🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

I establish, in sum, an entire method… without which one can say that everything in a certain field that remains implicit concerning what defines these fields, namely the presence as such of the subject… well, this method that I establish consists of, makes it possible to ward off, if one may say so, everything that this implication of the subject introduces into this field as fallacy, as falsity at the foundation.

Something one becomes aware of, with a bit of distance, is that this method truly has all that generality; of course, it was not from such a general aim that I started out—indeed, I would even say more—something I myself only noticed in hindsight: that one day it may happen that this method is used to rethink things precisely where they are most interesting, in the political domain for instance—why not?

It is certain that, with sufficient modifications, some of the schemas I provide will find their application there; indeed, it might even be the place where they will be most successful, because in the domain for which I originally forged them, nothing is guaranteed in advance.

Given that perhaps it is there, it is on this terrain—the terrain of the psychoanalyst—that a certain “One” passes… which is precisely the one manifested by what I call—and they are not univocal—the fallacies of the subject… finds the strongest resistance. Nevertheless, it remains that this is where these concepts will have been forged, and one could even go further and say: that the entire contingency of the adventure, namely the very mode of what these concepts will have had to face, that is to say:

— for example, analytic theory as it has already been forged, as they must introduce corrections into it,

— this analytic theory and the very dialectic of what their introduction into analytic theory will have entailed in terms of difficulty, even resistance—even apparently accidental, external resistance—all of this, in some way, contributes to the modes under which I will have tightened them.

I mean that what one can call the resistance of psychoanalysts themselves to what is their own field, may well be what offers the most striking testimony to the difficulties that need to be resolved. I mean: to their very structure.

So here is why, today, we arrive at an even more intense terrain, at the moment when it is a matter of me speaking to you about what I have located at the fourth corner of the quadrangle, which we will designate… I suppose my audience today was present at both of my previous lectures… which we will designate—this quadrangle—as the one that connotes the moment of repetition.

Repetition, I said, to which corresponds as the founding moment of the subject, the passage to the act. I showed you, I insisted—and I will return to it today because it is necessary to return to it—on the importance, in the status of the act, of the sexual act. Without defining it as an act, it is absolutely impossible to locate, to conceive, the function that FREUD gave to sexuality in relation to the structure of what one must call, with him, satisfaction. Subjective satisfaction, Befriedigung, which can only be conceived from the place where the subject is instituted as such. It is the only notion that functions in a way that can give meaning to this Befriedigung.

To give to this sexual act the structural markers without which it is impossible for us to conceive its place in what is at stake, namely Freudian theory, we have been led to activate one of the most exemplary mechanisms of mathematical thought. Certainly, when I use such means, it is well understood that there is always something partial, partial for anyone who will only know of mathematical theory what I myself have used as an instrument.

But of course, the situation may be different for anyone who knows the place of such a mechanism which, with no doubt my own share of inexperience, I extract, believe it nonetheless: — not without knowing what the ramifications are of what I am using within the whole of mathematical theory, — and not without having ensured that anyone wishing to make more in-depth use of it would find—in the entirety of the theory, at the precise points I have chosen to found such a structure—all the extensions that would allow them to give it a proper expansion.

Some echo has come back to me that upon hearing me speak of the sexual act, using to structure its tensions what the ternary nature of the Golden Ratio provided me, someone let slip through their teeth this remark:

“The next time I go fuck, I’d better not forget my slide rule!” [Laughter]

Certainly, this remark has all the amusing character that one attributes to a witticism, yet for me it still must be taken with a grain of salt, from the moment the author of this amusing quip is a psychoanalyst. For in truth, I think quite precisely that the success of jouissance in bed is essentially made up—as you will see, I will dot the i’s—of the forgetting of what could be found on the slide rule. Why?

It is so easy to forget… and I will insist on this once again shortly. It is indeed the very mechanism of what is, in sum, satisfying in what, on the other hand—subjectively—translates as castration. …but it is quite clear that a psychoanalyst cannot forget that it is to the extent that another act concerns him… which we shall call, to introduce its term today: the psychoanalytic act… that some resort to the slide rule may evidently be required.

The slide rule—of course, to avoid any misunderstanding—will not, on this occasion, be used to read on it—we are not there yet!—what can be read at the intersection of two little lines, but for what it carries in itself as a measure, which can only be called the logarithmic one, it indeed provides us with something not entirely unrelated to the structure I am evoking.

