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Seminar XXII of Jacques Lacan, R.S.I.Text established by Jacques-Alain Miller.Translated by Jack W. Stone, with the assistance of Ellie Ragland, Greg Hyder, Filip Kovacevic, and Zak Watson.

Introduction to this Publication

A wager which is that of my teaching, why not hold it to the extreme, since somewhere note has been taken of it, and not print it as it is? The hesitation is not necessarily mine. My relation to [rapport au] the composite public who listens to me amply motivates it. That I testify of an experience I have specified as being analytic and mine, is there supposed for veracious. Seeing where this experience leads me by its statement (énoncé), has the value of a supervision [contrôle] (I know the words I employ). The "categories" of the symbolic, of the imaginary and of the real are here put to the proof of a testament. If they imply three effects by their knot, if this is discovered by me not to be able to sustain itself except by the borromean relation, these are the effect of sense, the effect of jouissance, and the effect . . . I have said of non-rapport to specify it from what seems most to suggest the idea of a rapport, to wit, the sexual. It is clear that these effects are implications of my categories themselves: which may be futile even if they indeed seem to be inherent to "thought."

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I explain in the measure of my means what the knot, and a knot of a sort that mathematics is still little devoted to, can add of consistency to these effects. One will remark, however, to leave said consistency on the level of (au ras de) the imaginary takes here the value of distinguishing it in a triad which keeps its sense, even in demonstrating that the real is excluded from it. This is the type of problem I find again at every turn (without looking for it, it should be said). But the measure itself of the effects that I say can only modulate my dire. To add there the fatigue of this dire itself does not lighten for us the duty of accounting for it: on the contrary. A marginal note, like page 8, may be necessitated to complete a circuit elided in the seminar. It is not the touching-up which is here "futile," but, as I stress, the mental itself, to the extent that it exists.

Jacques Lacan

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Seminar of November 19, 1974There isn’t a microphone. So you’ll have to tell me if you can hear me.1There are people—I know it because they have told me—who go on strike (vivent la

grève) as if it were a holiday (fête). I know it, of course, through analysis. We find things out in analysis. We even know that there are people twisted enough for that. But why not? It’s subjective, as one says. That means that there are some people who can make all kinds of things turn out all right. Nonetheless, I’m not one of them. As analyst, I can only take a strike as a symptom, perhaps in the sense that I’ll arrive at with you this year, by convincing you that the symptom, when it’s referred to one of the three categories, is real. The troubling thing—and this is what makes me have reservations—is that it’s an organized symptom. That’s what’s malignant, at least from the point of view of the analyst.

Well, if I’m going to strike all the same, it’s not that it will be a holiday for me. It happens that this strike is for me like a ball and chain. I mean that it happens that today, namely at the beginning of the 74-75 [academic] year, I didn’t have the slightest desire (envie) to do a seminar for you—as is shown by the fact you never saw a poster advertising the title of it as in previous years. Nevertheless, I must say that your numbers here today have shaken me.2 You know that each year I ask myself what could be the reason for such large numbers. I haven’t figured it out yet, but all the same, I consider it an appeal, an appeal based on the fact that what I wrote—nothing more than wrote, I mean what is written on the board in little signs, the a, the S1, the S2, the of the subject, namely the analytic discourse—is something that riles you up. I say riles you up. It’s not a “you,” a “riles you up” in a neutral sense. It’s true that to have written it, as an approximate attempt, means that perhaps one could do better. I hope that we will do better.

But finally, this year I really have to tell you that I have other concerns. I’ll only be given credit for that—in your eyes, I hope—if I continue to pursue my seminar here. I have other concerns, and I wonder if it is necessary that I put them first. I mean that among you—and I see that you are numerous here—there are people who belong to my School. And perhaps, after all, my weariness comes from what is eating away at me, namely that this seminar keeps me from being more being more closely involved with the School.

This year, I’m taking a stand, to energize this School, of which certain of you have heard an echo. I’m not going to place this concern that I have in a public forum. Not, of course, that it’s anything private, quite the contrary, since what’s involved is the fact that elsewhere, there are other teachings besides mine. It’s strange, strange in the specifically Freudian sense, unheimlich, that it is from those who still aren’t in a position, properly speaking, to be authorizing any analysis, but who are on the way to it, from them comes the resistance to the reasons why I energize them. I energize them to make effective—what? In a testimony that they give from whatever point they’re at, to make effective the pass that, as some of you know, I am trying to introduce in my School. And in the pass it’s simply a matter of each making a contribution to the analytic discourse by testifying about how one enters it.

It is strange that among them there are those who are trained analysts and who when I

1 Lacan’s seminar for the year was scheduled to begin on this day, but there was a strike called.

2 With a possible pun on se branler, ‘to masturbate’.

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literally—this is what I did in the area where I would like certain teachings to take place—when I literally beg for their help—and that’s what I did—refuse it in the most categorical way, going so far as to oppose me with insults that make their way into journals, for example—that’s not what has any effect on me—but who, as if it isn’t already bad enough to have this insult dragged into a journal, namely Le Monde, as if by chance, then blow it all out of proportion and add to it. Yeah!

If I speak to you this year, I’ll take things from the angle of an identity of self to self. The question is to know whether that applies to the analyst. Could the analyst be considered an element? In other words, could he make a set? Make a set, that’s something I’ll try to explain to you. It’s not the same as forming a union (syndicat). Those are two different terms. To make a set could mean, does mean, to be able to make a series. And the question I want to ask is, where does that series stop? In other words, could an analyst, taking the example of that to which I just alluded concerning the insult, act like an imbecile? It’s a very important question. How are we to determine what I call imbecility? Surely it has a meaning, even in analytic discourse. Elsewhere too, of course. Within each discourse, nobody slips up: one is in imbecile or not. In relation to the discourse of the master, the discourse of the university, and the scientific discourse, I say that there can be no doubt about this. But how do we define imbecility in the analytic discourse? There’s a question, a question that I introduced, my goodness, as long ago as the first year of my seminar by stating that analysis is certainly a remedy against ignorance, but it has no effect on stupidity (connerie). Pay attention for a minute! I already said that stupidity isn’t imbecility. How do we situate imbecility and distinguish it from stupidity?

The troubling and difficult thing about this question that I raise is perhaps the thing you keep quiet about. I don’t insist on it too heavily, but even so, we have to admit that there are subjects for whom analysis, I mean the analytic experience, doesn’t succeed when they submit themselves to it. And I’ll say explicitly that this makes them imbeciles. At the start there has to be something to seek out. Maybe that means that they would be more useful elsewhere, utilizable elsewhere. I mean that elsewhere they have obvious talents. This leads us back to the ethics of each discourse, and it’s not for nothing that I advanced the term “ethics of psychoanalysis.” That ethics isn’t the same, and maybe those people that ethics makes a huge success elsewhere are the ones who don’t succeed in analysis. A simple hypothesis, but one that maybe—and it may not be without detours—maybe if I bring myself to do it, we will finally put to the test—that’s a manner of speaking, really I will put it to the test—starting from what I told you, that there is no other ethics than that of playing the game according to the structure of a discourse, and there we will rediscover the meaning of my title form last year: they are not duped, those who don’t play the game of a discourse, and thus they find themselves in error. They’re not necessarily any the worse for all that. Only it’s at their own risk.. Those who err in each discourse aren’t necessarily useless to it—far from it! It’s just that it would be better if to lay the foundation for a new one starting out from these discourses, one were a little bit duped by them.

There! So all the same it would be pointless to tell you that I’m going to hang it up, that I wonder what I’m going to do this year. That would be pointless to do for two hours well you listen to it. Ah, well, I’m not going to do it. I’m going to stop here, and ask of you only that you trust in the knowledge that if you return here on December 10, the second Tuesday, you can rely on the little posters on which will be written the title of this year’s seminar, if I do it. It is

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completely unnecessary—and I will say even counter-indicated—that you bombard Gloria with phone calls. The poor thing can’t handle any more. One of two things will happen. Either the poster will be put up there, and then I’ll also have to think, the poster will be there in the corridor two days ahead of time, or it won’t be. And if it isn’t, well, you can say I’m taking a year’s sabbatical. If it is, I’ll count on your being as numerous as you are today.

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Seminar of December 10, 1974

Real, symbolic, imaginary--these three words each have a sense. These are three different senses. But that they are different, does that suffice to make them three? If they are as different as I say, doesn't that create an obstacle? Where is the common measure? The unity here could become a function of measure: one counts--one, two, three. It is still necessary to found the equivalence of these unities on a sign--to make two little lines, or to write equal. And if by chance they were others, so to say, the one to the other? We would indeed be in a difficult situation, and, after all, what would show it would be the sense itself of the word "other." But there isn't only one. The first other--first because I begin with it--is defined, for example, by the distinction exterior/interior. It is that of Freud, whether or not he wanted it to be, in his second topic, which is supported by a geometry of the sack. The sac is supposed (censé) to contain--it is funny to say--the drives. It is this that he calls the Id (Ça). He obviously finds himself forced to add there a certain number of utensils: a sort of lunulla, which all at once transforms it into a vitellus, on which an embryo is differentiated. This is obviously not what he means, but his schema suggests

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it. And I will not tell you all that he is still forced to add, not counting I don't know what hachure he titles the Superego. Such are the disadvantages of imaged figurations. This topology of the sack is indeed what we have business with in topology, insofar as the sack chalks itself on a surface, and makes a round, of which there is an interior and an exterior. It is with this that we are lead to write inclusion in a set. We utilise this sign, , from which one can slip to this, . If i e, i e--a manifest stupidity. There you have the first other. Only, there is another, which I have marked with an A, which is defined as not having the least rapport--so little as you imagine it. When one begins to take words as one's vehicle, one finds oneself quickly in a trap, because my so little as you imagine it puts the imaginary back into the mix. With the imaginary, you have every chance of getting bogged down. With the imaginary, one has departed for the infinitesimal, and it is a real pain (mal de chien) getting out of it. Let us begin again. That they are three, this real, this symbolic, and this imaginary, what does that mean? There is a slope that leads you into homogenizing them. What is firm is--what relation do they have between them? It is here that I would like to clear for you a path this year. We could begin by saying that the real is what is strictly unthinkable. This would make a hole in the business, and that would allow us to interrogate what there is of what, don't forget, I have started from--three terms inasmuch as they carry a sense. What is this sense? In analytic practice, it is with sense that you operate. But on the other hand, you only operate to reduce it, since you always operate with the equivoke--I speak here of those who are worthy of the name of analysts. The equivoke is not a sense. The equivoke is fundamental to the symbolic, to that by which the unconscious is supported, as I structure it. Sense is that by which something answers that is other than the symbolic, which is--there is no other way of saying it--the imaginary. What is the imaginary? Does it even exist?--since you puff over it just in pronouncing the term. Well! I would say that if the speakingbeing demonstrates itself to be devoted to mental debility, it is because of the imaginary. This notion in fact has no other point of departure than the reference to the body. And the least of assumptions implied by the body is this: what represents itself for the speaking being is only the reflection of its organism. Only, something quickly makes us stumble--from a body one presumes--it is even its definition--that it has specified functions in its organs. Such that an automobile, even a computer the last we heard, is also a body. To say it all, it does not go without saying that a body is alive. What best attests that it is, is precisely this mens that I have introduced with "mental debility." For it is not given to all bodies, inasmuch as they function, to suggest the dimension of stupidity. Where does this come from? Language (La Langue), and not just any language, Latin, has coined a word for it. This is what puts back in their place those who impute precisely to Latin this stupidity, while it is the only language that has not come up with an opaque term, the ηουs, or who knows what other metaphor--for a knowledge of which we cannot know if it ex-sists, since it is the knowledge supposed by the real. The knowledge of God, it is certain that it ex-sists, we have given ourselves enough trouble to spell it out. It ex-sists, but only in the sense I inscribe by ex-sistence, otherwise than is usually done. It sists perhaps, but no one knows where.

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All we can say is that what con-sists gives no testimony of it. It is then striking that the language that we suspect of being the most stupid is itself the one that has coined the term intellegere, to read between the lines: that is, otherwise than in the way the symbolic is written.

It is to this effect of the writing of the symbolic that is owed the effect of sense, in other words, of stupidity--shown to this day in all the so-called systems of nature. Without language, we could not have the least suspicion of this stupidity, which is also how the body is shown to be alive.

In truth, this mental debility, attested to, I do not hope to get out of in any way. I don't know why what I bring you would be less stupid than the rest. This would make sense of that banana skin that someone slipped under my foot in ringing me up to go to Nice and give a conference on, I kid you not, The Lacanian Phenomenon.

Well! I do not expect this to be a phenomenon. If I persevere--and you know that I persevere without looking twice--it is only because I believe myself to have grasped something, one couldn't say with my hands, but with my feet--the entrance in play of the trace that the analytic experience draws; which, it must be said, is not so easily supported, and notably by analysts. Such that, if there is a phenomenon, it can only be the lacananalyst phenomenon, or else laca-not-analyst.

At Nice, naturally, I could explain nothing of all that to them, since for them I was a phenomenon. The organizers, what they wanted was to attract a crowd. And there is always a crowd to see a phenomenon. Me, I was not going to say to them--You know, I'm not a phenomenon! That would have been Verneinung. In the end, I let loose for a good little hour and a quarter.

And then, I posed them some questions, I mean--I asked them to pose me some. This was a request (demande). You will believe me, if you wish, that unlike you, they posed them, for three quarters of an hour, and these questions were striking in this way: they were pertinent, in a second zone, of course. To the extent that I found myself in the situation, without having challenged the Lacanian phenomenon, of having demonstrated it. The Lacanian phenomenon--it is not certain that they grasped it themselves--is that I have effects on a public which has only heard from very far, by repercussion, what I articulate here, the teaching I do to clear the way for the analyst to the discourse that supports him, insofar as it is indeed from discourse, and always from discourse, that suffers this little thing that we try to manipulate in analysis. That's it, the phenomenon. And it is in sum a little vague. And I might have been tempted to write the three letters in an other order--instead of "RSI," "RIS," which would have made a laughing (ris), that famous laughing of water over which I equivocate in my Ecrits--on page 166.

I must comfort myself in saying that this phenomenon is not unique, it is only particular--I mean that it is distinguished from the universal. What is annoying is that it has been to this day unique at the level of the analyst. However, it is indispensable that the analyst be at least two: the analyst having the effects, and the analyst theorizing those effects. This is why I so appreciated being accompanied by a person who is an analyst.

Parenthesis closed; and I can now get to what I want to advance today. I have only found one way to give a common measure to these three terms, real, symbolic, and imaginary: it is to knot them as a Borromean knot. These rounds-of-thread, what is it that distinguishes each

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from the other? Absolutely nothing but the sense. And this is what gives us hope that we will take a step this year--hope in the short term, there is no other.

The hope is only for me in this business, but if I did not have the answer, as you know, I would not ask the question. Certainly, when you win something somewhere, it is forcibly at the expense of something else. And in other terms, if analytic discourse functions, we will certainly lose something elsewhere. But if all of the systems of nature arisen up until now are marked by a mental debility, what good is it?

I would like to return to the Borromean knot for an instant.The Borromean knot consists strictly insofar as three is the minimum (fig. 1). If you

unknot two rings in a chain, the others remain knotted. In a Borromean knot, if you break one of the three, all three are liberated. The remarkable thing, a fact of consistency, is that you can add an indefinite number of rings--it will always be true that, if you break one of the rings, all of the others, however numerous, will be free. See this figure, which at I have already sketched for you (fig. 2).

This property alone homogenizes all that there is of number after three. In the sequence of whole numbers, 1 and 2 are detached--something begins at three that includes all of the numbers, as far as they are numerable. This is what I put the accent on in last year's seminar.

That is not all. There is more than one way to Borromize a number of consistent torii. I have already indicated to you in its time that there are many probably, a quantity that there is no reason not to qualify as infinite, in the sense of the numerable, because you only have to make a loop in the following fashion (fig. 3). It is clear that you can make as many turns as you like to knot together two torii. There is no plausible limit to this arrangement. It will be no less true that the borromean knot, whichever, has for its inferior limit the number 3. The borromean knot will always carry the mark of the 3. On this basis, you have to ask yourself, to what register does the Borromean knot belong? Is it to the symbolic, the imaginary, or to the real?

I put forward beginning today what in what follows I will permit myself to demonstrate--the Borromean knot, insofar as it is supported by the number 3, is of the register of the imaginary. For the triad of the real, of the symbolic, and of the imaginary only exists by the addition of the imaginary as third. And it is by this that space, insofar as it is sensible, is found reduced to this minimum of three dimensions--that is, by its attachment to the symbolic and the real--where the imaginary is rooted.

Other dimensions are imaginable, and they have been imagined. It is for holding to the symbolic and the real that the imaginary reduces itself to what is not a maximum, imposed by the sack of the body, but, on the contrary, a minimum, which makes it so that we don't have a Borromean knot except beginning with 3.

Before leaving you, I am going to give you some punctuations of what we are going to have to demonstrate this year.

I would like to draw to your attention that it is not at all implied in the notion of the Borromean knot that it be a matter of rounds of thread or of torii. It is just as conceivable that, comformable to the intuition of Desargues in ordinary geometry, these rounds will open or, to say it simply, become cords, conceived of as rejoining themselves--why not?--at infinity. One can nonetheless define in this way what one calls a point.

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In Euclidean geometry--it is indeed strange--the point has no dimension at all, contrary to the line, the surface, the solid, which respectively have one, two, three. You know the Euclidean definition of the point as the intersection between two straight lines. Isn't there, I will permit myself to say, something that sins (pèche) here? For what, finally, prevents (empêche) these two lines from slipping over one another? Me, I would like, for defining a point, three straight lines disposed like this (fig. 4).

These straight lines are not here simple edges, strokes of a saw, shadows; they are effectively consistent straight lines, which realize the essence of the Borromean knot, which is to say, determining, gripping, a point as such. But it no longer suffices to speak here of a dimension which might be zero, which, in other words, does not dimension. We must invent something else.

Let us make the effort to say that these are not simply strokes, but three surfaces. You will obtain the said effect of a point in a fashion as valuable as with three cords.

With two infinite straight lines, take note of it, we can, by knotting a single round of thread, maintain the property of the Borromean knot (fig. 5). On this condition alone, that the two straight lines would not be able to overlap themselves between this knot and infinity except in a single fashion, that is, taking the straight line R, which must be pulled, if I can say so, forward, while line S can only be pulled behind. They must not be linked two-by-two. This is excluded by figure 6, where we see the blue infinite straight line pass beneath the one below and above the one above, to put it simply. On this condition, the Borromean knot functions. Labeling as I do the blue round as real, the black as symbolic, and the red as imaginary is situated by a flattening out, in other words, by a reduction of the imaginary. The imaginary always tends to reduce itself to a flattening out. All figuration is founded on this. Of course, it is not because you will have wadded up these rounds of thread that they would be less Borromeanly knotted. In the real--which is to say, in regard to the fact that one of them unknotted liberates the other two--that changes nothing.

But how is it that we need this flattening out to be able to figure any topology whatsoever? This is very certainly a question that touches on that of the debility I have qualified as mental, inasmuch as this debility is rooted in the body itself.

I have written a here, at the central point. In the imaginary, but also in the symbolic, I inscribe the said function of sense. The two other functions to be defined in regard to the central point are two jouissances.

One of these two jouissances--but which?--we could define as enjoyment of life (jouir de la vie). If the real is life--but is this so certain?--since this jouissance participates also in the imaginary of sense--we must situate it here. This is no less a point than the central point, the point called the object "a" since it conjoins on the occasion three surfaces which are also wedged together.

What then is the other mode of jouissance?These are the points we will have to elaborate on, since they are also those that we

interrogate.Moreover, Freud, to return to him, has stated something triadic: inhibition, symptom,

anxiety. Can we situate these three terms?

