graph via the Other to the significations from the upper S back to A. And let's explain this with an example from another of Freud's case histories—that of the Rat Man, real name Ernst Lanzer. Ernst shared a memory with Freud when he was very young. He'd done something wrong and was beaten by his father. In response, the Rat Man put up a verbal fight, but as he knew no bad language—for it relates, he called him all the names of common objects that he could think of, and had screamed, "You lamp, you towel, you plate," and so on, as Freud tells it. So shaken was the Rat Man's father by the fury of this outburst that he stopped; he declared, "The child will either be a great man or a great criminal." Freud notes the patient believed that the scene made a permanent impression upon him as well as upon the father. The beating stopped and never happened again, but the Rat Man attributed his later fear of violence and his own rage to this scene. In psychosis, we have something a bit different going on. Code messages and message codes separate out into pure forms in the psychotic subject—a subject who makes do with this preliminary Other alone. Lacan says, what's he talking about? At the onset of psychosis, we find what the German-Swiss psychiatrist Karl Jaspers called "elementary phenomena." This was picked up by Lacan as early as his doctoral thesis on paranoia in the early 1930s. Lacan gives an example in Seminar III of how this works. The subject sees a red car passing on the street; he doesn't know what this means, but he knows it means something, and that this meaning pertains specifically to him. This is the appearance of meaning as such, and it's one of the early signs that the illusion is about to crystallize. Thus we run from the barred subject via the image to the presence of meaning as such. In psychosis, we might also find certified auditory hallucinations, whereby the signifier is divorced from the signifying chain and thereby from any signification. So we can understand the location of the voice here in...

This context - so what about these - this is the image over from the other. Notice the big Other, as denoted by the capital A, and this is the image of a from the other. Notice the small a denoting the semblable, the mirror image. (A) is the point of the ego ideal, and (a) is the point of the ideal ego. What's the difference? If the ideal ego is the person you identify with, whether it's the person you would like to be, the ego ideal is the point from which that image takes on a value. The point that sanctions or invests that image as being worthy or lovable.

What Freud points out in chapters 7 & 8 of *Group Psychology and the Analysis of the Ego* from 1921 is that what's at work in identification is not a kind of mirroring, not a specular immediate identification, but the support given to that identification. As Lacan puts it in his remarks on this in Seminar 11, the ego ideal is the point from which the subject will see himself as others see him. Lacan introduces the ego ideal with reference to what he calls the unary trait, a concept more crucial than Lacan scholars usually give it credit for. Here he says that the unary trait performs the role of filling in the invisible mark the subject receives from the signifier, which alienates this subject in the first identification that forms the ego ideal.

What does this mean? Again, it's an idea that has its heritage employed in Chapter seven on identification in *Group Psychology*, for it gives the example of his patient Dora, who imitated the cough of her father. In this case, identification, for Freud, has appeared instead of object choice. Object choice has regressed to identification. Dora's identification is not to a person as such, but to a particular trait of that person, which borrows what Freud in German calls *eine Einzigkeit*, a single trait. Lacan reiterates the term that Lacan uses; he talks at length about this in the seminars of the mid-60s. Halfway through Seminar 11, for instance, Lacan refers to how prehistoric cavemen would signify the killing of an animal they'd hunted by marking it off with a single stroke, perhaps on a cave wall or on their weapon. The killing of the animal is represented by a 1, and the subject counts his first killings: 1, 1. Each mark is a signifier, and the Lacanian idea is that human subjectivity is essentially suspended in the gap between the signifiers.

But this doesn't mean that human subjectivity is some kind of effervescent antimatter or insubstantial pure lack. The marks or strokes just give him a place, enabling him to situate himself in a signifying structure. The subject is barred, but not entirely swallowed by the Other, a point Lacan makes in Seminar 11 when he tells his audience that this single stroke, this *eine Einzigkeit*, constitutes the subject at the level of which there is a relation of the subject to the Other.