The psychoanalytic act has this striking feature—to name it thus in reference to the entire theory—it has this striking feature, which will allow us to make a remark that may have seemed to some on the margins of what I have stated thus far, and which is this: I have insisted on the character of act in what pertains to the sexual act.

One might observe in this regard, that everything stated in analytic theory seems destined to erase… for the benefit of those beings who are, for various reasons, suffering or dissatisfied, and whom we take responsibility for… the character of act that there is in the fact of the sexual encounter.

The entire analytic theory emphasizes the mode of the sexual relation, declared rightly or wrongly… in any case, for various reasons, and on grounds which I have on multiple occasions taken the liberty to raise objections to… to qualify as more or less satisfying this or that form of what is called the sexual relation.

One might wonder whether this is not a way of eluding, or even drowning out what is vivid, sharp in the proper sense… since it concerns something that has the same structure of cut that belongs to any act… what properly pertains to the sexual act.

As it is a cut that, as all our experience overabundantly demonstrates, does not occur by itself, and does not, strictly speaking, yield a result of mere fairness, since all sorts of structural anomalies… perfectly articulated and located, if not fully conceived in their true scope within analytic theory… are its result, it is quite clear that eluding what pertains to the very relief of the act is undoubtedly something linked to what I shall call the temperament, the tempered mode under which the theory advances, with the manifest intent of not dragging along too much scandal.

The worst being, of course, this one—which does not seem, for all that, to be diminished by such prudence—that the sexual act, from then on—whatever our aspiration to the freedom of thought—the sexual act, contrary to what may have been affirmed in this or that context and in the objective examination which pertains to ethics, well, it must be said… whether or not theory acknowledges it, whether or not it emphasizes it, it matters little to us… experience, it seems, overabundantly proves that since times which are not recent, among the many attempts that have been made, more or less inherited from otherwise complex experiences that were those of what is called “the time of the man of pleasure,” what some exaggerated formulas from libertarian circles at the beginning of this century, for instance, have led to—of which a few specimens still lingered, floating, in other environments, on other, more serious terrains—I mean revolutionary terrains, one could still see maintained the formula that, after all, in the end, the sexual act should not be taken to have more importance than that of drinking a glass of water.

This was said, for example, in certain zones, certain groups, certain sectors, in the circles surrounding LENIN. I remember having once read in German a very pretty little volume, called Wege der Liebe [Paths of Love], if I still recall the title correctly… it was, after all, the beginning, before the war, of something that closely resembled the paperback book, and on the cover was the charming little face of Mme KOLLONTAI—it was the first team—and she was, if memory serves me right, ambassador to Stockholm… they were charming tales on this theme.

As time has passed and socialist societies have taken on the structure you are familiar with, it becomes clear that the sexual act has not yet been relegated to the level of something one satisfies at a snack bar. In all honesty, the sexual act still carries with it—and must continue to carry for a long time—that sort of strange effect of I-don’t-know-what… of discordance, of deficit, of something that cannot be resolved and that is called guilt. I do not believe that all the writings by the lofty minds who surround us and who title their works with things like The Morbid Universe of Guilt, for example, as though it had already been exorcised! It was written by one of my friends—I always prefer to cite people I like. [Laughter]

All of this does not at all resolve the question, nor does it mean that we do not indeed still have to deal—probably for a long time to come—with what remains entangled in this universe, around what we may call the failures—yet failures whose status must precisely be considered: these failures may well be essential to them—the failures, I say, or non-failures, of the structure of the sexual act.

Accordingly, I believe I must return, very briefly of course, but still return once more to what is insufficient in the definition that might be given to us from a certain register of pious homily, regarding what is called the genital stage, concerning what would constitute the ideal structure of its object. It is not entirely pointless to refer back to this literature. That, in truth, the dimension of tenderness evoked there should be something certainly respectable, I have no reason to contest—but that it be considered there as a dimension somehow structural: that is something on which I do not think it is pointless to raise an objection.

I mean first of all, that neither is it absolutely…

– What’s happening? [one of the wires of the recording device begins to burn]
– What?

On the topic of this famous “tenderness”… [Laughter] One could reflect on that for a moment. There is one face of tenderness, and perhaps all of tenderness, that one could pin down with some formula fairly close to this one:

“What we find fitting to feel as pity in the face of the impotence to love.”