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Inhibition, as he articulates it himself, is always an affair of the body, that is, of function. And to indicate it already on this schema, I will say that it is what somewhere stops interfering in a figuration of the hole of the symbolic. Is what an animal encounters, where there is a central inhibitor in the nervous system, of the same order as this imaginary arrest of functioning for the speakingbeing? How would it be conceivable that the putting in function, for the being presumed non-speaking, in the nevrax, in the central nervous system, of a positive inhibitory activity would be of the same order as what we know to be exterior to sense, exterior to the body? How, in other words, can we topologize this surface in way that, as I have said to you, it is assuredly only on two surfaces that it is figured? How can inhibition have any business with this effect of arrest which results from its intrusion into the field of the symbolic? We will have to discuss this.

It is anxiety, insofar as it takes its departure from the real, that is going to give sense to the nature of the jouissance which is produced by the overlapping, in the Eulerian sense, of the real and of the symbolic.

Finally, to define the third term, it is as symptom that we identify what is produced in the field of the real. The notion of the symptom was introduced well before Freud by Marx, as the sign of what does not work in the real. If we are capable of operating on the symptom, it is because it is from the effect of the symbolic in the real.

Inasmuch as this knot, although only reflected in the imaginary, is indeed real, and encounters a certain number of inscriptions by which some surfaces respond, I can advance that the unconscious is what answers from (répond de) the symptom. Thenceforth, we shall see, it can be responsible for its reduction.

Marginal Note for Figure 3

It is obvious (!) that this kind of Borromean chain has an "end"--without which it is unknottable one by one (one-by-one round). For traction does not make a knot: dissociation of force and ex-sistence.

Thus there are two fashions to buckle it (in the "sense" of making it hold in a knot).One is to close it in a circle. Which is true of all other Borromean chains. But this must

be put aside for the moment.The true Borromean chain remains open: cf. the three-linked chain.There is nothing easier than to reproduce this three-linked chain with what we sketch

here. Here is the flattening out that demonstrates it (fig. 7).As soon as this chain is longer, if only by a single round, the round (F) that closes it here

must double itself at the other end of the open Borromean "chain." It can also be filled in for in its function of One by what follows it: 1=2. Whence the privilege of the three-linked chain, which, as we shall see, distinguishes it from the four-linked chain, where the order begins to be no longer any whatsoever. We shall dot the i's concerning this.

J.L.

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Concerning the Lecture of December 17

I speak here of the mental debility of systems of thought that suppose (without saying it, save in the blessed time of the Tao, even of ancient Egypt, where this is articulated with all the necessary stupification), that supposes therefore the metaphor of the sexual rapport, non-ex-sistant in any form, in that of copulation, particularly "grotesque" for the speakingbeing, which is conceived of as representing the rapport that I say does not ex-sist humanly. The focus (mise á point) which results from a certain ventilation of said metaphor, elaborated in the name of philosophy, doesn't go forasmuch very far, no farther than Christianity, fruit of the Triad which in "adoring it" exposes its true nature: God is the not-all that it has the merit of distinguishing, in refusing to confuse him with the stupid idea of the universe. But it is indeed in this way that it permits itself to identify him with what I expose as this to which no ex-sistence is permitted because it is the hole as such--the hole that the Borromean knot permits us to distinguish (to distinguish from ex-sistence as defined by the knot itself; that is, the existence of a consistency submitted to the necessity (=not ceasing to write itself) of not being able to enter the hole without necessarily exiting it, and beginning with the following "time" ("the time" [la fois] of which the crossing of its putting flat creates faith [foi]). Whence the correspondence I try to arrive at of the hole with a real which will find itself conditioned later by ex-sistence. How might I manage the approach to this truth with an audience as maladroit as I reveal myself in the maladress I demonstrate in managing the putting flat of the knot, even more its real, which is to say, its ex-sistence? I will therefore leave that there, without correcting it, to show the difficulty of the access to a discourse commanded by a wholly new necessity (cf. above). What I must demonstrate, in fact, is that there is no jouissance of the Other, genitive objective, and how to arrive there if I strike so truly from the outset that the sense being attained to, the jouissance which consonates there puts in play the damned phallus (=the ex-sistence itself of the real, that is, taking my register: R at the second power) or, again, what philosophy aims to celebrate. This is to say that I am still completely bogged down; I speak of the Philo, not of the Phallo. But there is enough time not be hasty, by fault of which we will not just miss what is at issue, but err irremediably, which is to say, "love wisdom," a necessity of Man. To be corrected. This is why it requires the patience with which I exercise the D.A. (to be read: discours analytique). There always remains recourse to religious idiocy, which Freud never lacks: I say this in passing, although politely (we owe him everything).

J.L.

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Seminar of December 17, 1974

The Borromean knot is a writing. This writing supports a real.Can the real then support itself by a writing? But of course, and I will say more--there is

no other sensible idea of the real than that given by writing, the stroke of the written (trait d'écrit). I will now introduce what I am going to say to you this morning with some remarks, three in number. I suppose that you must have asked yourselves the question of whether the knot I proffer to unite RSI is a model, in the sense one understands, for example, of those mathematical models which permit us to extrapolate as to the real. A model is a writing. Based on this fact alone, it is situated by the imaginary. Not an imaginary without substance. These questions that are formulated, are imagined beginning with this written, are founded on it, are secondarily posed to the real. But this real is nothing but a supposition. This supposition consists precisely in the sense of this word, real. Well then, I claim that the Borromean knot, as I use it, is an exception--although situated in the imaginary--to this supposition. All that it proposes in fact is that the three that are there

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function as a pure consistency. It is only by holding to each other that they consist--holding to each other really. To say this implies a metaphor. Whence the question, what is the err--in the sense in which I understood it last year--the err of the metaphor? Follow me well: if I state--which can only be done through the symbolic, through speech--that the consistency of these three loops is only supported by the real, it is because I make use of the distance (écart) in sense permitted between RSI as individualizing these loops, specifying them as such. The distance in sense is there supposed taken at a certain maximum. But what is the maximum allowed for a distance in sense? This is a question I can only pose to a linguist. How would a linguist define the limits of metaphor, which is to say, of the substitution of one signifier for another? What is the maximum distance allowed between the two? Second remark. To operate with this knot in a suitable fashion, you must use it stupidly. Be dupes. Do not enter this subject in obsessional doubt. Don't dawdle (chipotez) too much. Take Maupertius. He gave at the Berlin Academy, under the title The Physical Venus, a report on the point of knowledge arrived at in his epoque concerning the reproduction of living bodies. He was pleased--his title indicates it to you well enough--to emphasize only sexed reproduction. Note the date--1756. This shows the time these speaking brutes that are men have put into accounting for the specifics of sexed reproduction. This Physical Venus illustrates for us the cost of playing the non-dupe. Maupertius was in fact wrong not to stick with what his time furnished him as material, which was already a lot. Leeuwenhoek and Swammerdam had already established through the microscope the existence of what one then called "animacules," that is, spermatozoa, and they distinguished them very clearly from eggs. We know that ordinarily there are two different bodies supporting them, and that this defines these bodies as of the opposed sex. Save for some exceptions, of course--look at the snail. But Maupertius, to say it all, was not stupid enough, and as a result he misses the point of discovery constituted by this massive distinction for the real apprehension of the differences between the sexes. If he were more of a dupe, he would have erred less. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . He is a non-dupe--he makes hypotheses. I invite you to repudiate the hypotheses, and, here, to be stupid enough not to ask yourselves questions about the usage of my knot. It will not serve to go farther than there from where it emerges, that is, the analytic experience. It is this experience that it accounts for. There is its worth. Third remark, also preliminary. The imaginary founds the consistency of this knot. As regards this imaginary consistency, jouissance can only ex-sist, that is, parody it; as regards the real, something other than sense is at issue in jouissance. The signifier, based on this fact, is deprived of sense--it is what remains. And all that remains comes to propose itself as intervening in jouissance. Must we understand that the I think suffices to insure ex-sistence? Certainly not, and Descartes stumbles. But it is no less true, up to a certain point, that ex-sistence is only defined as effacing all sense. Descartes himself also floated between the ergo sum and the existo--but assuredly the notion of existence was not then assured. I will say that for something to exist,

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there must be a hole. Is not this hole simulated by the I think, since Descartes empties it? It is around a hole that existence suggests itself. Now this hole, we have one at the heart of each of these rounds. Without these holes, it would not even be thinkable for something to be knotted. But it is not a question here of what Descartes thought. It is a question of what Freud touched on. How therefore can we situate with our knot what ex-sists to the real of the hole? I propose symbolizing it by an intermediary field, intermediary insofar as put flat--writing in fact requires (impose) as such a putting-flat. This intermediary field is given us by the opening of the round into an infinite straight line, isolated in its consistency. I must now explain myself concerning the notation where I have indicated that what there is of ex-sistence metaphorizes itself by phallic jouissance. It is to the real as making a hole that jouissance ex-sists, and I situate it therefore by the field produced by the opening of the round connoted R. Jouissance's ex-sistence to the real is the fact analytic experience has brought us. With Freud there is something like a prosternation before this phallic jouissance, of which his experience led him to the discovery of the nodal function, and around which is founded the sort of real with which analysis is concerned. That phallic jouissance is tied to the production of ex-sistence, is what I propose to you this year to put to the proof. Let us remark that this jouissance only situates itself by the wedging that results from the nodality proper to the Borromean knot. There are two other fields that are situated in the same fashion. As a result, this knot, as I have said, is doubled by another triplicity. To what does ex-sistence ex-sist? Certainly not to what consists. Existence as such is supported by what, in each of these terms, RSI, makes a hole. There is in each something by which it is from the circle, from a fundamental circularity which defines itself, and this is what it is to name. From the time of Freud, what is named is only imaginary. Conformed to this necessity according to which it is to the imaginary that goes the substance, Freud designates by the function of the ego nothing other than what makes a hole in representation. No doubt he does not go as far as to say it, but he represents it, in his fantasmic second topic . . . . . . . . . . . . . . . . Which holes constitute the real and the symbolic? Something offers itself to us, which seems to go by itself: it is to designate by life the hole of the real. Moreover, this is an inclination that Freud himself did not resist. As for the function of the symbolic, if we interrogate with our knot the structure necessitated by Freud, we find it on the side of death. In the symbolic, in fact, something is urverdrängt, something to which we never give sense, although we are capable of saying that all men are mortal. But this statement, because of the all, makes no sense. The plague had to be propagated in Thebes for the all to cease to be of a pure symbolic, and to become imaginable. Everyone had to feel themselves concerned in particular by the threat of the plague. It is revealed at the same time that if Oedipus forced something, it was completely without knowing it. He only killed his father in failing to take the time to Laïussize.3 If he had done so for the time it took, this would have been the time of an analysis, since that was what he was on the road for--he believed, because of a dream, that he was going to kill him who, under the name of Polybus, was well and good his veritable father.

3 Larousse defines "Laius" as a "long-winded speech."

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What Freud brings us concerning the Other is this: there is no Other except in saying it, but it is impossible to say completely. There is an Urverdrängt, an irreducible unconscious, the saying of which is not only defined as impossible, but introduces as such the category of the impossible. Religion is true. It is certainly more true than neurosis, in that it denies that God is purely and simply what Voltaire believed as firmly as iron--it says that He ex-sists, that He is the ex-sistence par excellence, which is to say, in sum, that He is repression in person. He is even the person supposed repression. This is why religion is true. God is nothing other than what makes it so that beginning with language, there cannot be established a rapport between the sexed. Language, where does it come from? Does it only come to stop up the hole constituted by the non-rapport constitutive of the sexual? I have never said that--because the non-rapport is only suspended in language. Language is thus not a simple stopper, it is that in which is inscribed the non-rapport, and this is all that we can say. God himself is not in language, but he brings with him the set of the effects of language, including psychoanalytic effects, which is not to say little. To fix things where they merit being fixed, which is to say, in logic, Freud does not believe in God, because he operates in his own line, as is shown by the dust he throws in our eyes to agitate us. Not only does he perpetuate religion, but he consecrates it as the ideal neurosis, in attaching it to obsessional neurosis, which well merits being called ideal properly speaking. In doing this, he is himself a dupe, in the good fashion, one who does not err. He is not like me, who can only testify that I err. I err in these intervals that I try to situate for you with sense, phallic jouissance, indeed with the third term that I have not clarified, because it is it that gives us the key to the hole, the hole such as I designate it. It is the jouissance that concerns not the Other of the signifier but the Other of the body, the Other of the other sex. Why did Freud qualify Eros with the One, in daring to refer to that Platonic enormity, the myth of the unified body, of the two-backed body, the body all round? We embrace another body in vain, which is only the sign of an extreme difficulty (embarass). It is a fact of experience, for which Freud, however, did not account--and why?--it happens--Freud catalogues it, as he had to, with regression--that we suck this body, but what can that really do? Apart from breaking it in pieces, one does not truly see what one can do with another body. I mean a body called human. This justifies the fact that if we seek what might edge this jouissance of the other body inasmuch as it surely makes a hole, what we find is anxiety. There was a time when I chose this theme of anxiety. I chose it because I knew that this would not last--I had in fact some faithfuls who employed themselves in reviving some motions of order which could in what followed make me declared inapt to transmit analytic theory. It is not at all that this caused me anxiety, nor even difficulty. What I taught then concerning Inhibition, Symptom, and Anxiety, shows this: that it is altogether compatible with the fact the unconscious is conditioned by language to situate some affects there. Is it not by language that we are affected in a prevalent fashion? Inhibition, Symptom, Anxiety, I have staggered these terms on three planes, demonstrating that they are as heterogeneous to each other as my terms real, symbolic, and imaginary.

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What is anxiety? It is what, at the interior of the body, ex-sists when something awakens it, torments it. Look at little Hans. If he rushes into phobia, it is to give body--I demonstrated it for a whole year--to the difficulty he had with the phallus, with this phallic jouissance that had come to associate itself with his body. He then invents a whole series of equivalents to this phallus, diversely hoofed. His anxiety is the principle of his phobia--and it is in rendering this anxiety pure that one arrives at making him accommodate himself to this phallus, like all those who find themselves in charge of what I on one occasion qualified as the bandoleer. Man is married to this phallus. He has no other woman than that. This is what Freud said in every possible way. What else did he say when he stated that the phallic drive is not the genital drive? The genital drive is not natural at all in man. And if he did not have this devil of the symbolic to push him from behind so that at last he ejaculates and that this serves for something, it wouldn't be long until there would be no more of these speakingbeings--of these beings who do not speak simply to be, but are speakingbeings, which is truly the height of futility.

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Seminar of January 14, 1975

What I say interests--you are the proof of it--everyone. It interests me, but not as it does everyone, and this is felt in what I say--which is why it interests everyone.

Why is this felt? Because what I say is a clearing of the way concerning my practice, and it takes its departure from this question--which I would not ask if I did not have the answer in my practice--what implies that psychoanalysis works?

You see here (fig. 1) a nice little four-looped Borromean knot. It is Borromean since it suffices to cut any one of these three rounds of thread for the other three to be freed. Nothing prevents you from making a Borromean knot as long as you like. Notice however that as it is drawn here the number of rounds is not homogeneous, and that one can distinguish a first and a last. The last--let us say that it is the round to the extreme right--is that which holds together the whole chain, and makes it so that we have four there. If I proceed by the same model to make a

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five-looped knot, I will have to give this last round another way of being knotted, since it will hold one more.

In making use of rounds of thread in composing these Borromean chains, I illustrate something that is not without relation to the sequence of numbers.

You know how, by means of some axioms, Peano articulates it. It is the function of the successor, of the n + 1, that he stresses as structuring the whole number--which supposes nonetheless to start with one that is not the successor of any, which he designates by zero. All that these axioms produce will be from then on, conforming to the arithmetic requirement, homologous to the series of whole numbers.

The knot is something else. Here in fact the function of the plus-one is specified as such. Suppress the plus-one, and there is no more series--by the sole fact of the sectioning of this one-among-others, the others are liberated, each as one. This could be a wholly material way of making you feel that One is not a number, although the sequence of numbers is made of ones.

It must be admitted that there is in this sequence of numbers a consistency such that one has the greatest of difficulties not holding it as constituant of the real. All approach to the real is woven for us by the number. But to what is owed this consistency that there is in the number? It is not natural at all, and it is indeed this that makes me approach the category of the real as knotted to what I am also lead to give a consistency, the imaginary and the symbolic.

If I make use of the knot, it is because in these three something that I originate of the symbolic, of the imaginary, and of the real, has the same consistency. It is on this basis that I produce the Borromean knot, and this to justify my practice.

Isolating consistency as such, one has never done this. Me, I isolate it, and to illustrate it I give you the cord.

This is to make an image. For I do not deprive myself of making images. What do we have there on the board if not images?--the most astonishing thing about which is that you find your bearings there. That these lines are continuous or broken, depending on whether they pass above or below, is already miraculous. But how far do you see into this? Would you know to say that this knot here (fig. 1) is the same as this (fig. 2)? Take it upon yourselves to fiddle with the thing. With a chain of three, it is impossible to pass from one disposition to the other. This could work however--but beginning with how many rounds? I will leave it to you to search for the rule.

And I will return to consistency. Consistency is subjacent to all that we say. Is it because of what one calls non-contradiction? I say no, and I illustrate it with these figures. They have a consistency that I am indeed forced to call real, and which is that of the cord. It is supposed that a cord . . . that holds.

A metaphor? One never thinks of what there is of metaphor in the term consistency. And what is still stronger is that I communicate this real consistency by way of an intuition that I can call imaginary, since I make use of images.

We have here in, in our hands, with this cord, a supposed foundation of consistency, which is indeed something other than the line.

This distinction does not however go by itself. How do we detach ourselves from the idea that the geometric line is not without some thickness? By what could its continuity be supported?--if not by some consistency, that is, by something that would make a cord. This idea

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is at the basis of the mirages mathematicians have been fighting over for a long time. For example, in the first dust in the eyes that the functions called continuous have been given. It seemed that one could not construct a line which does not have somewhere a tangent, straight line or curve. And it took time for mathematicians to awaken to this: that one could make a perfectly continuous line which had no tangent. This is to say the importance, the pregnancy of the image of the cord.

But is this indeed an image? It is not for nothing that I say to you: Hold well to the cord. In fact, when the other end of a cord is knotted, on can hold on to it. This has to do with the real.

It is here that I have chosen to remind you that in the tenth of those good Rules for the Direction of the Spirit, Descartes did not believe it superfluous to remark, "As all spirits are not equally carried to spontaneous discovery by their own powers . . . we should not immediately occupy ourselves with more difficult and arduous things, but we must first delve into the less important and more simple arts; those above all where order reigns more, like those of the artisans who make canvas and carpets, or those of the women who embroider or make lace, as well as all the combinations of numbers and all the operations that relate to arithmetic and other similar things."

There is not the least suspicion that Descartes, in saying this, had the feeling that there is a relation between arithmetic and the fact that women make lace, even that carpet makers make knots. Never, in any case, is he in the least occupied with knots. We already had to be quite far into the 20th century for something to be outlined that could be called knot theory.

Knot theory is in its infancy. There are cases where it does not at all permit us to prove whether, yes or no, the tangle you have traced is a knot. And this despite the conventions that you might be given in advance to account for the knot as such.

To what is our maladresse with knots owed? Is it to intuition? Is it because vision always more or less makes a surface? I demonstrate to you, these knots render tangible, that this goes much farther than that. It is that, fundamentally, the being who speaks (and what can you say of the others? Not much. We must wait until we have advanced farther into their sounds)--the being who speaks is always somewhere, badly situated, between two and three dimensions.

This is why you have heard me produce this, which is the same thing as my knot: an equivoke on the word dimension, which I write dit-mension, mension [lying] of the dit [said]. One doesn't know very well if we indeed have three dimensions in the dire, if we find it so easy to move around there. τα ζωα τρεκει--assuredly we are ζϖον there, we walk. But we must not imagine that walking has the least relation with space in three dimensions.