Two reasons why we're dwelling on the unary trait: first, because the idea from Freud is that when identification occurs via this single trait or characteristic, it's not a form of identification that is linked to a libidinal attachment or love interest in the person. The *Einzigkeit* simply provides what Lacan calls, in Seminar 8, the sign of the Other's assent. It's the reference to the ego ideal that gives the fantasy of the ideal ego its weight. The gaze of the Other is internalized; it occurs *as* a sign. There is no need, as Lacan puts it, for the whole organized field or for some sort of massive introjection. What this means is that a particular trait, an X, is valued by the Other in some way; that's why it's a sign, as something that has a meaning to someone, and in that respect gives the child a fixed point he can relate to amongst all the specular identifications and mirroring relations around him. So all of the ideal egos that follow will depend on the ego ideal.

The second reason we're dwelling on the unary trait is because it's a kind of frontier concept between the imaginary and the symbolic. It's the object raised to the status of the signifier. It's not an imaginary representation of the object, like a little sketch of the animal that's killed on a cave wall; it's simply a notch, a stroke, or a mark. This is what Lacan means when, in Seminar 9, he says that the *Einzigkeit* functions as a support for difference. It designates the paradox of radical otherness. This unary trait can give the subject a place in the symbolic order; it provides both a substantive presence and a singularity, a uniqueness that is the opposite of the pathological coincidence of self and other, which is a feature of the imaginary register.

Now notice that in Graph 2, the ego ideal comes in the place where we found the barred subject in Graph 1, the elementary cell of the graph. What's this about? Like I was trying to present a retroversion effect by which the subject at each stage becomes what he was to be. A beautiful line from earlier in *Écrits* may help us explain this: "What is realized in my history is neither the past definite as what was, since it is no more, nor even the perfect as what has been in what I am, but the future anterior as what I will have been, given what I am in the process of becoming." Packed into this difficult quotation, we find the idea of after-witness mentioned earlier. We also see notions of fate, destiny, repetition, and transmission. And even though he says he won't talk about the mirror stage here, Lacan goes on to give it a more developed elaboration than the purely specular one that the theory received in his original 1936 Marienbad paper. In particular, here we get the idea of an anticipation of bodily mastery that is at the core of the mirror stage theory. In short, this is the idea that we identify with an image outside ourselves, an image which presents to us a model of corporal unity in order to achieve motor coordination and mastery over our own body, but that comes at the price of our fundamental alienation in the image of the Other. Hence Lacan's line: "There arises the ambiguity of a mis-recognizing that is essential to know myself."

To explain this, we now have to trace the journey along the bottom quadrant of Graph 2, the journey that goes from the barred subject to the ideal ego to the ego and to the ego ideal. Let's explain this vector running from the idea of ego to the ego a bit more. This is the image of the Other, or the image as Other in the Imaginary register. The I here is the image, the a the Other. In order for the infant to achieve motor mastery, coordination, and to be able to identify its image—why not the image it sees in a mirror as its own?—it has to model itself on the image of another. This is how the ego is constructed. There is no other way to get to the ego except via the image of the Other. This vector is at the level of the Imaginary, Lacan's realm of images, but as we can see from its connection to the ego ideal and the barred subject, it's not possible to separate off the Imaginary from the Symbolic. The fretful preoccupation with the image in the Instagram age shows this dynamic in action. We ceaselessly share and admire images, images through which we see ourselves, but only at the expense of how others present their own image—that is, how they would themselves like to be seen.

What Lacan says about this dynamic is so relevant to our day and age that it almost feels surprising that it's written 60 years ago, not late last night. But for Lacan, the rivalry inherent in this Imaginary dual relation has a really dark side. The ego is thus a function of mastery, but it's at the same time a game of constituted rivalry, he says, which casts a shade of hostility onto the Other that can rapidly boil over into an intense, violent outburst, as we see in these passages from *Subversion of the Subject* and in the mirror stage paper and in his paper on aggressivity. There's a rivalry inherent in the Imaginary register anytime it's not mediated by a symbolic operator, whether that symbolic operator is inefficient or simply not present. Lacan warns in no uncertain terms that it can become murderously violent. So much of Lacan's work is about how this alienation in the image produces aggressive outbursts, and so many of the clinical cases that interested him exhibit this feature. His commentary on the infamous case of the Papin sisters and his doctoral thesis on self-punitive paranoia, in which his subject M.A. stabbed a well-known actress of the day, serves to show how seriously Lacan took this.