Structuring that, at the level of the drive as such, is not easy. But likewise, to illustrate what should be articulated concerning what pertains to the act and sexual satisfaction, it might be useful to recall what experience imposes on the psychoanalyst, regarding ambiguity… they call it ambivalence. The word ambivalence has been so overused that it no longer means anything at all! …the ambiguity of love.

Is a sexual act any less a sexual act… is it merely an immature act to be relegated—for us—to the field of an unfinished subject, still stuck in the backwardness of some archaic stage… if this sexual act is committed in hatred, quite simply? The case seems not to interest analytic theory. It’s curious: I have seen this case raised nowhere.

To introduce the consideration of this dimension, I had to, in a seminar already long past—well, from the time when the seminar was a seminar—I had to make use of the well-known play by CLAUDEL, more precisely the trilogy that begins with The Hostage. Are the loves of TURELURE and Sygne DE COÛFONTAINE an immature conjunction or not?

What is admirable is that I believe I have thoroughly highlighted the merits and consequences of this tragic trilogy. I must also say: without anyone, to my knowledge, among my audience, perceiving its implications. That is not surprising, since I did not take care to expressly emphasize this precise question, and generally, from everything I have gathered, listeners tend to avoid this point easily.

There are two kinds: – those who follow Monsieur CLAUDEL in the religious resonance of the plane on which he situates a tragedy that is surely one of the most radically “anti-Christian” ever forged, at least with regard to a respectable and tender-emotion Christianity. – those who follow him in that atmosphere believe that Sygne De Coûfontaine, of course, remains intact throughout. That is not what she herself seems to articulate in the drama. But no matter: one hears through certain filters. Curious thing: the listeners who would seem unlikely to be bothered by that filter—namely the listeners not already religiously inclined—seem just as unwilling to hear anything about what is precisely at issue.

In any case, since we have no other references at our disposal—I mean at hand here, from a lectern—I still leave open the question of whether a sexual act carried out in hatred is any less a fully realized sexual act, shall I say. Raising the question at this level would open onto many paths, which would not be unproductive, but into which I cannot enter today.

Let it suffice for me to point out, in the prevailing theory concerning “the genital stage,” another feature which seems poorly connected to the others commonly employed—namely, the limited, moderate, tempered character, so to speak, that mourning would take on in this context. The sign of genital maturity being that this object realized in the partner… since, after all, we are dealing with a formula that tends to adapt to morals as proper as one could wish… this object, it would be normal and a sign of maturity to be able to mourn it within a timeframe we shall call decent.

There is something here, first of all, that suggests it would fall within the norms of what is called emotional maturity, that it should be the other who goes first! It brings to mind that good joke, which was probably the one […] Freud mentions somewhere. The gentleman—Viennese, of course, it’s a Viennese story…—who says to his wife:

“When one of us dies, I’ll go to Paris.” [Laughter]

Curiously, I notice by this crude path of contrasted opposition that nowhere in the theory is there ever any mention—concerning “the mature subject”—of the mourning that he, himself, will leave behind. That could just as well be a characteristic seriously worth considering, regarding the subject’s status! It’s likely that this would interest the clientele less… So on this point too: total blank!

There are other remarks which this minor incident [the burning wire incident], given the time it has cost us, forces me to shorten. I would simply like to say this: that the emphasis placed, as well as the profusion of developments regarding what is called the “situation” or again the “analytic relationship,”—could this not also serve to allow us to evade the question of what the analytic act actually is?

The analytic act, of course, one might say, is interpretation. But since interpretation is undoubtedly—ever more so in the direction of decline—the very point on which it seems most difficult for theory to articulate anything, we shall for now do nothing more than take note—quite literally—of this deficiency, and we shall observe that… in a manner not without bearing, I must say, some promise… we nonetheless have something quite strict in theory that combines the function of the analyst… I do not say the “analytic relationship,” which I have just precisely pointed to in order to state that, on this occasion, it serves as a screen… that the analytic function, therefore, seems to approach something of the order of the act.

This is not without promise, as we will see. For this reason: if the analytic act is indeed to be specified at this point… of course, for us the most vivid and interesting to determine: the bottom-left point of the quadrangle that concerns us, at the level where it is a matter of the unconscious and the symptom… the analytic act has, I would say in a fairly complete manner, the structure of repression, a kind of “alongside” positioning.

A representative—if I may express it thus—of its deficient representation is given to us precisely under the name of acting out, which is, in this schema, what I must introduce today.