There is little doubt that our body has three dimensions, however much we mash it up (créve la boudouille), but this does not prevent what we call space from always being more or less flat. All space is flat--there are mathematicians who have made this very explicit (l'avoir écrit en toutes lettres). All manipulation of a real is situated from there on in a space of which it is a fact that we know very badly how to manage it outside of techniques that impose giving it three dimensions. I add that it is striking that there is a technique--analysis--that one can reduce it to what it apparently is, to wit, chatter, which forces my hand, forces me to weigh the question of space as such.

In treating of space in the same fashion as is imposed by the fact of the technique, does not science encounter a paradox? We might have the suspicion--does not matter create a

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problem at every instant? A problem, as defense against advancing, is something to crush before coming to see what it defends.

Perhaps science has not yet accounted for treating matter as if it had an unconscious if it knew something of what it does. This truth had a little moment of awakening in the time of Newton. They objected to him--But finally? This space, this gravitation! What are you telling us? How can each of these particles know how far it is from all of the others? In a word, they evoked the unconscious of the particle. This truth became extinct very rapidly--they renounced understanding anything in those little formulas, and this is all very well; all of their value is there. Besides, it is in the measure that one returns to them that one has arrived at more complicated formulas, knotting a few more dimensions into the business.

Analysis, this technique that I have in common with a certain number of the persons who are here, what place does it occupy in regard to what science does?

Science counts. It counts the matter, in the matter. But if there were no language that, already, bore the number, what sense would counting have there? Is it that the unconscious has an accountant in it? I'm not saying something that one might count, I am speaking of the accountant, this character whom you know, who scribbles figures, and I ask--is it that there is an accountant in the unconscious? It is completely obvious that--yes.

Every unconscious is an accountant. And an accountant who knows how to do addition. Multiplication, it hasn't yet gotten to that, and this is what gives it some difficulty. But could I say that it knows how to count the blows? It is extremely maladroit--but it must count in the manner of these knots. It is from there that proceeds this famous sentiment of culpability, which makes counts and does not find itself there again, does not find itself again there ever. It loses itself in its counts. But it is there that it is touched upon that there is at minimum a knot.

This knot, nature has a horror of it. It is another song than that of the void--nature has a horror of the knot, and especially a Borromean knot.

This is why I take this thing (machin) up for you again, and I advise you to practice manipulating it. This thing is nothing less than the Urverdrängt, the original, primordial repression. Manipulating this little knot will give you nothing of the repressed, since this repressed is the hole--you will never have it. But en route you will familiarize yourselves--at least your hands--with this which you cannot in any fashion understand.

It is in fact completely excluded that you know this knot. This is the reason why, history shows it, geometry has gone through everything, cogitating cubes, pyramids, diverse forms of porcupines, inventing rigor, which means nothing other than solids, while it had within hand's reach something that was worth as much as the stones, and without which one could not measure the fields--cords. No one seems to have given these cords the least attention before the modern époque. ( . . . .).

It is getting late. I lead you back to this figure that I have already presented to you (figure 3).

I write sense in this joint here of the imaginary and the symbolic. There are two points there, which do not proceed with the same movement relative to the two rounds, but are confused when their wedging is produced.

There, I write phallic jouissance. Why? Because there is something called ex-sistence.

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Existence has a history. This is not a word that one employs so willingly, at least in the philosophical tradition. How did the people of the first centuries speak? We no doubt have some aperceptions concerning the vulgar Latin language such as it was spoken on a considerable surface--the core-language out of which came, by differentation, the romance languages. But we have no evidence that one employed either existo or existere. This term emerged in the philisophico-religious field. Curious! Thus religion had to inhale (hume)--the religious inhaling (humante)--philosophy for a word to come out which seems however to have had, it is the case to say, many reasons for being.

This naïve production, so to say, of the language, had to be untangled. Aristotle is the first to situate existence by the universal, that is, beginning with the dictum of omni and nullo--what is said of all can also be applied to whichever. Whence the notion that universality implies existence. What followed consisted in demonstrating to Aristotle, which took a long time, that this was not at all the case. Of course--we don't everyday make a clean sweep of the idea that universality does not imply existence. But what is grave is to believe that existence implies universality, that, with existence, we chatter about something participating in the general. It is there that my little knot intervenes. This Borromean knot is destined to show you that existence is of its nature ex-sistence, that which is ex. It is what turns around the consistent and makes an interval. But in this interval, that has twenty-six ways of being knotted. I say twenty-six ways in the measure that we have no familiarity with these knots, neither manual, nor mental--which is the same thing. A lot of people have had the suspicion that man is no more than a hand. If he only were a hand! But there is his whole body. He thinks with his feet also--at least he ought to. I now pose the question: what is it that resists the proof of ex-sistence, to be taken as what is wedged in the knot? We must here follow the path of Freud. Freud did not have of the imaginary, the symbolic, and the real the notion that I have--which is the minimum; for call them what you like, provided that there are three consistencies, you will have the knot. However, if he did not have the idea of R.S.I., he nonetheless had a suspicion. And what he did does not go without relating itself to ex-sistence, and departing, to approach the knot. Besides, the fact is that I could have extracted my three from his discourse, with time and patience. I began with the imaginary, I had to chew on the history of the symbolic, with this linguistic reference for which I have not found all that would have arranged things for me, and I have finished by bringing out this famous real in the form itself of the knot. Freud, therefore, contrary to a prodigious number of persons, from Plato to Tolstoy, was not a Lacanian. But nothing prevents me from supposing my three, R.S.I., to him--a banana skin slipped under his foot--to see how he untangles himself from it. For Freud, the three do not hold, they are only posed the one over the other. Also, what did he do? He added a round (fig. 4), knotting with a fourth the three consistencies set adrift (. . . .). He calls this fourth consistency psychic reality. What is psychic reality for Freud? It is the Oedipus complex. The Oedipus complex is not for all that to be rejected. It is implicit in the knot as I figure it, and it ties the three, but at a minimum. To dispense with a fourth, to obtain the Borromean knot, it suffices to make, at two points, pass above what was below. In other words, the real must surmount the symbolic.

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The surmounting of the symbolic by the real at two points is quite precisely what analysis is about. Be careful not to take this term surmount in the imaginary sense, believing that the real has to dominate here. Besides, it suffices that you turn this thing around to see that, in the contrary direction (sens), this does not work. Turned around, the knot still has the same appearance--you do not have its mirror image; it is still levogyre. It is not a matter, between the symbolic and the real, of a changing of the order of the layout (plan)--it is simply a matter of their being knotted otherwise. For being knotted otherwise is what is essential to the Oedipus complex, and it is how analysis operates. It is in entering the niceties (finesse) of these fields of ex-sistence that we will proceed this year. (. . . .).

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Seminar of January 21, 19754

…………………………………………………………………………..

The question evoked at this time of my statement (énoncé) is the following, which responds to the notion of consistency inasmuch as this supposes the notion of a demonstration: what can be supposed a demonstration in the real? Nothing supposes it other than the consistency of which the cord is here the support. The cord is the foundation of accord. And, to make a leap, I will say that the cord thus becomes the symptom of that by which the symbolic consists. A formula that does not go badly with what language testifies to--to wear down to the thread5 (montrer la corde), by which the wearing of the weave is designated. When the cord is shown, it is because the weave no longer is camouflaged in what one calls the fabric. Fabric (Etoffe) is of a permanent metaphoric usage--it is what, for a nothing, would give the image of a substance. The formula to show the cord tells us that there is no fabric that is not a weave. I had prepared for you on a piece of paper a weave made wholly of Borromean knots with which one could cover the surface of the blackboard. It is easy to aperceive that one ends up with a hexagonal weave. Do not believe that that the sectioning of any one network of this weave will free anything whatsoever of what it is knotted to. If only one is cut, the six rounds in between, freed by this cut, will be held by the six-times-three--eighteen--other rounds to which they are knotted in a Borromean fashion. If I have, just now, brought forth prematurely--it’s the law of language: something must be brought forth before it can be commented on--the term symptom, it is because the symbolic is indeed what, for consistency, gives the simplest metaphor. Not that the circular figure is not first a figure, which is to say, imaginable, since it is there itself that one has founded the notion of good form. This notion is indeed proper to make us enter into the real what there is of the imaginary. And I would say more--there is a kinship between good form and sense. The order of sense is naturally configured from what the form of the circle designates the consistency supposed to the symbolic. It is in accord with this image, in way that is in some manner primary. One had to await psychoanalysis to aperceive that it is tied to the order of the body in which the imaginary is suspended. Who doubts--it is even on this thin thread that all that one calls philosophy has lived to this day--who doubts that there is another order than that in which the body is supposed to move? But, for all that, this order of the body does not explain much. Why does the eye see spherically, when it is incontestably perceived as a sphere, while the ear hears a sphere just as much, although it presents itself in the form of a snail's shell (limaçon)? That these two forms so manifestly diffeomorphic, if I can express myself thusly, perceive spherically--is this fact clarified by taking things from the angle of my object a? One can say that the petit a has several forms; except it does not have them, forms, but is in a

4 This session is already available in a translation by Jacqueline Rose, as Chapter 7 of Feminine Sexuality: Jacques Lacan and the école freudiennne (New York: W.W. Norton & Co., 1982), 162-171.

5 Rose's translation of idiom translated more literally as "to show the cord."

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dominant fashion thinkable orally or shittily. The common factor of the a is its being tied to the orifices of the body. What therefore is the incidence of the fact that eye and ear are orifices on the fact that perception is for both spheroidal? Without the petit a, something is missing from any possible theory of reference, from any appearance of harmony. And why? Because the subject is only ever supposed. Its condition is of only being supposable. If it knows (connait) something, it is only from being itself a subject caused by an object that is not what it knows--what it imagines itself to know. The object that causes it is not the other of knowledge (connaissance). The object strikes it through, this other. The other is thus the Other, which I write with the big O (le grand A). The Other is thus a matrix with a double entry. The petit a constitutes one of these entries. And the other? What are we going to say of it? Is it the One of the signifier? This is at least thinkable, since it is what permitted me one day to couple the One with my petit a. On this occasion, I had utilized the golden number to introduce what I was led to by experience: that between this One and the petit a, there is no rationally determinable rapport. Never is there any graspable proportion between the One and the a; in other words, there is no reason that the overlapping (recouvrement)6 of the one by the other might end. The difference will be as little as one might figure it, there will even be a limit there, but at the interior of this limit, there will never be any conjunction, any copulation whatsoever of the One with the a. Is this to say that the One of sense has something to do with the matrix that strikes the Other through with its double entry? No, for the One of sense is not to be confused with what makes the one of the signifier. The One of sense is being, the being specified by the unconscious inasmuch as it ex-sists, as it ex-sists to the body at least; for if there is something striking, it is that it ex-sists in discord. There is nothing in the unconscious that makes an accord with the body. The unconscious is discordant. The unconscious is what, by speaking, determines the subject as being, a being to be struck through with this metonymy with which I support desire as for all impossible ever to say as such. If I say that an a is what causes desire, this means that it is not its object. It is not its complement, direct or indirect, but only this cause that--to play on the word as I did in my first Rome Discourse--this cause that chatters on (cause toujours). The subject is caused by an object, which is only notable from a writing, by which a step is made in the theory. What is irreducible in that it is not an effect of language. The effect of language is the patheme, the passion of the body. But from language inasmuch as it has no effect is inscribable this radical abstraction which is the object that I write with the figure of writing a, and of which nothing is thinkable--except that all that is a subject, a thought subject, which one imagines to be a being, is determined by it. The One of sense has little to do with this--it is only an effect of the One of a signifier, which in fact only operates in being able to be employed to designate no matter what signified.

6 See Rose's more explanatory translation (164). Here I am taking recouvrement (covering over, recovery, recuperation, overlap) to refer to an overlapping that always leaves a remainder.

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What will we say of the imaginary and the real here mingled in the One of the signifier? What are we to say of their quality, whether of what Charles Sanders Pierce calls firstness, or of what distinguishes them as different? How are we to distinguish (répartir) on this occasion something like life or death? Who knows where to situate them? --since the One of a signifier chatters (cause) on both the one and the other slopes? Thus one would be wrong to believe that it is the imaginary that is the mortal, and the real the living. Only the ordinary usage of the signifier can be called arbitrary. But where does this arbitrary come from, if not from a structured discourse? Am I here evoking the title of a revue, which appeared at Vincennes under my auspices, ORNICAR?7 Is this not an example of what the signifier determines? Here, the fact of being ungrammatical would only figure a category of grammar, but this is how it demonstrates configuration as such; which, from the Icarian perspective, only decorates. Language is only a decoration. There is only rhetoric, as Descartes underscores in his tenth rule. Dialectic is only supposable from usage in respect to an ordinary pathematically ordered, which is to say, to a discourse, which does not associate the phoneme, even understood in the broad sense, but the subject determined by being, which is to say desire. What is the affect of ex-sisting? /. . ./. What, of the unconscious, makes ex-sistence? This is what I underscore with the support of the symptom. I say the function of the symptom, a function to be understood as the f in a mathematical formulation, f (x). And what is the x? It is what, of the unconscious, can be translated by a letter, inasmuch as it is only in the letter that the identity of self to self is isolated from any quality. From the unconscious any One, inasmuch as it sus-tains the signifier by which the unconscious consists, is susceptible of being written with a letter. No doubt there must be a convention. But the strange thing is that the symptom operates even this wildly. What does not cease to write itself in the symptom arises from there. Not long ago, someone I listened to in my practice--and nothing that I say to you comes from anywhere else, which is what creates the difficulty--someone articulated something to me, comparing the symptom to points of suspension [ellipsis]. The important thing here is the reference to writing to situate the repetition of the symptom, as it presents itself in my practice. That the term emerged from elsewhere, from the symptom as Marx defined it in the social, takes away nothing of the well-foundedness of its use, if I may say so, in the private. That the symptom in the social is defined by folly (la déraison) does not prevent it from, for each of us, being signaled by all sorts of rationalizations. Every rationalization is a particular rational fact; which is to say, it does not come from an exception, but from no matter whom. No matter who must be able to be an exception for the function of the exception to become a model, but the reverse is not true--it is not that no matter who can drag in the exception for it, based on this fact, to constitute a model. That is what usually happens (l' état ordinaire)--no matter who attains to the function of exception that the father has, one knows with what result: in most cases, that of his verwerfung by the filiation he engenders, with the psychotic result I denounce.

7 See Rose, 170n2.

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A father only has a right to respect, if not to love, if said love, said respect, is--you are not going to believe your ears--père-versely oriented; which is to say, makes of a woman an object a that causes his desire. But what a woman a-ccomodates (a-cueille) of it thus has nothing to do with the question. She is occupied with other objects a, her children, for whom the father nonetheless intervenes--exceptionally, in the best case--to maintain repression, in the happy mi-deum,8 the version proper to him of his père-version. Père-version, the only guarantee of his function as father, which is the function of a symptom, as I have written it. It suffices that he be a model of the function. That's what the father must be, inasmuch as he can only be an exception. He can only be a model of the function in realizing the type. It little matters if has symptoms if adds to them that of the paternal père-version, which is to say that its cause is a woman, whom he has acquired to make children for him, and that, whether he wants to or not, he takes paternal care of these children. Normality is not the paternal virtue par excellence, but only the happy mi-deum, just said; that is, the right not-said (non-dit). Naturally, on the condition that it is not too obvious, this not-said; which is to say that one does not see right away what is in question in what he does not say--which is rare. It is rare that it succeeds, this happy mi-deum. This will renew the subject, when I have time to take it up with you again. But I have already said it in passing in an article on Schreber--there is nothing worse than a father who proffers the law on everything (sur tout)--No father educator above all (surtout), but rather in the background (en retrait sur) of all the schoolmasters. I have been led to speak to you of a woman, since I have told you that the woman does not exist.

The woman is perfectly delineable, since she is all the women, as one says. But if the women are not all? Let us say that the woman is all the women, but then, this is also an empty set. Is not the value of set theory that it puts a little seriousness in the usage of the term "all"?

The question of a woman is only posed from the Other; which is to say, from that for which there is a definable set, definable by what I have inscribed on the board, Φ, the phallus.

The phallus; this is not the phallic jouissance. Is it therefore the jouissance without the organ or the organ without the jouissance? It is in this form that I interrogate you to give sense--alas!--to this figure. And I will jump ahead--for whoever is encumbered by the phallus, what is a woman?

She is a symptom.She is a symptom, and this is seen from the structure that I am in the process of

explaining to you--to wit, that there is no jouissance of the Other as such, that there is no guarantee, encounterable in the jouissance of the body of the Other, which might make enjoying

8 Rose's translation of le juste mi-dieu. See Rose, 171n4.

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(jouir de) the Other exist. A manifest example of the hole, of what is only supported by the object a--but always by a misdeal, by confusion.

A woman, in fact, is no more than a man an object a--she has her own, I have just said, with which she is occupied, and they have nothing to do with that by which she is supported in whatever desire. To make her a symptom, this A-woman, is to say that the phallic jouissance is also her affair, contrary to what one hears.

The woman has to undergo neither more nor less castration than the man. In regard to what is at issue in her function as symptom, she is altogether at same point as her man. Still, we must articulate what corresponds for her to this ex-sistence of a real that is the phallus of just now, over which I have left your tongues hanging. It has nothing to do with the little gadget of which Freud speaks.

The points of suspension of the symptom are in fact, if I may say so, interrogative points [question marks]--in the non-rapport. This is what justifies the definition I give you, that what constitutes the symptom, this something that smooches with the unconscious, is that one believes in it. There is so little sexual rapport that I recommend that you read a very beautiful novel, Ondine. You will see that a woman in the life of a man is something in which he believes. He believes that there is one, sometimes two or three, which is indeed the interesting thing--he cannot believe in only one; he believes in a type, in the genre of sylphs or ondines. What is it to believe in sylphs or ondines? I remind you that one says "to believe in" (croire á), and that the French language even adds this reinforcement: croire y, believe there (lá). Y croire? What does this mean? If not to believe in beings inasmuch as they can say something. I ask you to find an exception to this definition. Were it a matter of beings that could not say anything, that could not enounce what could be distinguished as truth and lie, believing in them would mean nothing. This is to say the fragility of this croire y, to which the fact of the non-rapport is manifestly reduced, which is not to be doubted, seeing how it is confirmed everywhere. Whoever presents us with a symptom believes in it (y croit). If he asks our aid, our help, it is because he believes that the symptom is capable of saying something, and that it only has to be deciphered. It is even the same with a woman, except that it happens that one believes that she effectively says something. There is what pushes in the cork: in believing in her, one believes her. One believes what she says. This is what is called love. And this is how, on occasion, I have qualified the feeling (sentiment) of the comic--it is the well-known comic, the comic of psychosis. That's why one says currently that love is a madness. However, the difference is manifest between believing in it, in the symptom, and believing it. This is what makes the difference between neurosis and psychosis. In psychosis, the subject not only believes in the voices, but he believes them. It is all there, in this limit. Believing her, a woman, is, thank God, a widespread state--this gives us some company; one is not all alone, and in that love is precious. It is rarely realized, as everyone knows, and only lasts for a time. For of what is it a question in love, if not to fracture this wall where one can only raise a knot (bosse) on one's forehead, since there is no sexual rapport?

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Love is no doubt classified in a certain number of forms that Stendhal has laid out for us quite well: love-esteem, which is not at all compatible with love-passion, nor with love-taste--but the major love is that which is founded on this: one believes her. One believes her because one has never found proofs that she is not absolutely authentic. But one is blinded there. This "believe her" would serve as the cork to the "believe in her"--a thing that can be very seriously put in question. Believing that there is One, God know where that will lead you--it will lead you as far as to believe there is a The, a fallacious belief. No one says the sylph or the ondine. There is an ondine, there is a sylph, there is a spirit, there are some spirits for certain, but all that only ever makes a plural. From then on it is a matter of knowing if the fact that for believing in her, there is no better means than believing her, is wholly a necessity. I have introduced today, in relation to the story of some points of suspension, that a woman is a symptom. That adheres so well to practice that, as no one has said it up to now, I have believed it my duty to do so.