But let's take an example from more recent times. On the 30th of July 2008, a man called Vincent Li boarded a Greyhound bus traveling from Edmonton to Winnipeg in Canada. He sat next to a 22-year-old man named Tim McLean, who barely acknowledged him and fell asleep, his head against the window of the bus. Shortly after, Li pulled out a hunting knife and began stabbing McLean. As the terrified passengers evacuated the bus, Li began cutting off his victim's head and dismembering him. With Li locked aboard the bus, he brandishes McLean's severed head to the passengers and begins to eat the eyes and part of the heart of the body. When he's finally arrested, police find other body parts stuffed into his pocket. At his court appearance, Li is bereft with remorse; the only words he utters to the judge are the plea: "Please kill me." He's devastated to hear that the Canadian legal system does not allow for capital punishment. In this sad and shocking case, we see exactly the phenomenon that Lacan is talking about. Just as in the Papin case, and just as in M.A.'s case, a paranoid delusion fixes on the image of an ideal—in this case, the young and trendy McLean—and there follows an abrupt and violent outburst that leads to the destruction of that image. Because the ego is founded on the image of another, and because, as Lacan hypothecated in the M.A. case, paranoia has this self-punitive dimension in which the paranoid destroys the Other he would like to be, when this image is destroyed, the ego is destroyed with it; hence Li's desperate plea to be killed, something we also see in the case of Christine Papin, who after the crimes attempts to gouge her own eyes out and eventually dies from malnutrition in prison.

Now let's look at the third form of the graph. We have a new upper portion framed by a question: "Ke Vô? What do you want?" which Lacan took from a 1772 novel by the French author Jacques Cazotte, *Le Diable amoureux* (The Devil in Love). It's no accident that the curve the graph forms around this resembles a question mark. We also have two new symbols in the third form of the graph: this diamond symbol, or lozenge, which in French is called a *losange*, and which does quite a lot of work in *Écrits*. It indicates the relation between the other two symbols it conjoins. Lacan says that it registers the relations: envelopment, development, conjunction, disjunction, and we'll explain later the use Lacan makes of it in this formula. It's helpful to see this losange as the soldering together of the mathematical symbols for "less than" and "more than," because taken together they don't just indicate a relation, but a contradictory relation. How could something be both less than and more than? Secondly, we have the appearance of a lowercase d, which indicates desire, but in order to explain desire, we're going to have to first explain demand, which Lacan writes with an uppercase D.

What is demand, for Lacan? It's not a demand for anything as such, any particular object, whether one that can satisfy a need or not. Instead, it's a demand for recognition, or as Lacan says, a demand for love as such. It's an appeal to the Other. Notice that there's no need in the graph. Lacan criticizes those analysts of his time who were so caught up on the notion that subjectivity is formed in relation to the experience of helplessness by the newborn infant in its caregivers' willingness or otherwise to satisfy its needs. We talked about need only in order to distinguish it from demand and desire. Need is almost totally out of play for Lacan because we never really find a pure need; it's always polluted by the order of language, which means that what we experience as need is never pure, even basic biological needs. Let's take the example of the newborn infant: it wants to be fed; it cries; it may or may not get the bottle or a breast, but it may cry for other reasons, and the caregiver may still respond with a bottle or a breast. Thus, the experience of even the most basic needs is already conditioned through the significations given to them by the Other. As Lacan says, needs have been diversified and geared down by and through language to such an extent that their import appears to be of a quite different order. Needs are always expressed as demands, which are never demands for a particular object, but an appeal to the Other as such. "There is no demand," he says, "that does not in some respect pass through the defiles of the signifier."