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Seminar of February 11, 1975

. . . I have just spent eight days where?--Believe it or not, in London. Should I say a word about English psychoanalysts? I only know one who is English, and he must be Scottish. It is no doubt the English language (lalangue anglais) that is the obstacle here--which not very promising, since it is becoming universal. Those who read me from time to time may have an idea of the difficulties that there can be in translating me in the English language (lalangue)--one has to force it. I am not the first to have noticed the resistance of the English language to the unconscious. It’s not just English. On returning from a trip to Japan, I believed myself to see a certain duplicity in pronunciation, doubled by the duplicity of the system of writing, a special difficulty of the language (lalangue) to operate (jouer) at the level of the unconscious, and precisely in what would appear to make it easier. . . . I must today clear the way to a certain number, I would not say of equivalences, but of correspondences. I have encountered them many times in the jottings with which I prepare what I have to say to you, but I look at them twice before I share them with you. I am rather careful and try not to speak at random. Is there someone who knows if Lytton Strachey's Queen Victoria has been translated in French? No? How annoying. It hit the streets in the form of a Penguin Book, which is now "out

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of print." 9 Me, when I was returning from England, last Saturday and Sunday, I couldn’t put this book down. This does not mean that I’m going to speak about it today, for to make it into something that would enter into my discourse, I would have to squeeze it, to wring it, to get the juice out of it, and I don’t have time for that. However, it would not be without interest. It would have perhaps shown you one more origin of this stupifying phenomenon which is the discovery of the unconscious. The 19th century was dominated to an astonishing degree by the action of a woman, Queen Victoria. No doubt it needed this kind of ravage for there to be what I call an awakening. An awakening is a lightening flash. When that happens to me--not often--it situates itself—this is not to say it is like this for everyone—at the moment when I emerge from sleep.I then have a brief flash of lucidity. It does not last long, to be sure—I return like everyone else into this dream called reality, into the discourses in which I take part, and among which I strive painfully to clear the way to analytic discourse. I believe Lytton Strachey’s book will render you sensible, with a particular relief, of the fact that love has nothing to do with the sexual rapport, and this begins with a woman. Queen Victoria, now there was a woman; not the woman, who does not exist, but a woman among others, certainly very isolated in the English context by that prodigious selection that must not be confused with the master discourse. It is not because there is an aristocracy that there is a master discourse. Besides, this aristocracy does not have much to do with a local selection. The true masters are not the people of the world, the good people, the people of good society, the people who know their social standing, or think they do. What fatality made it so that a certain Albert of Saxe-Coburg fell into the paws of the Queen? He did not have any leaning toward women. But when one encounters a vagina dentata, if I can say so, of the exceptional stature of Queen Victoria . . . A woman who is queen is truly the best vagina dentata one can come up with, it is even an essential condition—Semiramis must have had a vagina dentata, one sees it quite well when Degas draws her. Elizabeth of England too, and that had consequences for Essex. Why did the above named Albert—when one refers to the museum that subsists in their memory, one does not refer to Victoria and Albert, but . . . hand Albert—why did the hand Albert not suffer the fate of Essex? But are we sure he didn’t?—because he did perish rather early, from a death called natural, but you will want to look at that more closely. Peace to his soul, in any case. This seems to me a marvelous statement, illustration, of this truth I found without it, the truth of the sexual non-rapport. By what mysterious encounter did Freud arise after this spectacular exercise of what women have of power? I do not know besides if this is a power. We are very fascinated by categories like power, like knowledge. But these are foolishnesses, foolishnesses that give way completely to women, who don’t care about them, but whose power immeasurably surpasses all of the categories of the man. Can women, should women, attempt some kind of integration into the categories of the man? What I say does not at all go in that direction. They know so much more simply by virtue of being a woman. It is not so much that they know how to treat of the unconscious—I’m not

9 In English in the original.

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too sure of that—but their category in regard to the unconscious is without doubt of greater strength. They are less bogged down in it. They treat it with a savagery, a striking celerity; think, for example, of Melanie Klein. I leave that to the meditation of each of you. Women psychoanalysts are certainly more at ease with the unconscious. But a woman does not occupy herself with it without it being at her expense; in doing so, she loses something of that luck which, from nothing but being one among women, is in some way without measure. If I had to incarnate the idea of freedom--something which I obviously cannot even think of doing—I would obviously choose a woman; not just any woman, since they are not-alls and the just any (n’importe-laquelle) slips toward the alls (toutes). Let’s leave that aside, because it is a subject where, finally, like Freud himself, I lose my Latin. I will say again that this Queen Victoria is a reading that no one should miss, if it has a little touch, a little vibration of what I am saying—and I will move on to another subject. The art itself that has dealt with subjects called geometrical because an interdiction of a religious nature is placed on human representation, arab art to call it by its name, produces freizes and braids, but not a Borromean knot, although the Borromean knot offers itself to an abundant wealth of figurations. There is no trace of it in any art. This is a very surprising thing, which is not easy to explain. Why hasn’t anyone felt the importance of this knot? Perhaps it is because it needed the emergence of certain consistencies, which are precisely those I give to the symbolic, to the imaginary, and to the real. If I give them this consistency, it is to homogenize them. To homogenize them is to bring them back to the value of what is commonly--one asks oneself in the name of what--considered the most low: it is to give them the consistency of the imaginary. And because there is something that needs to be put right. The consistency of the imaginary is strictly equivalent to that of the symbolic and that of the real. Each is in the same relation with the two others. And it is indeed there that it is a matter of making an effort that is of the order of the effect of sense. Analytic interpretation in fact implies a see-sawing in the bearing (portée) of this effect of sense. It carries (porte) in a way that goes a lot farther than speech. Speech is an object of elaboration for the analysand, but what are some of the effects of what the analyst says?—for he does say. It is not nothing to formulate that the transference plays a role there, but it doesn’t clarify anything. It would be a matter of explaining how the interpretation carries, and that it does not necessarily imply an enunciation. Too many analysts are in the habit of not opening it—I am speaking of the mouth. I dare believe that their silence is not just out of bad habit, but out of a sufficient apprehension of the bearing of a silent dire. I dare believe it, but I’m not sure of it. Beginning when we enter this field, there is no proof, if not in this: that an opportune silence does not always succeed. What I am trying to do here—alas, I babble a lot—is destined to change the perspective on what there is of the effect of sense. It is a matter of gripping this effect of sense, and with a knot that is the right one for it.I am myself very astonished at succeeding in substituting this effect of sense inasmuch as it makes a knot, and in the right way, for what I will call the effect of fascination, which is produced at a point designatable in this knot itself. It is on this cord that are borne most of the effects of art, and this is the only criterion that one might find to separate art from what science

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comes to coordinate. A man of letters, like Valéry, for example, remains in effects of fascination, although there is room for analyzing them. The effect of sense required by analytic discourse is not imaginary. Nor is it symbolic. It has to be real. What I am occupying myself with this year, is a thinking of what might be the real of an effect of sense. One is habituated to the effect of sense being carried by words, and not being without reflection, without an imaginary undulation. On my little schema (Figure 1), the effect of sense is at the joint of the symbolic and the imaginary. With the consistent circle of the real, it has, in principle, only a relation of exteriority. I say in principle, because this exteriority supposes the knot flattened out. It is flattened out because we only think flat—but one can also figure it otherwise (figure 2). What we pose with the Borromean knot already goes against the image of a concatenation. The discourse in question does not make a chain. There is no reciprocity in the passage of one of these consistencies into the hole offered it by the other, which is to say that no one of these consistencies links itself to another, so as to make a chain with it. And this is how the relation of the symbolic, the real, and the imaginary is specified. From then on the question is posed of knowing whether the effect of sense in the real is owed to the usage of words or to their ejaculation. A lot of things have always been given to be thought, but one does not make the distinction between this usage and this ejaculation. One believed that it was words that carried. While if we give ourselves the trouble to isolate the category of the signifier, we see clearly that ejaculation retains an isolable sense. Is this to say that we must trust in that for the dire to make a knot? Speech (La parole) very often slips, lets slip. It is asked of the analysand to furnish all that passes through his head, which does not at all imply that there is nothing there but bla-bla-bla, for there is an unconscious. Based on the fact that there is an unconscious, there are in his speech already things that make a knot; there is alreadly the dire, if we specify the dire as being what makes a knot. It does not suffice to call this knot real. The imaginary is not an imaginary round. If the knot holds, it is because the imaginary is taken in its consistency proper. As for the symbolic, it is not to be taken in the everyday sense of the word, as everything in analytic technique indicates. It is not only bla-bla-bla. The real is that there is something common to the three in consistency. Now, this consistency resides only in the fact of being able to make a knot. Is a mental knot real? That is the question. The mental knot has the real of the ex-sistence, as I write it, of these equivalences which I just told you that it was my aim to produce today. I have spoken prudently of correspondences. I speak now of functions, and this is how I advance the word “equivalence.” We are forced not to put the real in consistency. Consistency, to designate it by its name, I mean by its correspondence, if of the imaginary order. What is demonstrated at length in human history and should inspire in us a singular prudence, is that all the consistency that has proved itself is pure imagination. I make the imaginary return here in its accent of sense. Consistency, for the speakingbeing, is what is fabricated and invented. In this occasion, it is the knot, inasmuch as one has woven it. But precisely—"woven" is just the word we’re looking for in this business—it is not because one has woven it that it ex-sists. Even if I do not draw the figure of my Borromean knot on the board, it ex-sists, for as soon as it is drawn, anyone can

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clearly see that it is impossible that it does not remain what it is in the real: a knot. And this is why what I advance can be useful in their practice to analysts who listen to me--if they know that what they weave of the imaginary doesn’t any less ex-sist. This existence is what responds to the real. What we have introduced to the notion of ex-sistence is the inscription, x. f (x)—there exists an x that can be carried into a function, whether this be a function in the general sense of the term, or simply an equation. In the case of an equation, it happens that there is no root. This leaves us neither hot nor cold—we make it exist; we invent, for example, the imaginary root, and that gives us some results. One sees here that the term imaginary is not a synonym for pure imagination. If we can make the imaginary exist, it is because it is a matter of another real. I say that the effect of sense exists, and that in this, it is real. This is not an apologetic; it is a consistency, an imaginary consistency, no doubt, but there is indeed, it seems, a wholly everyday domain of the imaginary function that endures and holds. I can only enter into dialogue with someone whom I have fabricated to understand me at the level where I speak. It is indeed because of this that I am astonished that you are so numerous. I cannot believe that I have fabricated each of you to understand me. In analysis, it is not a question of that. It is a question only of accounting for what ex-sists as interpretation. The astonishing thing is that in working on the three functions of the symbolic, the imaginary, and the real, I have at a distance fabricated enough people who have had only to open my books—there is not an Englishman who has done more than that—to find something which allows them to respond to me. How can a construction be made to ex-sist of which the consistence is indeed not imaginary? For that, there has to be a hole. And this is what leads us to the topology of the torus. I do not see why a theory of knots needs to pass through the function of filter, for example, or requires consideration of open and closed sets, when these terms open and closed take on an imaginary consistency always different from that required by the practice of knots. The hole of which I speak detaches itself from the thought that makes a circle, from the thought that flattens out, and which on this basis distinguishes inside and outside. It suffices to imagine the circle as a consistent cord to see that the inside and outside are exactly the same thing. There is only one inside, which the one that we imagine at the interior of the torus. But the introduction of the figuration of the torus consists precisely in not taking that into account. I showed you last time how to make a four-looped Borromean knot. One begins with three independent torii, and knots them with a fourth (Figure 3). I figured for you last time how, by a figure of a fourth torus, these three figured here as independent can be knotted. Freud, I said, elides my reduction to the imaginary, symbolic, and real knotted together. It is by his Name-of-the-Father, identical to what he calls psychic reality, and which is nothing other than the religious reality--it is by this function of the dream that Freud installs the tie between the imaginary, the symbolic, and the real. Well then, let us transform figure 2 so that the third circle does not knot anything (Figure 4). The three rounds are disjoined. How can we draw the fourth that would knot them? You will easily conceive of the figure that I am going to sketch if you think of the form of

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the astrolabe, materialized dozens of times (trente-six fois) in the course of the ages—it must be said that we are only capable of doing geometry with solids. Here is a circle seen from the front. The equatorial circle that I am drawing now is seen flat, and it is for this that I feign drawing it in perspective. Let us now make a third, sagittal circle. Let us sketch the little dotted line to give the notion of how you should see it in perspective. It suffices to sketch this fourth line for the three disjoined rounds of the symbolic, imaginary, and real to be found knotted (Figure 5). Four these three to be knotted must there necessarily be one more, of which the consistency would be referred to the function of the father? The Borromean knot demonstrates the contrary. It is indeed this question that made me begin my seminar on The Names of the Father. I had not yet found the figuration I introduce here, but there is not just one fashion to illustrate how Freud makes the conjunction of the symbolic, the imaginary, and the real hold for me, by the Names-of-the-Father—as is patent in his text. Is this supplementary function of the Father indispensable? I show you that this could be disputed. It is not because it is indispensable in theory that it always is in fact. If I titled this seminar the Names and not the Name of the Father, it was because I already had certain ideas about the filling-in-for (suppléance) the Name-of-the-Father. But it is not because this filling-in-for is not indispensable that it does not take place. Perhaps it is because our imaginary, our symbolic, and our real, for each of us, are still disassociated that there has to be the Name-of-the-Father to knot them. But do not imagine—this would not be my style (dans mon ton)—that I prophecy that, in analysis and elsewhere, we could dispense with the Name-of-the-Father without each of the three would going its own way. Besides, how would the reduction of a knot to its minimum constitute a progress? It would be a progress in the imaginary, which is to say, in consistency. In the current state of things, you are as inconsistent as your fathers, and it is precisely from being entirely suspended in them that you are in your present state.

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Seminar of February 18, 1975

Last time, disappointed that Mardi Gras had not rarefied the plenitude of this room, I let myself slip into telling you what I think. Today, I would like it a lot if someone would ask me a question. A certain Spinoza endeavored to spin, to deduce, according to the model given by the Ancients. This more geometrico defined a mode of properly mathematical intuition that does not at all go by itself. The point, the line, are fomented by a fiction; and also the surface, which is only supported by the split, a break specified as being of two dimensions--but since the line, properly speaking, is a dimension without consistency, it isn't saying much to add a dimension to it. And the third dimension, built from a perpendicular to the surface, is also very strange. It is nothing but an abstraction, founded on the cut of a saw. How, without finding the cord again, can we make this abstraction hold?

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On the other hand, it is no doubt not by chance that things are produced in this way. No doubt there is a necessity here arising from the weakness of a manual being, homo faber, as they say. But why has this homo faber who manipulates, who toils (tisse) and spins, passed to the point, to the surface, without stopping at the knot? Perhaps this has some relation with a repression. Is this repressed the primordial one, the Urverdrängt, which Freud designates as what is inaccessible in the unconscious? The Borromean knot, I have told you, remains a knot if we open one of its loops and transform it into a straight line. But we must extend it to infinity (Figure 1). This is why I say that the straight line is hardly consistent. We have glossed over this from the moment that a geometry called spherical made of this infinite straight line a new round, without grasping that this round is implied beginning with the position of the Borromean knot. We perhaps didn't have to make this detour. Whatever the case, you saw me, last time, extend the geometry of the Borromean knot from three to four. This was to make you experience the difficulty of what I have called the mental knot. Flattening it out, as I have attempted, is to submit it to so-called thought, to which in fact extension is stuck. Far from being distinct, as Descartes supposes, thought is nothing but extension. Let us remark that for this there has to be an extension that is not just any, but an extension of two dimensions, which can be daubed on a surface. Thus, it would not be out of place to define the surface I just showed you in geometry, that which is imagined, that which is essentially supported by the imaginary--the surface is what gives us something to daub on. It is singular that the only way anyone has succeeded in reproducing this ideal surface is precisely the one from which everybody recoils: the braiding of a canvas. The painter daubs on a canvas, since it is all he has found for taming the gaze (dompter le regard). As for me, I find myself flattening out what I have to communicate to you of the knot on the surface of a blackboard. How can we draw the fourth round so that three independent rounds of thread make a knot with it? I have figured it by a flattening out that brings in perspective, and which I give you again here in a little different form (Figure 2). I then wanted to flatten the figure out in a way that reproduces it while modifying it, and there I have found that I have made an error. More exactly, I have slipped up (raté), explicitly, out of laziness, and also to give you an example of the unnaturalness of representing the knot. Here is the correct figure (Figure 3). Why has the failed act (acte manqué) functioned here?--if not to show that no analysis avoids something that resists in this theory of the knot. I have made you feel it, and in a somewhat experimental fashion. . . . What is the essential thing about the round of thread? If one responds that it is the hole in the middle, one is induced to make consistency, ex-sistence, and the hole correspond to the imaginary, to the real, and to the symbolic respectively. Is this right? (Figure 4). Saying that the hole is the essential thing about the round does not entirely satisfy me. In fact, what is a hole if nothing surrounds it? Consistency nonetheless indeed seems to be of the order of the imaginary, since the cord goes off toward the vanishing point of the mathematical line. Ex-sistence, in regard to the opening of the round and in regard to the hole, indeed belongs to the field supposed, if I may say

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so, by the rupture itself. It is within, in-there, that the fate of the knot plays itself out. If the knot has an ex-sistence, it is by belonging to this field. Whence my formulation that, in regard to this correspondence, ex-sistence is of the order of the real. The ex-sistence of the knot is real, to the point that I could have thought that the mental knot, it (ça) ex-sists, whether or not the mens figures it. It has still to explore the ex-sistence of the knot, and it does not mentalize it without difficulty. It is the order explored beginning with my experience, I remind you, that has led me to this infernal trinity. I am not thinking here of bringing a cord into play that is not Freudian. Flectere si nequeo superos Archerontes movebo--here is illustrated what I have called the truth of a certain religion. It is not completely by chance that it arrives at a divine trinity, and this, contrarily to the tradition to which it is connected. I will confide in you in saying that the desire of man is Hell, because Hell is what he lacks. Thenceforth, it is what he aspires to. We have the testimony for this in neurosis. The neurotic is someone who has not attained to what for him is the mirage where he would find himself satisfied, to wit, a perversion. A neurosis is a failed (ratée) perversion. It is because you are a lot more interested than you suppose in this nodalization of the imaginary, of the symbolic, and of the real that you are there, it seems to me; why else would you take this strange satisfaction in hearing these stammerings? For me, I can no more than clear the way for the consequences of what I say. We have established that the ex-sistence of the knot was supported by this field, and that it was of the order of the real. On the other hand, what supports a body? The body only has an appearance for you by being what resists, what consists before dissolving. There is a consistency of the body, just as there is a consistency of the line, and consistency is of the order of the imaginary. As a consequence, by elimination, we are led to pose that the hole is of the order of the symbolic, which I have founded by the signifier. This is what we have to now interrogate. Is the symbolic the hole? The real, existence? The imaginary, consistency? These categories are not easily manageable. They have, however, left some traces in history. It was by a traditional philosophical extenuation, of which Hegel gave the summit, that something sprang forth under the name of someone named Kierkegaard. You know that I have exposed his promotion of existence as such as convergent with an experience appearing much later in Freud. Think of his stressing of repetition as more fundamental in experience than the resolution called thesis-antithesis-synthesis on which a Hegel threaded history. The standard unit (étalon) of this function is found in jouissance. The relations lived by the Kierkegaard in question are those of a knot never avowed, which is that of a faulty father (pére à la faute). It is not a matter of his own experience, but of that of he who in relation to him is found to occupy the place of the father. At the same time, this place of the father is found problematic . . . It is only on this date that existence is promoted as such. No doubt it does not have the same accent as I give it by fragmenting it with a dash. If it is in this époque that existence emerges, emerges for me, and that I write it otherwise, and that it becomes tangible in the knot, I do not believe that this puts me in continuity with a philosophical interrogation. Rather, there is a rupture. The emergence of the unconscious as a knowledge, a knowledge proper to each particular person, is of a nature to change completely the notion of knowledge that has

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dominated since Antiquity. In fact, if knowledge depends on relations of the sequence of generations with the symbolic, with this hole of which I have just spoken, how can we not interrogate its status? Is there a knowledge in the real? The supposition always made, a supposition not avowed, is that by all appearances there is, since the real walked (ça marchait), turned in a circle. We, in the real, we touch on a knowledge in a wholly other form . . . When one poses knowledge as immanent to the real, one puts it in the form of the ηουs, thanks to which the real knows what it has to do. And when it is not the ηουs, it is the All-Power, the wisdom, of God. The Newtonian world is not thinkable without God, for how would each of these masses know its distance from all of the others? Voltaire believed in the Supreme Being: I am have not received his confidences; I do not know what idea he had of it. That could hardly be far from the idea of the All-Science, the idea that it is He who makes the machine work. It's the old story of the knowledge in the real that has sustained all the old metaphors of the potter. Aristotle was a populist--it was the artisan who gave him the model for his causes. Everything superb about the ηουs reduces itself to that, which makes it so his theory has been welcomed with open arms wherever the metaphor of the potter is primary. A divine hand made the pot. But is God always busy making it turn? Does he let it turn by itself? Refinements of knowledge. The question is to be taken up again beginning with this: knowledge is only supposed from a relation to the symbolic, which is incarnated by a material as signifier. But what is a signifying material? We only have the tip of its nose in Aristotle, when he speaks of the στοιχειον. It is certain that the idea itself of matter is only thinkable as an issue of the signifying material, where this idea finds its first examples. Our own experience is that of the symptom. The symptom reflects in the real the fact that there is something that does not work (marche) where?--not in the real to be sure, but in the field of the real. This is owed to what? To what I support in my language by the speakingbeing--if it did not speak, there would not be the word being . . . There is a coherence, a consistency, between the symptom and the unconscious. I define the symptom by the fashion in which each jouit from the unconscious insofar as the unconscious determines him. The origin of the notion of the symptom is not to be sought in Hippocrates, but in Marx, in the liaison that he makes the first between capitalism and what?--the good old days, what one calls the feudal time. Capitalism is considered to have some quite beneficial effects, since it has the advantage of reducing to nothing the proletarian man, thanks to which he realizes the essence of the man, of being stripped of everything, and of being the Messiah of the future. This is how Marx analyzes the notion of the symptom. He gives lots of other symptoms, to be sure, but the relation of this one with a faith in man is incontestable. If we do not make of man anything whatsoever carrying an ideal future, if we determine him by the particularity in every case of his unconscious and of the fashion in which he jouit from it, the symptom remains at the same place Marx put it, but it takes another sense. Not a social symptom, but a particular symptom. No doubt particular symptoms have types: the symptom of the obsessional is not the symptom of the hysteric. For the obsessional, there is a very particular symptom, which I'm going to tell you about. No one has the least apprehension of death; if this were not so, you would not be so tranquil

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there. For the obsessional, death is a failed act. This is not so stupid, for death is only approachable by an act. Still, for it to succeed, someone must commit suicide knowing that it is an act, which only happens very rarely. This was however very widespread when philosophy had a certain aim--an aim other than to sustain the social edifice. There were then persons who came to group themselves in schools in a way that had some consequences. But what is of the nature to make you suspect the authenticity of the engagement in these schools, is that there is no need to have attained to any wisdom whatsoever, that it suffices to be a good obsessional, to know from a sure source that death is a failed act. I will stop there today. I have not even been able to get to the bone of what I wanted to say to you. Someone has objected to me that by dint of saying that the woman does not exist, I have made her (la) exist. Don't you believe any of it.

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Seminar of March 11, 1975

. . . R.S.I, these are just letters, as such supposing an equivalence. What results from my speaking them, making them serve me as initials, speaking them as real, symbolic, and imaginary? This takes on a sense. The question of sense is what I am trying to situate this year. The property of sense is that one names something in it, which gives rise to the dimension of what one calls "things," which only take their seating (assise) from the real.

I have been led to the showing (monstration) of the knot, although I sought to do a demonstration of analytic discourse. Now Freud's work makes no use at all of the symbolic, the imaginary, and the real. But it implies them, for it revolves around the Name-of-the-Father. The Names-of -the-Father are that: the symbolic, the imaginary, and the real. These are the first names insofar as they name something. As the Bible indicates apropos of this

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extraordinary thing it calls the Father, the first time of this human imagining (imagination) that is God is consecrated to giving a name to what?--to each of the animals. The Bible did not come from nothing, but from a tradition. A tradition is always stupid (conne). This is even why one has devotion--there is no other manner to be reattached to it than devotion. All that one can hope from a tradition is that it be less stupid than another. How is this judged? There we reenter the more and the less. This is judged by the plus-de-jouir as production. The plus-de-jouir is all that we can get our teeth into. It is because it is a matter of the jouir that one believes in it. The jouir is at the horizon of this more and this less. It is an ideal point, which one calls what one can. One says: the phallus. I have already stressed, in its time, that for the speakingbeing it is the essence of the comic. As soon as one speaks of something that has a relation to the phallus, it is the comic--which has nothing to do with the joke. The phallus is a comic like all comics--sad. Reread Lysistrata. You may laugh; you will find it bitter. It must also be said that the phallus is what gives body to the imaginary. A little film brought me by Mme Aubry as an illustration of what I called then the Mirror Stage struck me a lot. You know how, on some not very assured foundations, I account for the jubilation connoting this moment for the child. I suppose that this jubilation is due to the prematured body, uncoordinated until then, feeling reassembled, its unity seized by way of the image, its mastery assumed. For animals born ripe, it does not seem--without our being able to confirm it--that this is produced to the same degree. There is not for them this jubilation. Well, there is a tie between this and a gesture I was able to grasp in this film. The child before the mirror--I don't know if it was a little girl or a little boy; it little matters, the gesture has the same value--the child passed its hand before what was perhaps a phallus or perhaps its absence, and pulled it back sharply from the image. This ellipsis appeared to me the correlate of the prematuration, and the announcement of what will later be called modesty. The phallus, thus, is above all the real insofar as one elides it. If you return to what I have cleared the way to this year in trying to make consonate consistency, ex-sistence, and hole with the imaginary, real, and symbolic, I will say that the phallus is not the ex-sistence of the real. There is a real that ex-sists to this phallus, which is called jouissance, but rather this is its consistency. It is the concept, if I may say so, of the phallus. With "concept," I echo the word Begriff, which doesn't go so badly, since in sum the phallus is what is taken in the hand. The concept is not without relation with this announcement, this prefiguration of an organ that is not yet taken as a consistency, but as an appendix. The ape also masturbates, and this is how he resembles man. In the concept, there is always something of the order of apishness. The only difference between the ape and the man is that the phallus consists no less for him in what he has of the female than in what he has of the male--a phallus worth the same as its absence. Whence the special accent that the speakingbeing puts on the phallus, in the sense that jouissance ex-sists to it. This is the accent proper to the real, the real inasmuch as it ex-sists, which is to say the real as real, a real at the power of 2. All that he knows of the two is power, a semblance (semblant) whereby he remains the one-alone. This is what one calls being--beginning with 12 = 1.

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There must be a tie between that and sense, whereby the1 is applied so well to the 0. It was Frege who made the discovery, and I have blathered on occasion about the difference between Sinn and Bedeutung, where the difference between 0 and 1 is seen, all in suggesting to you that this is not a difference, for there is nothing better than the empty set to suggest the 1.

There it is. How then does the symbolic, ordinarily called the bla-bla, or the word--how does it cause sense?

That is a question I do not ask you without having the answer. Is it in the idea of the unconscious? Is it what I have said since the first Rome discourse? Question mark. No, it is not in the idea of the unconscious; it is in the idea that the unconscious ex-sists, which is to say, it conditions the real, the real of this being I designate the speakingbeing. It names things, as I have just evoked apropos of the first flirtation of the Bible with an earthly paradise. It names things for the speakingbeing, a being that, although a species of animal, differs singularly. What does this mean, "animal"? An animal is what reproduces.

Only, how is this animal parasited by the symbolic, the bla-bla? There, it seems to me--it seems to me, but it is not very probable--I am distinguished from people of my species of animal, who since time immemorial, it must be said, know that they speak, but do not explicitly make much of it. And what shows that they do not explicitly make much of it is not that they haven't said it, since everything is said in the bla-bla, but that they dream of not being the only ones (les seuls). This has them by the guts. Let us write laisseuls to evoke let them alone, in this parlance. These days, this is manifested in the frenetic need to discover the language of the dolphins and of the bees. Why not? This has always been a dream. Formerly, this dream had other forms: one dreamed that there was at-least-one God who spoke, and who, above all, did not speak without it having some effects. What you don't hear about is the tangled feet with which the sub-speakers, the angels--the commentators?--approach him.

Finally something more serious comes, a very small advance-- not a progress, to be sure, for there is no reason for us not to continue tangling up our feet. In linguistics we have nonetheless distinguished naming,10giving a name, consecrating a thing with a speaking name. Naming (nomination) is not communication. It is in naming that the parlotte is knotted to something of the real.

What is the relation of this naming, as the title of a book says, with necessity? Long ago, the person named Plato accounted for having to have the idea, the ειδοs, as a third. The ειδοs is a very good translation for what I call the imaginary, since it means the image. Plato saw very well that without the ειδοs there was no chance that words would stick to a thing. That did not bring him to the point of speaking of the Borromean knot, but only because chance had not furnished him with it. The idea was for him the consistency of the real. Nonetheless, the idea being in his time nothing without something namable, one deduced with university discourse the realism of the name. It must be said, the realism of the name is better than the nominalism of the real--believing that one can use just any name to designate the real. Not that I am marking a preference, I am simply underscoring that nominalism is an enigma paying homage to the effect of the name on the real, to what is added to it when one names it. In the realism of the name, itself founded on the imaginary, a dire is missing--one is interdicted from admitting this homage.

10 In English in the original.

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This is found again in the prestige of the university. But it does not appear to us, us other analysts, to constitute an advantage. We remain in thought. You will tell me that I run on (m'en paye), and even to the point of tiring you. It's that I make an effort to disentangle myself from what is fundamental to thought, what I will call the typical imbecility, typical of thought, of the human humor in regard to the real, which, however, it has to deal with (traiter). Whence the urgency that the sense of this word be discernible. Up to the present, what I have said about tradition keeps all of its value. It is no more saleable than religion, the green pastures.11 To go there, right to the end, the true blue (vrai de vrai) at-least-one God is He who taught the speakingbeing to give a name to each thing--the name of the name, the name-of-the-Father. The non-dupe errs without it, for the zist or zest-for-eternity. To back up a little, this results in the real being what ex-sists to sense, inasmuch as I define it by the effect of lalangue on the idea, on the the imaginary supposed by Plato to the speakingbeing animal among others, among the other animals-in-the-flesh (au corps)--or the devil in the flesh, if you like. Why not, since we are in mental debility. One mentally debilitated is as good as another, why not Plato? Aristotle (Aristote) too, who argues about the idea of the ass (âne) to say that the ass is an ass, and that there is no Ass with a capital A; he too assistotles (anistote). The real has to be conceived of as expelled from sense. It is the impossible as such, the aversion to sense. It is also the version of sense in the anti-sense and the antesense, the shock in return of the word, inasmuch as the word is only there for that--which is not for nothing, if it accounts for what it is in question, for the refuse (immondice) from which the world (monde) is pruned (s'émonde) in principle--insofar as there is a world. This does not mean that it gets there. Man is always there. The ex-sistence of filth (l'immonde), of what is not the world, is the real plain and simple. It is quite worthwhile to push this as far as the elaboration of the quantor. Some such x exists; and instead of an (un) x, it is better to say une x. To what does it ex-sist? That is what one must ask oneself. It ex-sists to the ideic consistency of the body, which body reproduces it. It ex-sists to the symbolic inasmuch as the symbolic turns in a circle around an inviolable hole, without which the three-looped knot would not be Borromean. That is what the Borromean knot means--the hole of the symbolic is inviolable. Why not then write it like this (Figure 1)? The symbolic is the red circle I put there. It is imposed on the imaginary, which I put there in green, the color of hope. One sees how the real ex-sists there, no more compromising itself by knotting itself with the symbolic in particular than it does with the imaginary. In whatever direction (sens) one makes this imaginary and this real turn, they will cross each other without making a chain. These two consistencies can just as well be straight lines to infinity. But we must stipulate that, however one conceives of this point at infinity dreamed up by Dessargues as specific to the straight line, a straight line that makes one of its ends return to the other, there is no question of its folding back on itself without the line which first passed over the other line passing over it again.

11 In English.

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There is no other way to demonstrate that the Name-of-the-Father is nothing other than this knot than to suppose the rounds unknotted. Let us no longer pass the symbolic in front of the imaginary. How can we knot three independent consistencies? There is a way, which is that one there, which I call the Name-of-the-Father (Figure2)--it is what Freud does. At the same time, I show the radical function of the Name-of-the-Father, which is to give a name to things, with all the consequences that this entails, including a jouir, notably. I have already made some traces for you of this four-looped knot, one of which failed. I give you yet another, the same, but in profile (Figure 3). This story thus leaves us in the three, since the adjunction of the four is superfluous. As one might expect, the distinction in the symbolic of giving-a-name is a part of the symbolic.

What you see here (Figure 4) in a particularly clear way, I have repeated because it perhaps does not leap into view there (Figure 5). This is the Borromean knot before its flattening out. The Borromean knot is what, to two circles that circle each other, introduces this third which penetrates the circles in way that the other is, in relation to this third, in the same relation as with the first circle. I now ask the question: is there a discernible order here? Is the Borromean knot a whole (tout), a conceivable whole, or else does it imply an order?

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At first approach, one could say that it implies an order if, for example, one colors each of the circles. Coloring a circle will mean--as someone who sent me a text expressed it very precisely--that it remains identified to itself. If they are colored, there is an order: 1 2 3 is not 1 3 2. The question, however, is to be left in suspense, for the order is perhaps indifferent in regard to all of the effects of the knot, which would indeed make us think that the rounds are not to be identified. It was inasmuch as three rounds make a Borromean knot, none of which makes a chain with another, that they support for us the idea of the symbolic, the imaginary and the real. What has suggested this to me is a little letter from someone named Michel Thomé, who shows what he calls an error in perspective in figure 6 of chapter 10 of my seminar Encore--a figure that I have not drawn here, and which was introduced by him who was good enough to edit me, and whom I did not supervise. I have stressed that, from one circle to another, the first to be knotted of three, the most simple form of the Borromean knot is, as I am served by the term, the circle tied in two ears (Figure 6). The error in perspective consisted in not crossing the lobes of the two ears (Figure 7), which resulted in these knots lacing themselves together . . . But that isn't all. Michel Thomé very well deduced that a Borromean knot of a special type resulted. You see that these two remain knotted if one sections the third. The Borromeanism of this knot is thus only manifested for any number whatsoever of rounds in cutting a single one among them, which we can call the last, by means of which each of the others will be freed from the one following it until it gets to the first, not all at once, it is true, but one after another. On the other hand, if you begin by cutting what I call the first, all of the others to the last will remain knotted. This puts in evidence certain knots that one can call Borromean in one direction (sens) but not in the other, which evokes the cycle and orientation. I do not insist, because it is only those who devote themselves to a study of these knots who can take a true interest in this. But I remind you that I had myself drawn a knot whose only interest was in not being able to be produced from this error in perspective given its fecundity by Michel Thomé. It is not strictly producible except by being made explicit, if I may say so, by the confusion of the two loops (Figures 8) that hold to each side, the forms of the ear that I have proposed as the most simple form for engendering the Borromean knot. You see that there could be here (Figure 8, e) an external round, which would hold these two ear loops, and so on. If you reunite these two loops, you obtain the following form, which is a loop altogether distinct from the forms that I will call, on this occasion, Thoméan, to indicate that they are products of an error in perspective.

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I do not insist, and I pursue what there is of the Name-of-the-Father, to lead it back to its prototype. God is the woman rendered all. I have told you she is not-all. But in the case where she would ex-sist from a discourse which would not be of the semblance, we would have the x.x, the God of castration. This is a wish, a wish that comes from The Man, a wish that women existed who would command castration. The trouble is that there aren't. That the woman, the all woman, does not exist, does not imply, contrary to Aristotelian logic, that there are some who command castration. Guard this, which is the most beloved, as they say in Rabelais. Naturally, this arises from the comic. Nonetheless, this not-all does not mean that any says the contrary, and that an x of the woman exists that formulates do not guard it. It's very little for them, the saying no. They don't say anything, simply. They don't say anything, except as the-all, which I have said was God. The-all, if she existed. There is none to bear castration for the other, and this is at the point where she would like the phallus for herself, as one says. There is nothing more phallogocentric, as someone has written somewhere, than a woman, to the extent that none of them wholly (toute) want it, said phallus. They want it each, to the extent that it does not weigh on them too heavily. I have stressed this in the so-called dream of the beautiful butcheress. She indeed wants the smoked salmon, on the condition of not serving it. She only gives it inasmuch as she does not have it.

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This is even the definition I have given of love. To give what one does not have, this is love, the love of women, inasmuch as, one by one, they exist. They are real, and even terribly so. They are even only that. They only consist inasmuch as the symbolic ex-sists, which is to say the unconscious. This is indeed how they ex-sist as a symptom of which this unconscious provokes the consistency, this, apparently in the field of the real flattened out. This is what has to be called really, which means--one has not paid enough attention to this distinction between the adverb and the adjective--in the fashion of the real. But in reality, in the fashion in which is imagined in the real the effect of the symbolic (Figure 9).

I excuse myself to Pierre Soury, who sent me a very beautiful little schema concerning

the Borromean knot of which I will not have time to speak today. These two schemas involve an orientation, a direction--the three essential elements of the Borromean knot are oriented in a centripetal fashion, which he opposes for me with the contrary form, centrifugal (Figure 10). I remark to him in passing that if we do not identify by coloring them which of these three rounds is the symbolic, which the real, and which the imaginary, these knots, far from being nontransformable the one into the other, are the same, seen from another side.

I should add that, taking things from the other side, the real and the symbolic are inverted, which is not foreseen in his schema. However, this leaves intact the question of whether it is indifferent, in this form, not flattened out, that the order exists or not. I therefore

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signal to Soury that there is a distinction to be made between the order of the three terms, the orientation given to each, and the equivalence of the knots. The imbeciles of mad love who had the idea of making up for (de suppléer) the unreal woman titled themselves surrealists. They were themselves symptoms, symptoms of the aftermath of the war of '14, to the extent that social symptoms--but it is not said that what is social is not tied to a knot of resemblances. Their idea of making up for the woman who does not exist as the, for the woman of whom I have said that she was the type itself of errancy, put them back in the rut of the Name-of-the-Father, of the Father as naming, of which I have said that it was a device (truc) emerged from the Bible, but of which I add that it is a way for the man to pull his phallic marker (épingle) from the game. A God, as tribal as the others but perhaps employed with a greater purity of means, is only the quite useless complement--which is what I express with the conjugation of this four-looped knot--because he is the signifier 1 and without a hole, without a hole of which he would be permitted to be served in the Borromean knot, which has the body of a man--self-sexed, Freud stresses--and gives the man the partner he lacks. He lacks how?--because he is aphlicted, to write it like that, aphlicted really with a phallus which bars for him the jouissance of the body of the Other. There would have to be an Other of the Other for the body of the Other not to be some semblance (semblant) of his own, for him not to be so different from the animals as to not be able, like all of the sexed animals, to make of the female the God of his life.