Now on to desire, and notice that to get to desire, we have to pass through the Other. "Let us begin," Lacan says, explaining desire with the conception of the Other as the locus of the signifier. When Lacan says that there is no Other of the Other, he means that there's nothing to which the Other can refer to for legitimacy, no ultimate guarantor of truth and meaning. It's a locus, not a person, and therefore Lacan can say that anyone who claims to offer this ultimate guarantee is an impostor. Incidentally, although Lacan gets accused of embodying patriarchy, he also says here that it's not the Father who embodies this support; it's the Mother. Desire begins to take shape in the margin in which demand rips away from need, Lacan says, imagining a young baby who is hungry and cries out for milk. The need is the hunger; the cry is the demand. What's left over, the margin between the two, is desire. The thing about desire is that it is need-less, both in the sense of being split off from need and in the sense of being contingent, totally senseless.

The best way to explain the difference between need, demand, and desire is in reference to the object. Now this term "object" means something different in psychoanalysis to what it means in everyday talk. Normally we use the term "object" in the sense of a thing, like an object on a table, and we also talk about an object in the sense of an aim or goal: the object of your affection, the object of this exercise, for instance. The psychoanalytic object is kind of halfway between the two. Take happiness, for instance. Happiness might be a goal or an aim in your life, but there's no one object or thing that, if you got it, you could say would make you happy. This is why psychoanalysis opposes happiness, and why Freud thought that there was a fundamental discontent baked into civilization, thus in *Civilization and Its Discontents*, as Jay Laplanche points out, happiness is a category of what Freud calls the pleasure principle. So what's wrong with happiness is that it relies on the subject's inability or unreadiness to fully confront the consequences of their desire. The price of happiness is that we remain stuck in the inconsistency of our desire; we believe that having this or that thing will make us happy, and we fail to see that it's happiness itself which is infinitely hypocritical in that the quest for happiness only leads to the infinite metonymic deferral of desire.

So with these two meanings of object, we can make sense of the difference between desire and demand. Desire has an object in the sense in which we speak about the desire for something or someone, but desire has no object in the sense of an aim or a goal. It's infinitely metonymic, which means that as a byproduct of the split between need and demand, it appears only as a consequence of them. Demand has an object in the sense of an aim or goal, but its object is not material in the sense of a thing; its object is the recognition of the Other. All demand is demand for love, as Lacan says. This is what Lacan refers to when, in a cryptic passage, he talks about the odd symmetry by which desire reverses the unconditional demand for love in order to raise it to the power of an absolute condition. If we think about the example of sexual desire, this becomes clear. Sexual desire has an absolute condition: the presence of a certain object that is necessary to get off, but it doesn't necessarily have an object in the sense of a thing. The gaze and the voice are two examples that Lacan uses often. A certain look that someone gives is enough to excite sexual desire; same goes for the tone or tenor of someone's voice. Lacan calls them *objets a*, that is, little objects, with the a denoting ultra-small Other, a part of the Other as opposed to the big Other. There are objects that exist at the margins or edges of the body but lack a specifiable substance to them. They do not have a specular dimension in the same way as, we can't point to the gaze; we can't point to the look, because when we do, we just end up pointing at the eye. In a beautifully poetic way, Lacan describes *objets a* as "a substance caught in the net of shadow which, robbed of its swelling volume, holds out once again the filler of the shadow as if it were substance." Lacan calls *objet a* the object-cause of desire. Its paradoxical status as both the object and cause of desire is something he picks up on later in *Subversion of the Subject*, where he describes it as "like an *alma mater*, a precious treasure hidden in a worthless box." This is part of the extended reference he gives to the strange attraction of Alcibiades to Socrates in Plato's *Symposium*, building off the long commentary in Seminar 8 on that text in relation to transference.