The mental of the man--which is to say the imaginary, the aphliction of the phallic real because of which he knows himself born--has only the semblance of power. The real is the blank of sense; in other words, the blank sense by which the body makes a semblance, a semblance on which all discourse is founded, first and foremost the master discourse which makes of the phallus the signifier index 1. Which does not prevent that if in the unconscious there were not a crowd of signifiers to copulate with each other, to be indexed as abounding two by two, there would be no chance that the idea of the subject, of a patheme of the phallus of which the signifier is the One that divides it essentially, would come to light. Thanks to which it aperceives that there is some unconscious knowledge, some unconscious copulation, whence this mad idea--of this knowledge making (savoir faire) a semblance in its turn. In relation to what partner?--if not that which is also produced by a blind copulation--it is the case to say. Only signifiers copulate with each other in the unconscious, but the pathematic subjects that result from this in the form of bodies are lead to do the same--to fuck (baiser), as they call it. This is not a bad formula, for something informs them that they can do no better than to suck on the body signified Other, Other only by some writing in the civil registry. To jouir from it, it has to be cut in pieces. The Other body lacks no disposition for that, since it is born prematured. And the concept is not lacking--one calls that sado-masochism, I don't know why. It can be no more than dreamed of, from the unconscious naturally, since this is the road which must be said to be heartened by the Royal dire. King, one more name in the business, which everyone knows always springs to the business of the Name-of-the-Father. But it is a name to lose like the others, to let fall in perpetuity.

The Noms-du-Pere, the ânons-du-Pere12, what a herd I would have prepared to make reenter their throats their brayings if I had given my seminar; I would have hunited--a word

12 An ânon is a young donkey.

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coming from hone13 (hune) woman--some new stupidity (ânerie). This is why the hanalysts--on the waiting list, of course--lined up at the doors of The Interfamilial Analytic Association and annafreudhummed 14 in the wings the return to the cradle, while patching together tough motions of order against me. I am certainly not insensible to the weariness of ex-sisting (d'ex-sister-terre-terre), which one believes one will always attain to finally. But I can only persevere in my erre--Laurent, tighten (serrez) my herre with my discipline.

13 By prefixing une, uni, analystes, and erre with h's in this passage, Lacan is perhaps trying to evoke hi-han, which is what French donkeys say.

14 Annafreudonnaient in the original: a portmanteau of Anna Freud and fredonnaient (hummed).

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Seminar of March 18, 1975

I have already evoked the discovery made by Michel Thomé of an error in Figure 6 of the last published of my seminars. Felix Culpa, this was a fortunate error since it gave him occasion to invent some Borromean knots of a special type, which are only unmade beginning from one end. It is only in one direction (sens) and not in the other that all are unknotted. And in the direction in which all are unknotted, they are freed one by one, and not immediately. This invention is indeed for me the proof that I do not speak without effect. What I know thanks to these two friends, Soury and Thomé, puts me on the path. The knots are something quite original, with perhaps--I am not sure--the ambiguity of "the original." What would confirm this is that it is not so easy to get back there. And, then, the original is not what one begins with. Historically, the Borromean knot is not found under the hoof of a horse. One did not take an interest in it until very late. Me, when I caught wind of the knot--I found it in the notes that someone had taken at Guilbaud's seminar--I immediately had the certitude that this was something of great value (précieux) for what I had to explain. I immediately found the rapport of the rounds of thread of this knot, of these three particular consistencies, with what I had recognized from the beginning of my teaching; which I would no doubt have not emitted, being little inclined to it by nature, without a call, tied in a more or less contingent fashion to a crisis in analytic discourse. It is possible that with time I would have aperceived that this crisis had to be unknotted, but there had to be certain circumstances for me to pass to the act. The three rounds thus came to me like a ring to a finger, and I immediately knew that the knot incited me to articulate (énoncer) something that would homogenize the symbolic, the imaginary, and the real. What does this mean, "homogenize"? It is obvious, as Pierre Soury remarked previously in a little note he communicated to me--I take great care to give each his due--they are somewhat similar, but, he adds, "between the similar (pareil) and the same (même), there is room for a difference." Putting the accent on the similar is very precisely of what homogenization consists, the pushing forward of the οµοιοs, which is not the same, but the similar. What do they have of the similar? I believe I must designate this with the term consistency, which is already to advance something rather incredible. What indeed can the consistency of the imaginary, and of the symbolic and the real, have in common? Do I, by this statement (énoncé), render you enough sensible that the term consistency arises with the imaginary? Parenthesis. Figuring the knot is not easy. I do not say "figuring it for yourself" ("se" le figurer), because I completely eliminate the subject. I take my departure, on the contrary, from the thesis that the subject is determined by the figure in question. Not that it would be its double. But it is from the wedgings of the knot, from what in the knot determines the triple points--it is by the tightening (serrage) of the knot that the subject is conditioned. Figuring the knot is not easy (commode). I have already given you some proofs of this in my muddlings over the question of the oriented knot. To the real of the Borromean knot, you can add this: the differentation of each of these rounds. The simplest way is to color them. Although Goethe notes it nowhere in his Theory of

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Colors, color is in itself pregnant with differentation. There is a limit, certainly, since the number of colors is not infinite, but, finally, thanks to color, there is some difference. Thus, you introduce differentiation into the round by coloring in a different way each of the rounds. You can go as far as to orient them. I have then asked the question of whether this differentiation leaves the knot not similar, but always the same. It is effectively always the same, but there is only one way to demonstrate it: it is to demonstrate that, in every case--what does "case" mean?--it is reducible to the similar. I was indeed convinced that there is only a colored knot, but I waffled a little concerning the oriented knot. Orientation, in fact, concerns a yes or no for each of the knots, and I have been led astray by the relation of each of these yeses or nos with the other two. I have not gone so far as to think that there are eight or four knots, but I have battered my brains to know if there aren't two. Thus, it is no small result to have obtained from Pierre Soury, after having asked explicitly for it, the demonstration?--no, the monstration [showing] that there is only one oriented Borromean knot. Let us remark that he can only do this by way of what I have called the flattening out. This flattening out is something that merits being individualized, because the knot, I have shown you, is not at all flat by nature. That one must go by way of the flattening out to emphasize the sameness of the oriented knot, is this not a sort of fatum of thought, which in attaching it too closely to the true, lets the real slip through its fingers? This is indeed what I brought out last time in distinguishing the concept and the truth. The concept limits itself to a taking (prise), as the word capere indicates, and a taking does not suffice to insure that the real is what one has in hand. In the comments I make to you and that you have, I don't know why, the patience to accept, it is impossible for me to inform you at every instant what I do in speaking to you. Your presence proves to me that I do something that concerns you. But in what mode does that happen? To say that you understand something of it is not even certain at the level where what I say is sustained. But there is nonetheless something that is worthy, and it is this something that I situate in saying that we understand each other (on se comprend). We understand each other has no other substratum than we kiss each other (on s'embrasse). This, however, is not exactly what we do. There is an equivoke here, which, like all equivokes, has a smutty side. For my part, I force myself to put a little humor in my recognition of this smuttiness as presence. It is indeed this that gives weight to the way I slice the knot, in stating that there is no sexual rapport. This does not mean that the sexual rapport does not roam the streets. It remains to be put in evidence that everything has to be recentered on this frotti-frotta, this fiddling around (fricotage), to make a call to what? To the real, to the real of the knot. Freud made a step by simply aperceiving that one has never spoken of anything but that, and that everything philosophy did pursued the sexual rapport to overflowing (á plein bord). By stating that there is no sexual rapport, I designate a very local point. Marking an R, to be put between x and y, to designate the relation, is from the very start to enter into the game of the written. Now, for what concerns the sexual rapport, it is strictly impossible to write xRy. There is no logicizable elaboration, and at the same time no mathematical one, of the sexual rapport--this is the accent I put on the statement "there is no sexual rapport."

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This is to say that, without recourse to these different consistencies--homogeneous as such, certainly, but nonetheless different from being named imaginary, symbolic, and real--there is no possibility of a frotti-frotta. The difference between these consistencies cannot be reduced to a writing that would be supported, I mean, that would resist the test of mathematics, and that would permit us to insure the sexual rapport.

These modes are those about which I have had my say (pris la parole), symbolic, imaginary, and real, and I will not say that they are obvious. I force myself simply to empty them out (les évider), which does not mean the same thing, because évider reposes on vide [empty] and évidence on voir [to see]. Is this to say that I believe in it? I believe in it in the sense that it affects me as a symptom. I have already said what the symptom owes to the believing in it. I am trying to give to this I believe in it another form of credibility. It is certain that I will founder there. This is no reason to not undertake it, if only to demonstrate the beginning (l'amorce) of the impossible, already my impotence.

The knot is supposed by me to be the real in the fact of what it determines as ex-sistence, I mean in how it forces a certain mode of turn-around. The mode in which one round of thread ex-sists to another is that with which I displace the by itself unsolvable question of objectivity. Objectivity thus displaced seems less silly (bébête) than the noumena. It is strictly impossible to not make emerge, on the basis of the noumena conceived of in opposition to the phenomena, the metaphor of the hole--but you are going to see that this is an after effect.

There is nothing to say about the noumena, except that perception has the value of deception. But it is we who call it a deception, this perception. Perception itself says nothing. It does not say; it is we who make it say. We speak all alone--I remark this apropos of no matter what dire. We offer our voice, but this is a consequence, for the dire is not the voice; the dire is an act.

The noumena is nothing other than the hole, this hole that we find again in our symbolic, named as such, and beginning with the topology of the torus.

The torus is distinguished from the sphere by a mode of writing by which are also distinguished the homo, homeo, and automorphisms. Its foundation is always what one calls a continuous transformation. A transformation that encounters the obstacle of another cord supposed to consist is what makes the torus--which I would call on this occasion a gut-torus (tore-boyau).

Make a hole there in the torus, introduce your hand, and trap what is at its center (Figure 1). One sees clearly that there is discordance between this hand and what it grips. One can also suppose another torus at the interior of the torus (Figure 2). How far can we take this? . . .

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These cords supposed to consist give some support to the metaphor of the hole, and allow

us to elaborate mathematically a topology distinguished from that of the sphere. Every imaginary supposition participates implicitly in the sphere insofar as it shines (rayonne)--Let there be light! Only, concerning what there is of the consistency of the body, analysis reveals that we have to come to the intestines (boyaux). Far from the polyhedrons that have occupied the imagination, Timaein for centuries, it is the gut-torus that prevails. Besides, this is also a sphincter. This renders sensible for you the relation of the body to the imaginary. I now ask you the following question: can we think the imaginary, inasmuch as we are held to it by our body, in a way that reduces its imaginarity?--or its imagery, if you like? One is in the imaginary. However elaborated one makes it--and this is what analysis leads us back to--one is in the imaginary. There is no means to reduce its imaginarity. It is here that topology makes a step. It permits you to think--but it is a thought after the fact--that the aesthetic, in other words, what you feel, is not in itself transcendental. The aesthetic is tied to what is only a contingency, that it is this topology that is the right one for a body. Yet this is not a body all alone. If not for the symbolic, and the ex-sistence of the real, the

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body would have no aesthetic at all, because there would be no gut-torus. The gut-torus is a mathematical construction, which is to say it is made from this nonexistent relation between the symbolic and the real. The notion of the knot that I promote is imagined, is figured, between imaginary, symbolic, and real, without for all that losing its weight of the real. But why exactly? Because there is an effective knot, which is to say that the cords are wedged together. There are cases where this turn-around no longer works because of the triple points that suppress ex-sistence. This what I have indicated to you in saying that the real is demonstrated to have no sense. There is no sense because only sense as vanishing, reduced to this triple point, gives sense to the term real (Figure 3). Likewise, in this other triple point is situated jouissance insofar as it is phallic--which implies its liaison with the imaginary as ex-sistence. The imaginary is the step of (pas de) jouissance. Likewise, what gives consistency to the symbolic, is precisely that there is no Other of the Other. Is this to say that these figures are models? I have said that models recur to the pure imaginary. Knots recur to the real. They take their value from this: that they have no less bearing in the mental than the real, even if the mental is imaginary. Every couple, all that there is of the couple, is reduced to the imaginary. Negation is also a way of admitting--Freud insists on it from the start--a way of admitting there alone where the admission is possible, because the imaginary is the place where all truth is stated, for a denied truth has as much imaginary weight as an admitted truth: Verneinung-Bejahung. How is it that the real only begins at number three? Every imaginary has some two in the mix, as a remainder of this two effaced from the real. And this is how the two ex-sists to the real. Ex-sistence is the play of the cord until something wedges it; this is what plays on each cord, as ex-sistence, to the consistency of the others. Freud renewed the accent on the consistency of the real with an ancient term, the phallus--but how are we to know what the mysteries placed under the term phallus? In accentuating it, Freud exhausted himself, but this is done in no other way than its flattening out. It is a matter of giving weight to this consistency, and not only the ex-sistence, of the real. Naming (Nommer)--which we could write n'hommer15-- naming is an act, from adding a dit-mension, a dimension of flattening out. No doubt, Pierre Soury, in his monstration that there is only one knot, distinguishes the turning around of the plane, the turning around of the round, the turning around of the band, indeed, internal and external exchanges. These are only effects of a flattening out. An exemplary recourse to the distance between the real of the knot and this conjunction of domains that I wrote on the board, giving weight to sense. Whether this clarifies the practice of analytic discourse, I leave to you to decide. I propose, in closing today's meeting, this formulation of the triple identification that Freud advances. If there is a real Other, it is not elsewhere than in the knot itself, and it is in this that there is no Other of the Other. If you identify with the imaginary of this real Other, it is the identification of the hysteric with the desire of the Other--which passes to the central point. Identify with the symbolic of the real Other, and you have the identification with the trait unaire.

15 A portmanteau of nommer (to name) and homme (man).

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Identify with the real of the real Other, and you obtain what I have indicated by the Name-of-the-Father, where Freud designates what identification has to do with love. I will speak to you next time of these three forms of the Name-of-the-Father, those that name the imaginary, the symbolic, and the real, for it is in these names that the knot holds.

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Seminar of April 8, 1975

Cogitation remains glued into an imaginary rooted in the body, which is the imaginary of the body. Literature bears witness to this, philosophical as well as artistic--which besides are in no way distinguished from one another. To quickly lay down my cards, I am going to speak of the imaginary of the sphere and the cross. I have wandered into Joyce because someone asked me to speak before a congress. Well, if Joyce is glued into the sphere and the cross, it is not owed only to his having read Saint Thomas because of his education with the Jesuits. You are all as glued as he into the sphere and the cross. Moreover, this makes the plus sign. It may happen that an artist who plaques a bit of plaster on a wall will make something that by chance resembles this (Figure 2). But no one aperceives that this is already the Borromean knot. When you see this, what do you make of it imaginarily? You make two things that hook together, which bends them in this fashion (Figure 3). By means of which, the round slips over what is knotted in this way. It is not natural--what does that mean, "natural"?--it is not natural to your imagination to do the contrary and distort the round in this way (Figure 4). The Borromean knot is not necessarily what I have drawn for you a hundred times. This (Figure 5) is a Borromean knot as valuable as the one I usually flatten out.

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If I was one day taken hold of by the Borromean knot, it was in relation to this order of event (événement), of arrival (avènement), which is called analytic discourse, a social tie emerging in our day. This discourse has an historical value, yet to be established. It is true that my voice is weak for sustaining it, but this is perhaps all the better, because if it were stronger, I would perhaps have fewer chances of subsisting. I mean that, based on all of history, it appears to me difficult for the social ties prevailing until now not to silence any voice that sustains another, emerging discourse. This is what one has always seen up to now, and it is not because there is no more inquisition that we should believe that the social ties I have defined--the master discourse, the university discourse, even the hysterico-diabolic discourse--would not stifle what I might have of a voice. This said, me in there, I am a subject, I am taken in this business because I have put myself into ex-sisting as an analyst. This does not at all mean that I believe myself a mission of truth, as have believed some people who have come down on my head. No mission of truth since the truth can only be half-said (se mi-dire). So let us rejoice that my voice is low. In philosophy up to the present, there has been the good philosophy, the ordinary one, and then, from time to time, there have been kooks who believe themselves a mission of truth. The lot (L'ensemble) are simple buffoonery. But my saying it has no importance--fortunately for me, no one believes me. All told, for the moment, the good one dominates. I made a little visit over the vacation--a story of giving him a little sign before both of us dissolve--to the person named Heidegger. I like him a lot. There is something in him like a presentiment of sicanalisse, as Aragon used to say. But it is only a presentiment, because Freud

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doesn't interest him at all. However, Freud made something emerge from which I draw the consequences to give weight to its effects--which are not nothing, but this would suppose that the psychoanalyst existed a little bit more. He has nonetheless begun to ex-sist. How, for this knot I have come to--not, of course, without getting my paws tangled up in it as much as you--how can we make it so it tightens, this knot, to the point where the speakingbeing, as I call it, no longer believes, no longer believes in being, outside of the being of speaking? He believes in being; it would be crude to say that this is exclusively because there is the verb "to be." No, this is why I say "being of speaking." He believes that because he speaks he is healthy. This is an erre, and even a trait unaire. Thanks to which what I call an oriented nonsense (déconnage) has prevailed in what one calls thought, which is said to be human. I am letting myself go; I get the itch (la mouche me pique) from time to time. This erre merits being pinned to the word transhumant16--so-called humanity only owing to a naturality of transit, which postulates transcendence. My succeeding has no connotation of success in my eyes. I, like Freud, only believe in the failed act, but in the failed act as revealer of the site, of the situation, of the transit in question, with transference as its key. Simply, one must bring this trans back to its proper measure. My success, therefore--my succession is what this means--will it remain in this transitory? This is the best thing that can happen, since, in any case, there is no chance that the humant-trans will ever approach any of this. Therefore, peregrination without end is worth as much. Simply, Freud remarked that there is perhaps a dire which has value from up to now only being interdicted. This means said between, between the lines. He called this the repressed. I made this discovery of the knot without seeking it, of course. It appears to me a notable discover from recuperating, not the air of Freud, but his erre, which ex-sists rigorously, an affair of the knot. Now let us pass to something we can get our teeth into. That one (Figure 2) is the important one. Why the Devil hasn't anyone drawn on this plus which consists in writing the sign like that, in the right way (Figure 4)? Young Aragon got heated up in claiming that our time had gone so far as to suppress the crossroads, the quadrivii; he was thinking of autoroutes [turnpikes]--it's a funny word, autoroute; is this a route in-itself or a route for-itself? There are still a lot of crossroads and street corners, but he took to thinking that there would be no more crossroads, only tunnels. It is curious that he drew no conclusion from this. This is the surrealist mode; it has never led to anything; it has not spacialized the knot in the good way--thanks to which we are still in being, as Heidegger said to me, in-der-Welt. The in-der-Welt-sein. This is a cosmeticology, cosmetibuttologous (cosméti-culeuse) in addition. And thanks to this Welt, there is the Umwelt and the Innenwelt. This should make us suspicious, this repetition of the bubble. I have learned that in comic strips one speaks in bubbles. I never look at comic strips, and I am ashamed, because this is marvelous. In fact, it was a photo-novel from Nous Deux, with words--thoughts, that's when there are bubbles. Well, the question I ask here, in this form of a bubble, is what proves that the real makes a universe? I ask this question starting from Freud, who suggests that this universe has a hole, a hole that there is no means of knowing. Then I

16 In both French and English, transhumant is an adjective referring to the migration of livestock.

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follow the trail of the hole, and I encounter the Borromean knot, which comes to me there like a ring to a finger--there we are in the hole again. Only, when one follows the trail of things one grasps that there is not just one trick for making a circle. There is not only one hole. If you take two of these circles, if you knot both in the right way and if you add this infinite straight line, it makes a knot as valuable as the one I usually draw (Figure 6). Rather than make the infinite straight line, it is a lot more convenient to close this consistency, and we then return to the familiar knot.