This is the formula for fantasy: the subject in relation to the *objet a*. What Lacan calls the structure of fantasy is built from the three elements in the barred subject. We have the moment of a fading or eclipse of the subject, which is closely tied to the splitting of the I due to its subordination to the signifier. In a, we have the condition of an object, the object-cause of desire. The link between the two is what constitutes fantasy. To see this in action, we can turn to Freud's work on fantasy, where we see these three elements that Lacan shows here as comprising the structure of fantasy: where Lacan has barred subject-relation-*objet a*, Freud has subject-verb-object fantasy. Freud details the infinite combination of these elements, which is why Lacan says that his formula is designed to allow for 401 different readings. For Freud's idea was that the fantasies we're thinking—a particular of sexual fantasies here—could be formulated as a sentence. Freud picked one that he found cropping up with unusual regularity in his patients: "a child is being beaten," and he showed how the fantasy is rephrased in a series of grammatical inversions. Likewise, Freud says that every sadist is also a masochist; he or she can enjoy from both sides of this formula. As Lacan's son-in-law, Jacques-Alain Miller, puts it when commenting on the difference between the drive and the fantasy: "Fantasy is a mis-recognition of the drive. Fantasy is that by which desire sustains itself in order to mis-recognize the direction pointed out to it by the drive." The same goes for fantasy in a wider sense. Take the case of Schreber, for instance. Daniel Paul Schreber wrote what is probably the most famous account of psychosis from the inside in his memoirs, *Memoirs of My Nervous Illness*, in 1903, and it has fascinated people for over a century. Before Freud thought that the appearance of his paranoia directed towards his psychiatrist Flechsig was a result of repressed homosexuality which morphed into paranoia, the grammatical inversions in this case were: "I love the man," this idea is rejected, "I hate the man," also problematic, "The man hates me," in which we have the paranoid crystallization. Reading the losange, or lozenge, a combination of less than and more than, we see that, as we did above, this too presents a situation of impossibility. Now, regardless of what we think of Freud's reading of the Schreber case, we can see that it's these lexical configurations which propelled and sustained all the transformations in the fantasy scenario that Freud noted in the production of sexual fantasies. Thus, Miller defines fantasy as meaning related to satisfaction, and fantasy is their conjoining. As for Lacan, he describes his formula for fantasy as an absolute signification. This denotes the more general sense of the term "fantasy," what Miller describes as a compass or a rule that governs our lives. Fantasy is the pattern we repeat, the groove we fall into, our modus operandi. This is why in psychoanalysis it's always important to locate the fantasy to understand what particular relation that person has constructed between meaning and satisfaction. It may be the pattern of always putting oneself in the position of a victim, or always striving...

For dominance, for Freud, according to a brilliant analysis made by LeClair in a paper called "Unconscious Desire with Forehead Reading Freud," this formula was to reveal a secret. Seriously, go read this paper. The fantasy would draw towards it all of the little contingencies of life, of fit them into a single frame. This is why, in his third iteration of the graph, Lacan talks about how desire adjusts to fantasy like the ego does emulation to the body image.

Now on to the final, complete version of the graph. Because we explained demand earlier, we can now explain the drive, which is denoted with this formula: the subject in relation to demand. What does the drive have to do with the man? An ink between these two is already made by Freud, whose brilliantly enigmatic definition of the drive is as the demands made upon the mind for work in consequence of its relation to the body. Our definition gives twice in the three essays on the theory of sexuality and then the metapsychological paper from 1915, "Drives and Their Vicissitudes." Free and cheap Shak's alla Lakorn attempts to locate the drive on his graph here by saying that the drive is what becomes a demand when the subject vanishes from it. Okay, so we're talking about a kind of pure demand. But then he continues, "It goes without saying that demand also disappears," oh, except that the cut remains. For the latter remains present in what distinguishes that drive from the organic function it inhabits, namely its grammatical artifice. So manifests in the reversals of its articulation with respect to both source and object.

How do we make sense of this? Take the example of alcohol addiction. We have a split from the organic function: drinking to quench thirst. But for the alcoholic, drinking inhabits that function in the way that the Trojan horse inhabits our citadel: source and object reversed, as Lacan says here. In that the source of the drive, from where the organic need of thirst arises—the all zone in this case, with this locus at the mouth—is given over to the object. The organic need is cheapened in favor of the object: alcohol becomes more important than water, and thirst for water becomes thirst for alcohol. Vampire movies play on this trope very well. There's no better illustration of the all-drive at work than the undead vampire, driven by a lust for blood which neither quenches its thirst nor keeps it alive. Lacan's own example here of Pavlov's dog is also not bad either.