The interest in representing it in this way (Figure 6) is to show how the knot can be, if I may say so, doubly Borromean, which is to say that we pass to the four-looped Bo-Bo knot. Here I give you (Figure 7) a new illustration of the four-looped knot. But the question that this raises is the following--what is the order of equivalence of the infinite straight line and the circle? There was a man of genius called Desargues to whom it came to mind that any infinite straight line closed itself at a point at infinity. How could this idea have come to him? It is an absolutely sublime idea, around which I constructed my commentary on Las Meninas, of which it was said, if you believe the pen-pushers (gratte-papiers), that it was completely incompre-hensible. What is the equivalence of the straight line to the circle? It is obviously because they make a knot. This is a consequence of the Borromean knot; it is a recourse to efficiency, to effectiveness, to the Wirklichkeit. But if we find them equivalent in the efficiency of the knot, what is their difference? As you see, I painfully approach the "thinking the Borromean knot will give you pain." Because it is not easy to imagine, which gives a proper measure of what all thinking is. Even Descartes never made anything of his Regula decima, and this is a sign. Between the circle and the straight line, there is a play, which leads to their equivalence. But how can we formulate in what their difference of ex-sistence consists? The straight line ex-sists, goes off in the erre until it encounters simple consistency, while the circle is centered on the hole.

No one knows what it is, this hole. That, when it comes to the corporal, the accent is put by all analytic thought on the hole, plugs it up rather. This is not clear. That it be from the orifice that is suspended all that there is of the pre-oedipal, as one says; that it be there that is oriented the perversity which is integrally that of our conduct, is indeed strange. This does not clarify for us the nature of the hole.

There is another thing that could come to mind and which is completely unrepresentable--it is what one calls by a name that only flickers forth because of language: death. This doesn't plug it up any less, because one doesn't know what death is.

However, there is an approach that envisages space otherwise; it is topology. One cannot say that it leads us to very easy notions. One sees well there the weight of the inertia of the imaginary. Why is geometry found so at ease in what it combines? Is this because of the adherence to the imaginary or is it because of a sort of injection of a symbolic? A question that merits being posed to a mathematician. Whichever the case, with the topological notions of neighborhoods and of points of accumulation, the accent is put on discontinuity, while, manifestly, the natural slope of the imagination is continuity. The difficulty of the introduction

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of the mental to topology indeed gives us the idea that there is something to learn here concerning our repressed. The effective difficulty of cogitating on the Borromean knot, the facility, on the other hand, of doing so on the sphere and the cross, makes of this knot something like an example of a missed mathesis (mathesis manquée), missed by a hair, inexplicably, never familiar in any case. Why not see in the aversion that this manifests the trace of the first repression itself? And why not follow this path, like a dog that scents a trail?--although it is not scent that characterizes us.Besides, how are we to account for the effect of scent on the dog? Scent imitates an effect of perception, which in this case would be the supplement to the lack that we must indeed admit if we open our eyes to the ex-sistence of the Urverdrängt, the repression that analysis affirms not only as first, but as irreducible. This is what would be involved in following the trail, and this is what I do for you in the measure of my means. Naturally, I take care to tell you that I am not getting all worked up, that I do not believe that I have found the last word. Thinking that one has found the last word, would that be paranoia? No, paranoia is not that; it is being glued into the imaginary. A voice that sonorizes the gaze is what is prevalent there; it is an affair of the congealing of desire. But finally, all the same, this would be paranoia. It remains that this could be a vein to follow. Freud told us not to worry. There is no reason to have so much fear if this leads us somewhere. It is clear that this has only lead to the truth, which indeed shows the measure of the truth itself; to wit, what the paranoia of President Shreber demonstrates, that there is no sexual rapport with God. That is the truth. And it is indeed what puts in question the existence of God. We are there in a failing of creation. To say it, is to take confidence in something that probably dupes us. Only, not being a dupe is nothing other than to find oneself in the mess (essuyer les plâtres) of the non-dupe, which I have called the erre. But this erre is our only chance of truly fixing the knot in its ex-sistence, since it is only ex-sistence as a knot. It is what only ex-sists in being knotted in a way that it can only be tightened, even in the tangle. Saying that there is no sexual rapport departs from the idea of a ϕυσιs, which would make of sex a principle of harmony. Rapport even to this day means proportion. The idea that one can reproduce it with words, that words are destined to make sense, that being being results in non-being not being--there are still people for whom this makes sense. The Parmenidian sense at the origin has become empty chatter, and it has come to no one's mind that it is the sign itself that is wind: flatus vocis. I do not at all say that these people are wrong. On the contrary, they are precious to me because they prove that sense goes as far into the equivoke as one might desire. They prove that beginning with sense se jouit, I s'ouit17 myself, s'oui-jouisse . . . Naturally, there are better--although the best, as says popular wisdom, is the enemy of the good; likewise, the plus-de-jouir proceeds from père-version, from the a-pèritive of the jouir. On can do nothing there; the speakingbeing only aspires to the good, where it always buries itself in the worse. That does not change the fact that the speakingbeing cannot refuse it. Not even me. I am a grain, like you all, ground into this salad.

17 A pormanteau of ouïr (to hear) suis (I am).

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The annoying thing is that everyone knows that analysis has some good effects--which only last for a time. This does not change the fact that this is a respite, and that it is better--it is the case to say--than doing nothing. It is a little aggravating (embêtant), an aggravating against which one could try to swim despite the current. If there is this current, it is because, despite everything, nature has proven the existence of God. Everyone believes it. I defy any among you to say that I can't prove that he believes in the existence of God. This is even the scandal, which psychoanalysis alone stresses, because currently there nothing but it that proves it--I mean the scandal, not God. Formally, this is only due to the Jewish tradition of Freud, which is a literal tradition, which ties it to science, and at the same time to the real. It is the cap that it is a matter of doubling. God is père-verse. This is a fact rendered patent by the Jew himself. But to rise up again on this current, one will end well--I can't say that I hope it--by inventing something less stereotyped than perversion. This is even the only reason that I am interested in psychoanalysis, why I try to galvanize it. I am not stupid (bête) enough to have the least hope in a result that nothing announces, and which is no doubt taken by the wrong end--thanks to the cock and bull story of Sodom and Gomorra. There are even days when it comes to me that Christian charity would be on the path of a perversion that would clarify the non-rapport a little. You see where I am going. This is not, however, in my inclination.

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But, finally, one must not carry on (charrier), nor charity-on (chariter). There is no chance that one might have the key to the road accident (accident de parcours) that made it so that sex has ended up becoming a malady for the speakingbeing, and the worst malady, that by which it reproduces. It is obvious that biology has an advantage in forcing itself to become, with a little different accent, viology, the logy of violence; in forcing itself to the side of mold, with which said speakingbeing has many analogies. One never knows. A good encounter. One François Jacob is enough of a Jew to have permitted rectifying the non-rapport, which, in the current state of knowledge, can only mean replacing the fundamental disproportion of said rapport by another formula, by something that can only be conceived of as a detour devoted to an erre, but to an erre limited by a knot.

I think you have seen the papers distributed by Michel Thomé and Pierre Soury, which demonstrate that there is only one oriented Borromean knot. I would like to underline the remark I have made today; the fact that there is a means of making a cycle with two circles has some consequences concerning this proposition. I agree that there is an oriented knot when there are three rounds of thread, but not when there are more. Nonetheless, if you transform one of these circles into an infinite straight line, there is no longer only one oriented knot, but two. For the infinite line is not orientable. Beginning with what could one orient it? It is only orientable beginning with any chosen point on it, from which the orientations diverge. But if they diverge, that does not give it one orientation.

To hold ourselves to a simple formulation, let us remark that in the double circle (Figure 8), there is an orientation, which we will designate with the word gyrie. Not that we could say that this is a dextro- or levogyrie Everyone knows--it's why we couldn't send as a message to someone from another planet the distinction between right and left. It has to be admitted that it is impossible, like the quadrature of the circle. But we could with words distinguish the gyres as being two for the inhabitants of another planet. It would suffice that they have the notion of a horizon, which would also give them that of the plane.

If we flatten out these two circles by themselves, having supposed the notion of a horizon (Figure 9), we can distinguish the two circles from our Figure 8, the direction their respective gyres ( . . .). Thus we have here (Figure 8) two orientations, this one dextrogyre and this one levogyre. But we are incapable of saying which is dextro, which levo. We are incapable of transmitting it in a message. And no manipulation of the three-looped knot gives without ambiguity the definition of levo and dextro. On the other hand, the existence as such of two gyres is quite manifest. For there to be two gyries, two oriented Borromean knots, it therefore suffices that we make one of the three rounds into an infinite straight line, inasmuch as the infinite straight line is defined as non-orientable.

If the rounds are all oriented, either as centrifugal, going toward the exterior, marked e, or centripetal, toward the interior, marked i, we have the following possibilities, extracted quite correctly by Soury and Thomé: 3e/3i/1i, 2e/1e, 2i. Which only makes one oriented knot.

But with a line without an orientation, marked o, we have 1o, 1i, 1e. And this order is differentiated from another: 1o, 1e, 1i.

From the diverse flattenings out of Soury and Thomé it results that the knot remains the same--if I may say so--from all the points of view of the flattening out. But it suffices to take

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one from elsewhere, from the non-point-of-view, to demonstrate that there are two oriented Borromean knots.

Lets us sum up. If the three rounds are oriented, the knot isn't, since orientation implies that there are two orientations. But to the extent that one of these rounds is specified, two distinct orientations appear.

Specifying a round can be simply to color it, to signify that it remains identical to itself, and that it is therefore non-orientable. Coloring a round is thus equivalent to transforming it into a straight line. Which shows you in passing that coloring a round and orienting it can make two.

No doubt it will come to the minds of Thomé and Soury that the flattening out introduces a suspicious element here. Nonetheless, I indicate to them that the same articulations concerning orientation are relevant (valent) if we draw the two circles in the following fashion (Figure 10), which makes no reference to the exteriority of one of these curves in relation to the curve of the other. There is neither an external nor an internal; however, there is thus already a means to demonstrate that there are two oriented three-looped Borromean knots.

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Seminar of April 15, 1975

I imagined this morning on waking two little drawings of nothing at all; you may have seen the trouble I had reproducing them. It is a question (Figures 1 and 2) of two triangles of the most ordinary type, which overlap each other. Those of Figure 1 are knotted as a chain and, based on this fact, are in every respect comparable with two torii, one of which passes through the hole of the other. Those of Figure 2 are not knotted, and can be pulled free of one another. This is like a torus flattened so as to play--not to be knotted but to play--in the hole of the other. The case is the same for the two triangles in Figure 3, except that one of them is folded around what is presented as one of the sides of the other. I say side, because one imagines that a triangle has three sides, which is no longer the case in this geometry that is not one--topology. A topology is what permits us to grasp how elements that are not knotted two by two can nonetheless make a knot. We call a Borromean knot that which is constituted in a fashion such that in subtracting, in breaking one of these elements that I have figured--this is only a figure; this is not a consistency--all the others are equally unknotted from each other. This can be done

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for a number as large as one might enounce (énoncer), and you know that there is no limit to this enunciation. It is in this that it seems to me that the term sexual non-rapport can be supported in a sayable fashion; inasmuch as it is supported essentially by a non-rapport of the couple. Is it that the knot as chain suffices to represent the rapport of a couple? In a time when most of you were not in my seminar, I illustrated with two torii the tie to be made between demand and desire. With two torii, which is to say, with two orientable cycles. I drew (Figure 4) a torus that enters into the hole of another. I figured on each something that turns in a round, and I thus showed that what makes an encircling on this one is traced on the other, in a series of coilings around the central hole. What does that mean?--if not that demand and desire are knotted. They are knotted in the measure that a torus represents a cycle, and therefore is orientable. What makes the difference between the sexes, as you know, is situated at the level of the cell, and especially at the level of the cellular nucleus or in the chromosomes, which, being microscopic, appears to you to insure a definite level of the real. But why the devil want what is microscopic to be more real than what is macroscopic! Something usually differentiates sex. In one case, there is a homozygotism, which is to say, a certain gene that makes a pair with another; and in the other case, there is a heterozygotism. Now, one never knows in advance how this is distributed in each species; I mean, whether it is the male or the female that is homzygote. It is a matter of giving all of its weight to the proverb of which André Gide makes so much in Paludes: Numero deux impare gaudit--which he translates, The number two rejoices in being odd [impair]. As I have said for a long time, he is quite right, for nothing would realize the two if there were no odd, the odd inasmuch as it begins at number three--which is not seen immediately, and renders the Borromean knot necessary. The Borromean knot puts within reach something crucial for our practice: that we have no need for a microscope for there to appear the reason for this first truth, to wit, that love is hainamoration18, and not velle bonum aliculi, as Saint Augustine states (énonce). Bonum is well-being, and no doubt, on occasion, love is preoccupies itself a little, the minimum, with the well-being of the other. But it is clear that it only does so up to a certain limit, of which I have not up to this day found anything better than the Borromean knot to represent it. Let it be understood that it is not a matter of a figure, of a representation--it is a matter of the real. This limit is only conceivable in terms of ex-sistence, which, in its vocabulary, means the play permitted by the Borromean knot to one of the cycles, to one of the consistencies. Starting from this limit, love insists (s' obstine)--because there is something of the real in the affair--love insists on something completely the contrary of the well-being of the other. What I have called hainamoration, with the vocabulary substantified by the writing with which I support it. The notion of a limit implies an oscillation, a yes or no. Here, it is to wish the good of someone, or to wish strictly the contrary. Which might suggest to you the idea of a sinusoid. What is it like, this sinusoid? Like this (Figure 5). The limit is the circle. Is this sinusoid coiled? Does it make a knot in being coiled, or not? This is a question posed by the notion of consistency, more nodal, if I can say so, than that of the line, since the knot is subjacent. There is

18 A portmanteau of haine (hate) and enamoration.

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no consistency that is not supported by the knot. It is in this that the knot imposes the idea itself of the real. The real is characterized by being knotted. Yet this knot has to be made. The notion of the unconscious is supported by this: not only does one find it already made, but one finds oneself made--one is made; one is made by this act x by which the knot is already made. There is no other possible definition for my sense of the unconscious. The unconscious is the real. I measure my terms if I say--it is the real inasmuch as it is holed. I advance a little more than I have the right to, since there is no one but I who says it, who still says it. Soon, everyone will repeat it, and by the force of the rain that will fall on it, it will end up making very pretty fossil. In the meanwhile, it's something new. Up to now, there has been no one but I who said there was no sexual rapport, and this made a hole in a point of being, of the speakingbeing. The speaking being is not widespread, but it is like mold: it has a tendency to spread. Let us then be content to say that the unconscious is the real inasmuch as it is afflicted in the speakingbeing by the only thing that might make a hole, which assures us of the hole: to wit, what I call the symbolic, in incarnating it in the signifier of which, in the final analysis, there is no other definition than the hole. The signifier makes a hole. It is in this that the knot is not a model. What makes a knot is not imaginary, not a representation. Besides, its characteristic--and it is in this that it escapes the imaginary--is that each time I represent one, I cross it out. Since I don't believe myself less imaginative than anyone else, I think that this shows already to what point the knot repulses us as a model. There is no affinity of the body with the knot, even if the holes in the body play a sacred role for analysts. The knot is not a model; it is a support. It is not reality; it is the real. There is a distinction between the real and reality; the knot demonstrates it. To the extent that, fossilization arriving, you might pass your time making knots between your fingers--it is to be wished, besides; this would suggest to you a little more ingenuity. In thus folding back the unconscious over the symbolic, which is to say, over what of the signifier makes a hole, I accomplish something that will be judged by its effect, by its fecundity; but this appears to me imposed by our practice itself, which is far from able to content itself with an obscure reference to instinct, as one insists in translating the word Trieb in English. Instinct had its emergence, which of course is immemorial, but how can we know what it might have meant before Fabre? Fabre only supported it with one thing: how the devil can an insect know, have this knowledge that one establishes in the precision of its gestures? How does it know that it must--in some specific point of the body of some other insect, in some jointure, and in weaving beneath what one calls a carapace--and which is nothing but a figurative mythology--how can it attain to such a precise point in the nervous system, and, there, break something which makes it so the other will be ready to be put in conservation? This knowledge of the insect--how does it explain anything to transport it to the human? In the behavior that we see in the human every day, there is manifestly no instinctual knowledge; he sees no farther than the end of his nose. Certainly, he also, but from another source, finds himself knowing how to make (savior faire) a bunch of devices (machins). Savoir faire is a manner of speaking--saying that he knows how to make love is probably a great exaggeration. This pushes us to this idea I have endeavored to formulate, that the real is not all. Which implies at the same time that science

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perhaps only pulls up little bits of this real. Up to the present, the idea of the universe, it indeed seems, is indispensable to it for what it succeeds in rendering sure. Manifestly, it succeeds in rendering certain things sure when there is number. This is truly the knot in the affair--how is it that language carries a certain number of numbers?--and that one has succeeded in qualifying as real some numbers properly ungraspable, and which are not defined otherwise; to wit, by their not belonging to a series, by their not even being able to, by being fundamentally excluded. Which speaks volumes on the subject of knowing how these numbers--1, 2, 3, 4 --could have even come to mind. Me, I have taken a certain side, pushed by what? I will not say by my experience, because an experience only means one thing: that one is engaged in it, and I don't see why my engagement would be preferable. If I were the only one, all that I could say would have no scope. Which is why I try to situate psychoanalytic discourse; which is to say that I am not the only one to have this experience. Thanks to the fact that I too am a speakingbeing, I am lead to formulate what might account for it. There is someone--an asshole (connard) of the first water--who said that my theory was dead. It is not yet so dead as all that, but it will end up becoming that way with the encrustation of which I have just spoken. In the meanwhile, this guy--who obviously is not on my side--speaks of psychic reality. Me, I find that the psyche makes for incredible difficulties, that it brings with it a world of suppositions, God in any case. Where would the soul be if there were no God, and if God had not explicitly created us to have one? God is ineliminable from any psychology. What I myself try to do is to speak of an operative reality. This is a lot shorter, but it imposes itself. The asshole I just mentioned, who says that my theory is dead, who literally does not know what he is talking about, who does nothing but talk, who blablates--in his analyses, however, that operates, I'm sure of it. It operates with a certain limitation, but I am sure that it functions; if it didn't, he wouldn't continue being an analyst. Yes, even the speech of those who believe in psychic reality operates. What I would like to make you grasp, is that for you the structure of the world consists from your talk (à vous payer de mots). This is even what in the world is more futile--I mean that it flees--than the real, this real that I try to suggest for you in its proper dit-mansion by this dit which is mine; to wit, by my dire. There are some very serious people who occupy themselves with the dreams of animals. To be sure, they cannot know if the animal dreams, but they know that it has all the appearances of it. The animal sleeps and stirs. It is thus manifest that something traverses it. One says that it has images, and since no one doubts that ideas are images--ideas, this is even what that means; language is always a marvelous witness--one tells oneself that it has ideas. Which does not mean that it names them. But, finally, no one knows if a fly, a rat, dreams. One can imagine it, because one is always a little bit rat on some side; above all, one is failed (raté), and the experimenters in question are more so than others; they are ratified, they are the rat-men. These rat-men of science get excited over the idea that the dream is not there, as Freud says, to protect sleep. The annoying thing is that Freud didn't say that. Freud says that for the speakingbeing--not for the rat; he did not experiment with the rat--the dream protects, not the need, but the desire to sleep. This dimension alone adds to the real lantern supposed scientific. One imagines some needs, but Freud, who knows what he says, says that the dream protects