Now turning to this formula: the signifier of a lack in the other, which Lacan describes as a lack inherent in the other's very function as the treasure trove of signifiers. This means that there's no Other of the Other, as we saw earlier. But note that here there is a signifier that itself denotes this lack: a signifier that signifies a fundamentally lack of any possible signification. To make sense of this, think of the pure signifier: zero. What is zero ontologically? It's nothing, but as a signifier, it still needs to denote the fact of nothing. The paper for which Jacques-Alain Miller made his name, "Suture: Elements of the Logic of the Signifier," is a meditation on this paradox. Alain Badiou calls it the first great Lacanian text not to have been written by Lacan himself. This is not some abstract theoretical point; it's a personal question for each of us to deal with, because it signifies that there is nothing which can ultimately guarantee the other's consistency; that there is ultimately no answer to what the other wants from us. Okay, boy.

Now, in Lacanian jargon, one way to think of this signifier of the lack of the other is with Lacan's concept of the phallus. The phallus, for Lacan, acts as a signifier or memorial of lack; it's a kind of positivation of an absence. It occupies a very privileged place because the phallus is also the signifier of desire and the signifier of sexual difference too, which means that the signification of the phallus is the point around which all articulations of sexuality are referenced. To illustrate this with an example: the center of my city, London, is Charing Cross. It's the junction where six roads meet, and when people measure the distance of any other place relative to London, Charing Cross is taken as ground zero. The official center of central London is the point from which distances from London are calculated. The site takes its name from a memorial erected by King Edward the First to his wife, Eleanor of Castile. Grief-stricken, he placed monuments at each station marking the procession of her funeral cortege. Thus, Charing Cross is both an orientation point and a signifier of lack.

But the signifier of the lack in the other is also a very necessary structural element because it allows for the flexibility or mobility of the signifying chain. Without one special signified, and noting the lack in the other, there will be no chain of signifiers, no sliding of the signified under the signifier, and each signification will be fixed into a closed code. Imagine something like a jigsaw puzzle: if all the pieces were locked into place, nothing would move, and we would be stuck with one image defining the whole of reality. But with one piece missing, the others can shift; new significations can become possible. And thus, all the practices that depend on being able to play with the signifier and signified to create new significations—the world of art, literature, culture—all become possible.

At this point, Lacan gives his definition of the signifier: "A signifier is what represents the subject to another signifier." We can see that logically there has to be a chain of signifiers because, as he puts it, "This latter signifier is therefore the signifier to which all the other signifiers represent the subject," which means that if this signifier is missing, all the other signifiers represent nothing, for something is only represented—just to the left of the signifier—the lack in the other. We have jouissance, a difficult term in itself, and there's a full article explaining Lacan's idea of jouissance on that LacanOnline.com. But here we can approach jouissance by asking: what does Lacan mean when he says that jouissance is prohibited to whoever speaks as such? Or, put differently, it can only be said between the lines. Well, notice the pun that Lacan makes in French between dire and interdit—between saying and forbidden. Elsewhere, Lacan talks about jouissance as being a caustic enjoyment, a backhanded enjoyment which begins as a tickle and turns into an inferno. Complete enjoyment is impossible because it must run through the signifier. The child's entrance into language, with its inherent structural lack as we saw, means that enjoyment or excitation is sort of progressively drained from the body so that its only refuges are at the margins of the body—what we know as the erotogenic zones—the place where the objects a are found, in places of exquisite and complete results and with the critical function of protecting us from it. We get a kind of paltry jouissance. Bruce Fink's term, "desire," is a compensation for jouissance and the defense against it. Lacan says it's a kind of a cack-handed, roundabout way of enjoying—roundabout because it passes through the files of the signifier. And because of this, desire manifests itself in odd places: appearing in the half-said, in the slips or parapraxes, in the stifling or bungling of some other articulation. Desire is the very consequence of this impossibility.

Let's take an example from Freud's practice of what this looks like. He sees a man who is attracted to women who have what he refers to as a "certain shine on their nose." Freud's understanding of this is based on the fact that the patient had been brought up in an English nursery but had later come to Germany where he'd forgotten his mother tongue almost completely. The fetish, Freud calls it a fetishistic precondition, which originated from this earliest childhood, has to be understood in English, not German. The "shine on the nose," in German Glanz auf der Nase, was in reality a glance at the nose where the ability to look or gaze was restricted and the enjoyment curtailed. It's mangled and metabolized via the signifier, resulting in "glance auf der Nase," "shine on the nose," being what excites the man. Notice Lacan says that there's no agency forbidding jouissance; no one's telling us that we're not allowed to enjoy whatever kinky perversion we please. It's not the law itself that bars the subject's access to jouissance; he says it simply makes a bad subject out of an almost natural barrier. The symbol of this effect is the phallus, defined as the signifier of jouissance insofar as it finds incarnation in the erectile organ. But even this imaginary incarnation still retains symbolic effects because the phallus—phallic—is the male organ plus the idea of lack. And so Lacan gives it a symbolic formulation: the square root of minus one.

What does this mean? Lacan's English translator, Bruce Fink, helps us out: the phallus represents what is missing in the desired image, incarnated as the male organ. The phallus is negative jouissance; it's situated in the specular image; it is a part that's missing in the desired image. Thus, we have minus phi, not included here in the graph but which is the algebraic form Lacan uses for castration at the end of this vector. In symbolizing this loss, the phallus is transformed. Think of this as the post-castration phallus, and you get some sense of why reading the phallus as the penis makes no sense. Castration here refers to the evacuation of enjoyment to the margins of the body: a draining of excitation to the body extremities, at localized points that Lacan aligns with the source of the drive, or will: anal, scopic, oral. Hence why the phallus is the signifier of jouissance. So Fink tells us, think of the phi, this symbolic phallus, as a minus one. We go from a minus value to a plus that neutralizes the imagined loss. And Fink says that this is exactly what the signifier does: it makes the absent thing present. Just as a young child that Freud observes uses the signifies "fort" and "da" to make absence into presence when it throws the cotton wheel to the side of its bed and pulls it back again in an attempt to master the presence and absence of its mother. We make sense of pure loss and absence only when the thing in question is granted a representation. Now Fink refers us to Lacan's "The Signification of the Phallus" paper at this point and to a gorgeous German term that Lacan uses to illustrate this: Aufhebung. This curious term has a rich history in philosophy as it connotes several seemingly contradictory meanings, including to lift up, to abolish, to cancel or suspend, to preserve, and to transcend. In English, it's often translated "sublation," which means nothing to anyone. To quote Fink's explanation: "The phallus is the symbol of this positivation of the loss that language performs. It represents a lack despite it being present." And what is the best way to represent in an image something that is lacking but at the same time present? Veil it. This is why, in "The Signification of the Phallus," Lacan says that the phallus can only perform its function when veiled. A weird example that he offers at the end of "Subversion of the Subject" illustrates this: "Such is woman, concealed behind her veil. It is the absence of the penis that makes her the phallus, the object of desire. Evoke this absence in a more precise way by having her wear a cute fake one under a fancy dress, and you—or rather she—will laugh plenty to tell us about the effect. It's a hundred percent guaranteed for men who don't beat around the bush." That is, the effect here, I take to mean sexual attraction on the part of men who don't beat around the bush; I take to mean men who are straight.