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something that is called a desire. Now, a desire is not conceivable without my Borromean knot. I am trying to show you that my dire is oriented by the fact that only speech (parole) acts. Im Anfang war die Tat, which is says is other, and it believes that it is contradictory with das Wort. But if there is no das Wort before the die Tat, there is no Tat at all. Analysis seizes on the of course very limited point that speech has a Wirklichkeit. It does what it can. It can perhaps not do much, but, finally, this is nonetheless a fact. A fact all the more exemplary for giving us the hope of shedding a little light on what is manifest, that there is no action that does not root itself, I would not even say in speech, but in the oua-oua [bow-wow]. Das Wort is to say oua-oua. Only the unconscious permits us to see how there is a knowledge, not in the real, but supported by the symbolic, conceivable, not at the limit but by the limit, as being made (fait) from a consistency required for the hole, and imposing it based on this fact (de ce fait). The symbolic turns in a circle, but it only consists in the hole that it makes. All that one says of instinct only means this: that one must go to some real, some supposed real, to have a presentiment of the unconscious. In the sense that body means consistency, the unconscious, in a practice, gives body to instinct. Only the unconscious gives body to instinct. Why wouldn't all of this be a vain debate between specialists? It is, however, a dire that could have some consequences, if analysts said something. But outside of a few scraps, it is a fact that they say nothing. Have you yet seen anything readable come out of L'Institute psychanalytique de Paris, for example? You will tell me that there is my school. Precisely, my school, I have had an experience of it in the Journées. I was so happy, like a fish in the water; everyone said things that proved they had read me, and I did not return. And they were even, my faith, capable of putting out some pseudopodia that prolonged my teaching--I mean, that drew a certain number of consequences from it. That ex-sisted fairly (rudement) well in those journées [days]. My discourse is founded on a hole, the only hole that is sure, that constituted by the symbolic. A hole, to the extent that it is consistent, which is to say circled (cerné), suffices for knotting a strictly indefinite number of consistencies. And this begins at two--whereby the two is only supported by the fundamental hole of the knot (. . .). Certainly, the couple is by itself always unknottable, unless it is knotted by the symbolic. In my so-called Rome Discourse, I spoke of full speech, which was not bad, although it was worth what words are worth; to wit, the song of a starling. Full speech supports what makes a knot in the tu es ma femme [you are my wife]. Since I was laying into Lagache and Favez-Boutonnier, I did not say right away Tuer ma femme [To kill my wife]; that would have had a bad effect. Someone asked me recently in the name of what the acceptance committee proceeded to extend its beneficent hand over a number of people in the school. It is simply that--they will not have a bad effect. They will not have a bad effect right away; they will have it later, when they have gotten on a bit, and won a little authority. This couple that is unkottable whatever the full speeches that have founded it, analysis demonstrates that it is knotted in spite of everything. Knotted by what? By the hole, by the interdiction of incest. The Jewish religion emphasizes that. Do you know why they don't get such good press, the Jews? It's because they are not Gentiles. If they were Gentiles, they would not be Jews, and that would settle everything. There are people who have succeeded in making the interdiction of incest emerge in

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myths. The Hindus are even the only ones to have said that one must, if one has slept with one's mother, go off--I no longer know whether it is into the Sunrise (Orient) or into the Sunset (Couchant)--with one's own penis (queue) between one's teeth--after having cut it off, of course. But we do not have to consider the fact of the interdiction of incest as historical: it is, of course. For us, the interdiction of incest is not historical, but structural--why? Because there is the symbolic. This interdiction consists in the hole of the symbolic, so that appears, individualized in the knot, something that I do not call the Oedipus complex--it is not as complicated as all that--but the Name-of-the-Father, which means the father as name--which doesn't mean anything at first--and not only the father as name, but the father as naming. One cannot say that concerning this the Jews are not Gentiles. They have indeed explained what they have called the Father. They cram him (le foutent) in a point of the hole that one cannot even imagine--I am what I am; that's a hole, no? A hole, if you believe my little schema's, swallows up, and there are moments when it spits out again. Spits out what again? The name, the Father as name. That brings with it the interdiction of incest, and this is propagated on the side of castration, as indeed the Greek Gentiles have shown us in a certain number of myths. They raised a geneology founded exclusively on the father, Uranus, and so on, and so forth, up to the moment when Zeus, after having made love a lot, disappears into thin air (s'évanoit devant un souffle). But there is an additional step to take to understand the tie of castration with the interdiction of incest. The tie is what I call my sexual rapport. The Name-of-the-Father means that there can be, in the Borromean knot, an indefinite number of rounds. The vital point (point vif ) is that all repose on one, on one inasmuch as it is a hole, which communicates its consistency to all of the others. The year when I wanted to speak of the Names-of-the-Father, I would have spoken a little more of two or three. What a jumble that would have made for the analysts if they had a whole series of Names-of-the-Father. I am quite content to leave them dry, and to have never again taken up these Names-of-the-Father except in the form of the non-dupes who err. Obviously, they can only err, because the more there are, the more they will be entangled, and I congratulate myself for not having brought forth a single one. This is why I found myself at the end of these Journées having to answer the question of how we know what constitutes a cartel in the School. A cartel, why? I obtained some revealing answers, some pseudopodia, some things that made a very small knot. Why have I posed that a cartel begins with a three, plus one person, which, in principle, makes four; and why have I given as a maximum this five thanks to which that makes six? Is this to say that there is a three that must incarnate the symbolic, the imaginary, and the real? The question could be posed; I could be crazy. But have you never heard identification spoken of? What is it that I wish for? The identification with a group. It is certain that human beings identify with a group. When they don't, they're screwed, they have to be locked up. But I do not say by this at what point of the group they are to be identified. The beginning of any social knot is constituted from the sexual non-rapport as a hole, not two, at least three. Even if you are only three, that always makes four. The plus-one is there as this schema shows, giving the example of what a Borromean knot would make if one began with

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the idea of the cycle as it is made (last seminar, Figure 6) by two knotted rounds. Even if you are only three, that will make four, whence my expression "plus one." And it is in withdrawing one, a real, that the group will be unknotted, which proves that the knot is Borromean, and that it is indeed constituted of three minimal consistencies. Of three consistencies, one never knows which is real. Which is why they have to be four. The four is what (last seminar, Figure 6), by this double-buckle, supports the symbolic by what it is made for, the Name-of-the-Father. Naming (nomination) is the only thing that we can be sure makes a hole. And this is why I give the figure (chiffre) four as the minimum for the cartel, not without considering that one can have a little play in what ex-sists . . . But perhaps we can make clear that, after all, it is not only the symbolic that has the privilege of the Names-of-the-Father. It is not obligatory that naming be conjoined to the hole of the symbolic. I will point this out next year.

To return to Freud, isn't it strange that he only gives (énonce) three identifications? In these three, there is already everything we need to read my Borromean knot. With these three, Freud properly designates consistency as such. Certainly, this is not yet the knot, but do not forget that consistency, in the knot, is throughout, that it is the base.

Three that consist without making a knot are the triskele (Figure 6).The triskele is not a knot. They are only inscribed from consistency. Freud called this

the trait unaire. He could not better say the components (composants) of the knot. And he put it in our heads that there is no love except from what, of the Name-of-the-Father, buckles together the three of the triskele (Figure 7).

Let us note that of this triskele, three rifles that make a stack, the ones supported as a three by the others, the Bretons have made the coat of arms of modern Brittany. This takes us out of the cross; it is already that. While one can say that the cross of Lorraine, if one draws it in the right fashion, also makes a triskele.

It is therefore inasmuch as the triskele ex-sists that there can be identification there. Identification with what? With what is the heart, the center, of the knot, where I have already situated for you the place of the object a. This object dominates what Freud makes the third possibility of identification, that of the hysteric, with the desire the Other.

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Seminar of May 13, 1975

There are no states of the soul. There is a dire to demonstrate. And to promote the title under which this dire will be pursued next year if I survive, I will announce it: 4, 5, 6. This year, I have said RSI. Why not 1, 2, 3? . . . . we will go to the woods. You know what follows: 4, 5, 6, gathering cherries--7, 8, 9, in my new basket.19 I will stop at 4, 5, 6. Why? And why are RSI given as letters? That they are three can be said secondly. It is only because they are three that there is one that is the real. Which of the three merits the title of real? At this level of logic, it little matters. The sense cedes to the number, to the point that it is the number that . . . am I going to say dominates this sense? No--determines it. The number three has to be demonstrated as what it is if it is the real, that is, the impossible. What one wants to demonstrate at the point of saying it (en passe du dire) must be impossible, a required (exigible) condition for the real. It exists as impossible. Still, it must be demonstrated, and not only shown. Demonstrating is a matter for the symbolic. The symbolic is thus a step ahead of the imaginary. But this does not suffice, because it only sets the tone. One must not trust in the tone, but in the number. And this is what I try to put to the test. But is a number knotted still a number? That's where we are. I have retained you throughout the year around a certain number of flashes. I am not there for much, being determined as a subject by the unconscious, or else by my practice. This implies the unconscious as supposed--is this to say that, as wholly supposed it is imaginary? This is the sense itself of the word subject: supposed as imaginary. What is there in the symbolic that is not imagined? There is the hole. Someone who saw me in the grip of the knot said to me that I contradicted myself by having at one time appropriated for my purposes a Picassoian formula: "I do not seek, I find." To seek (Chercher) is a term that derives from circare. I find nonetheless, since I have found the hole (trouvé le trou), a mouse hole through which I am reduced to passing. Does it have something to do with what one imagines to determine it, that is, the circle? A circle can be a hole, but it is not always. It is only the consequence of the hole. While I am there, I will remind you of the Arab proverb which is found already in the last lines of my Propos sur la causalité psychique, and which states that there are three things that leave no mark: the man in the woman, the step of the gazelle on the rock, and, more inaccessible to our eyes made for signs of change, the mark on the touched coin, the mark that is not there--there is only wear. It is here that is sold cut-rate (se solder), it is the case to say, this something knotted in question. I find enough, enough for having to circulate. Hegel poses quite well that all that is political is rooted in the Police. There is nothing political that is not finally, in the final term of reduction, the police pure and simple. Now, the police have only one thing to say: Circulez!

19 A French nursery rhyme, in which 3 (trois) rhymes with bois [woods], 6 (six) rhymes with cerises [cherries], and 9 (neuf) rhymes with and is spelled the same as (neuf) [new]. In Lacan Géomètre (Paris: Anthropos, 1998, p. 203), Alain Cochet gives us the complete rhyme as follows:1,2, 3, nous irons au bois4,5,6, cueiller des cerises7,8,9, dans mon panier neuf10,11,12, elles seront toutes rouges [they will all be red].

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[Move on!]. The gyrie little matters. All of this only becomes serious if one begins with the hole, through which it is necessary

to pass. What is remarkable about the bo knot is that it makes a knot without circling in a fashion that utilizes the hole as such.

There is a difference between the knot and this (Figure 1), which utilizes the hole. This

makes a chain. The knot makes a chain without using the hole (Figure 2). Despite its appearance, in this form here, a form that is pure appearance, we again find the bo knot (Figure 3). In the measure that these two rounds, the two larger ones, are not knotted, the third, smaller one knots them. It first modifies (infléchit) one of them, then, having arrived at the other end, it modifies the other in its turn, and thus turns in a circle. If we suppose it symbolic, let us say that it will indefinitely turn around the false chain of the imaginary and the symbolic, unless this fourth round is interposed. How are we to recognize ourselves in this double circle, and precisely as not being knotted? For a knot to be Borromean, it does not suffice that it be a knot; each of the knotted elements must be freed by the rupture of one among them. Let us remark that one does not give to this expression, "it must and it suffices," its full sense, save in referring to the knot. "It suffices" implies--something that one always forgets because one does not make the hole, the only hole worth anything (le seul trou qui vaille), the discovery (la trouvaille)--that if the condition is lacking, nothing works anymore, which is the

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inverse of "it must" (il faut). This inverse is always eluded; I am going to demonstrate how right away. You knot two circles in a way that leaves them unknotted (Figure 4). If a consistency passes here, whether of a circle or of an infinite straight line, that suffices to make a Borromean knot. If you make another pass here (Figure 5), you have a figure that has the air of being a Borromean knot, but which is not, because it does not suffice to cut one of these consistencies for each of the other three to be freed. For that to happen, things must be disposed otherwise (Figure 6). This has the air of being similar, but here, one whichever of the elements being broken, the others are free. And, to begin with, what do the straight line as infinite and the circle have in common? It is this: the rupture of the circle is equivalent to the rupture of the infinite straight line in its effects on the knot--it frees the other elements of the knot. But these two ruptures do not have the same effects of remainder on the element. In fact, what remains of the circle after its rupture? A finite straight line as such, which is as much as to say something to throw out, a scrap, a bit of a cord of nothing at all. Allow me to figure the circle by this zero, cut by what separates, which is to say the two, that is: 0/2 = 1, this little 1 of nothing at all. On the other hand, the sectioning of the infinite straight line, with a big 1, gives us two half-lines which begin at a point, and go off to infinity: 1/2 = 2. This makes it felt for you how I understand that there is no sexual rapport. I no doubt give to the word rapport the sense of proportion, but the mos geometricum of Euclid, which has appeared for such a long time the paragon of logic, is completely insufficient. Also, in entering into the figure of the knot, there is a wholly other fashion to figure the non-rapport of the sexes--two circles not knotted. Each is in its fashion of turning in a circle as a sex is not knotted to the other. That is what my non-rapport means. It is striking that language has for a long time anticipated the figure of the knot--with which mathematicians have not begun to busy themselves until our day--by calling what unites the man and the woman a knot. These knots imply as necessary the elementary 3 with which I support them: the three indications of sense, of sense materialized, posed in the namings of the symbolic, the imaginary, and the real. I am introducing the word naming (nomination). I have had to respond with it recently apropos of the theory of reference, as logicians understand it. My knot brought me down to earth. The whole question is of knowing if naming again arises, as it seems, from the symbolic. The least one can say is that, for my knot, naming is a fourth element. I have already drawn this figure for you (Figure 7). A fourth circle knots the three at first posed as unknotted. In engaging in this four, one finds a particular path (voie) that only goes to six. What engages you in this path is what the three imposes, not of a distinction, but, quite to the contrary, of an identity between the three terms symbolic, imaginary, and real. This is true (Cela va) to the point that it seems to us necessary (exigible) to find again in each this trinity. I have had to foment to account for it the terms ex-sistence, consistency, and hole. I make of ex-sistence, of what is in play up to a certain limit in the knot, the support of the real. What makes consistency is of the order of the imaginary, since if the rupture involves

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something, it is indeed consistency, to give it its most reduced sense. There remains then--but does it remain?--for the symbolic the affectation of the term hole. Topology gives us a figure of it in the form of the torus. But is this figure suitable, since the torus has two holes, an internal hole with its gyrie, and an external hole, thanks to which the torus is demonstrated to participate in the figure of the cylinder? The cylinder is for us one of the best ways of materializing the straight line to infinity, of which everyone knows its rapport with what I call the round of consistency. Desargues was aware for a long time that the infinite straight line is in every way homologous to the circle, whereby he anticipated Riemann. Nonetheless, a question remains open, to which I give an answer by the attention I bring to the Borromean knot. Let us only consider this drawing (Figure 8). Let us say that this circle is the symbolic, and that the two straight lines figure the real and the imaginary. What is needed for it to make a knot? The point at infinity must be such that the two straight lines do not make a chain, whatever they may be and from wherever one might see them (les voie). I remind you in passing that this from wherever one might see them supports this reality I enounce of the gaze. The gaze is only definable by a from wherever one might see them. If you think of a straight line as making a round from a unique point at infinity, how can you not see that this has the sense that not only are they are not knotted, but that in not being knotted they are effectively knotted at infinity. Desargues, to my knowledge, neglected this question. I made use of Desargues at the time when I gave my seminar on Las Meninas at the Normale Supérieure, focusing on situating this famous gaze that is quite obviously the subject of the painting. I situated it in the same interval that I establish here on the board in another form; that is, what I define by the fact that the infinite straight lines, in their supposed point of infinity, are not knotted in a chain. The question begins for us there. It does not seem that Desargues ever interrogated himself on the point of knowing if the form in which he supposed these infinite straight lines implied that they were knotted or not. Riemann decided the question in a not very satisfying way by making of all the points at infinity, whatever straight line they belong to, a single and unique point.

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If we now study this knot (Figure 9)--which, curiously, presents a sort of analogy with this form (Figure 2)--if we study it as do mathematicians, we will define its structure, beginning with the notion of the fundamental group, by a certain number of trajectories that will be made from any point whichever. But contrary to what one might imagine, it is not the number that is characteristic of the fundamental group, it is the relation between a certain number of trajectories. We support there in its pure state the notion of rapport. And it leads us back to the knot, to the Borromean knot, since this rapport itself makes a knot, except that this knot lacks number. In taking the step (étape) of the Borromean knot, we support by the number itself trajectories of which it is a question in no matter what knot; even when the knot (Figure 9) only has one consistency. We take the number as an intermediary, as an element, to introduce us into the dialectic of the knot. Nothing is less natural than to think this knot. That there is something of the One, which I advanced in its time in supporting it by the circle, is what the movement of thought limits itself to--it makes a circle. Besides, this is why there is nothing more natural than to reproach its circle as vicious. To figure the rapport of the sexes, I have therefore found the figure of two 1's in the form of two circles knotted by a third because they are not knotted by themselves. It is a matter not only, in the bo knot, of the three being freed when the third is broken, but of the third knotting them explicitly because they are not knotted. I would have not made this function pass through your minds if I thought that today I spoke in vain: it is because they are not knotted that they are knotted. I want to conclude with

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this: without the fourth, nothing is, properly speaking, put in evidence of what is truly the Borromean knot. In every Borromean chain, there is a 1, then a 2, after which there is a third that makes a buckle (Figure 10). In any chain whichever--let us limit-ourselves to the chain 1 - 2 - 3 - 4 -- if we put whichever of the first two in the third rung, the 1 will from then on be knotted to the 2 and through the 3 and through the 4.

1 2 3 43

1 2

4Try it, for there is nothing better for thinking this knot than manipulating rounds of thread. It is clear that the 1 and the 2 are interchangeable; that is, at the beginning of a chain, the first and the second are indefinitely interchangeable. Now, if we place one of these two at the level of the 3, we see not only the 3 involved and passing to the place of the 2, but with the 3, the 4. That is how my interest in the four-looped knot is justified, which I will develop next year. With what should we couple the naming that here makes the fourth term? Are we going to couple it with the imaginary, inasmuch as, coming from the symbolic, it makes a certain effect in the imaginary? This is what it would seem to be a question of for the logicians when they speak of the referent. In fact, the Rusellian description, which emerges when one is interrogated on the identification of Walter Scott as author of the Waverly, concerns, it seems, what is individualized from the support thought of bodies. Now, it is in fact nothing like that. The notion of reference aims for the real. It as real that what the logicians imagine as real gives its support to the referent, to the imaginary naming. Between R and S, we have a naming index i, and then the I. This is what constitutes the tie between the real and the symbolic.

Ni R S

II will propose that this imaginary naming is what I am supporting today with the infinite

straight line. This straight line is not what would name anything whatsoever of the imaginary, but what inhibits the management of anything demonstrative. It is a bar, at the level itself of the imagination, to all that is articulated as symbolic. The body only enters into the analytic perspective inasmuch as it makes an orifice, and it is knotted to some symbolic or real. And it is precisely by a circle, an orifice, that the imaginary is constituted. The infinite straight line, which here completes the hole in question--a false hole, since an orifice does not suffice to make a hole--is quite precisely the inhibition that thought has in respect to the knot.

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From then on, we can interrogate in the same way, what, between the real and the imaginary, naming, index of the symbolic, is.

Ns R I

SIn the symbolic emerges something that names--one sees this, one believes, at the

beginning of the Bible. But one does not notice that the creationist idea of the inaugural Fiat lux is not a naming. The emergence of the symbolic from the real--that's what the idea of creation is--has nothing to do with the fact that, in a second time, a name is given to each of the animals who live in Paradise. Of what naming is it a question in what I indicate by Ns? The naming of each of the species, with a common noun, and not, in Russell's sense, a proper noun--what does it represent? An assuredly symbolic naming, but limited to the symbolic. Does that suffice to support the Name-of-the-Father for us? Is the Father he who has given things their names, or must he be interrogated at the level of the real? Must we not knot the term naming at the level of the circle with which we support the real? It is between these three namings, the naming of the imaginary as inhibition, the naming of the real as anxiety, the naming of the symbolic, flower of the symbolic even, as symptom--it is between these three terms that I will try next year to interrogate myself concerning what is suitable to give as substance to the Name-of-the-Father.