Towards the end of "Subversion of the Subject," Lacan brings these different formulas together to describe the situation of the neurotic, whose defining problem is a conflation of the other's lack with the other's demand. Consequently, the neurotic is he or she who takes seriously the other's demand, so seriously as to make of it their object. Now, the mistake that many analysts made, Lacan thinks, is to see this as evidence of frustration, whereas it's actually covering over the anxiety induced in him by the other's desire. Phobia is the perfect example of this, but the other neuroses can be defined in terms of their configuration of this fantasy. The obsessional strategy is to deny the lack in the other, to believe that nothing is lacking. He has a fundamental need to be the other's guarantor, Lacan says. And hysteria, rather than being a 19th-century pathologization of unruly women, in Lacan's countenance, is defined as a position in which the faithlessness of hysterical intrigue is the result of desire for desire itself—in other words, desire for a lack of satisfaction, for a margin to be retained in which something is lacking. The hysteric aims at infinitely perpetuating the other's desire and thereby will always strive to create situations in which the other is shown to be lacking. What the neurotic aims at, says Lacan, is to have the perfect master of his desire. The name of this agent, for Lacan, is the Father. Like the Other, the Father is less a person than a place, or more precisely, a function, which is to measure desire, not in the sense of restricting it, but in the sense of ensuring its proximal distance from an overwhelming enjoyment that Lacan calls elsewhere "the Thing," borrowing from its German term, das Ding.

Now, although it's not depicted on the graph, Lacan's masterly rereading of the Oedipus complex by way of what he calls the paternal metaphor—the substitution of the desire of the mother for the name of the Father—looms large. This function of the Father is thus an important operator, not in some vague fashion, but for the analyst using clinical practice. Lacan thinks that how we work with the position or function of the Father is one of the more useful levers we can pull in order to have a psychotherapeutic effect—an effect which is produced by shifting the subject's perspective relative to his or her fantasy. If the neurotic wants to find the perfect master of his desire, as Lacan says, the analyst should take care not to incarnate this figure in the transference but to bring it into play in order to destabilize or undermine it. Practically speaking, this means it's not always going to be the best strategy for the analyst to remain neutral, passive, or silent, because this would position them in the very masterly position they should attempt to question. Let's take an example from the Rat Man's case history. At one point, Freud notes simply, "December 28th: He was hungry and was fed." While it may seem unorthodox for a psychoanalyst to be preparing his patient a meal during a session, an intervention like this is justified if it produces more associative material, more grist for the mill of the analysis. This example isn't the one that Lacan uses, and Lacan says he's not making any recommendations on technique, but what he does say is super instructive: how the analyst must safeguard the imaginary dimension of his non-mastery and necessary imperfection, for the other is as important a moment to deal with as the deliberate reinforcement of an ever-renewed ignorance, so that no one is considered a typical case. So that no one is considered a typical case. At the end of "Subversion of the Subject," Lacan talked a bit more about the position of the neurotic—which is to say, most of us—relativity to castration. Castration slips under the barred subject in the fantasy life of the neurotic, he says. What covers over this castration is his ego. Yes, it's behind this ego that the neurotic hides the castration he denies, Lacan says. So if your approach to psychotherapy aims at strengthening the ego, it's missing the point, because it misses the point of castration as a defense against jouissance on the one hand and as a yardstick of desire on the other. And as such, it misses what lies beneath, namely that, contrary to appearances, he cleaves to this castration. The point is not to deny it but rather he doesn't want to sacrifice it to the other's jouissance—that is, to allow the other to exploit his lack for its own gain. The neurotic gets that things must come at a price, but to pay that price by allowing the other to enjoy is intolerable for him. So if we look at the arc that runs from fantasy and jouissance on the left to castration and desire on the right, we can see the central dilemma of the neurotic—that is, of most of us. To get over this curve towards castration, we have to reject jouissance, full enjoyment, and accept the fact that the best satisfaction we're going to get is the one that desire offers, despite its infinite autonomy, its twists and turns, its perpetual dissatisfaction with an object. This is what Lacan means when he ends the paper with one of the most beautiful lines in the whole oeuvre, and which we can take as something of a mantra for a life resigned to the reality of constant striving: "Castration means that jouissance has to be refused in order to be attained, on the inverse scale of the law of desire." Hit subscribe to see more videos from Lacan Online as they're released, and check out much more stuff exploring psychoanalysis through the work of Jacques Lacan on LacanOnline.com.