All those here who are analysts have at least a vague notion of this term. Its axis, its center, is given by this: that certain acts… having a structure on which not everyone necessarily agrees, but on which one can nonetheless recognize something… are liable to occur within analysis and in a certain relation of more or less dependency, with respect not to the analytic situation or relationship, but to a specific moment in the analyst’s intervention: something, then, which must bear some connection with what I consider as not defined at all—namely, the psychoanalytic act.

In such a difficult field, we are not to proceed like a rhinoceros in a china shop! We must proceed gently: to hold with acting out something—something upon which it seems possible to draw the attention of those with experience in analysis, in a way that promises agreement.

It is known that there is such a thing as acting out, that it is related to the intervention of the analyst. I indicated the page of my Écrits… it is in my dialogue with Jean HIPPOLYTE, concerning the Verneinung… where I highlighted a very fine example, an excellent testimony, which can be relied upon, as it is truly an “innocent” testimony, quite literally—it is the case of Ernst KRIS, in the article he wrote entitled Ego Psychology and Interpretation in Psychoanalytic Therapy, Psychoanalytic Quarterly, volume XX, no. 1, January 1951, pp. 15-30.

I have spelled it out at length and in detail, in that text of mine which is easy to find. I even mentioned the page, in one of those recent seminars, and it’s in my dialogue with Jean HIPPOLYTE, the one that follows Function and Field of Speech and Language, in other words, the Rome Discourse. I highlighted there what it implies, for KRIS, to have—in accordance with a methodological principle promoted by ego psychology—intervened in the field he calls “the surface,” and which we, for our part, will call the field of a reality appraisal.

This “reality appraisal” plays a role in analytic interventions. In any case, in the analyst’s frame of reference, it plays a considerable role!

It is not among the least of theoretical distortions, for instance, to claim that it is possible to interpret what are called transference manifestations by making the subject feel how the repetitions, which would constitute their essence, are improper, misplaced, inadequate, in light of—what has been written, printed in black and white!—this field of the analytic situation: the confinement in the analyst’s office, considered as constituting—this has been written—a reality so simple! Saying: “Can’t you see how out of place it is that such and such things repeat themselves here, in this field where we meet three times a week?”… as if the fact of meeting three times a week were such a simple reality! …certainly raises questions about the definition we are to give of what reality is in analysis.

Be that as it may, it is no doubt from a similar perspective that Mr. KRIS positions himself when, dealing with someone who—in his eyes, KRIS’s—pins himself down by accusing himself of plagiarism, having come upon a document that—in his eyes, KRIS’s—manifestly proves that the subject is not really a plagiarist, he deems it appropriate, as a “surface” intervention, to state that indeed, he, KRIS, assures him that he is not a plagiarist, since the volume in which he—the subject—believed to find the proof, KRIS went and located it, and found nothing in it particularly original from which the subject—his patient—could have profited.

I urge you to refer to my text, as well as to KRIS’s text, and also—if you can manage to get your hands on it—to the text by Melitta SCHMIDEBERG, who had the subject during an earlier period or phase of analysis. There you will see what is absolutely exorbitant in this passage via this intermediary, in tackling a case where, quite evidently, nothing is clearly stated: what is essential is not whether the subject is actually a plagiarist or not, but that his entire desire is to plagiarize, for the simple reason that it seems impossible for him to formulate anything of value, unless he has borrowed it from another. That is the essential drive. I can state it this firmly because that is what the drive is.

In any case, after this intervention, it is KRIS himself who informs us that after a short moment of silence from the subject—who, for KRIS, is absorbing the blow—he simply states this little fact: that for quite a while now, every time he leaves KRIS’s office, he goes and eats a nice little dish of fresh brain. [Laughter]

What is this? I don’t have to explain it, since already at the very beginning of my teaching, I highlighted the fact that this is an acting out. In what way… in what way that was not absolutely articulable at the time as I can do now… in what way, if not in this: that the object petit (a), oral, is there in a certain sense made present, served on a platter—quite literally—by the patient, in connection, in relation, with that intervention.

And then what? Afterwards? Of course, this is of interest to us now… although of course it always holds an ongoing interest for all analysts… this is of interest now only if it allows us to advance a bit in the structure.

So, this is called acting out. What are we going to do with this term?

First, I don’t think we will stop at this: falling into the trap of using what is called “Franglais.” For me, the use of “Franglais,” I must say—no matter what fondness I may have for the French language—does not bother me in the slightest. I really don’t see why we shouldn’t allow our use of the language to include occasional employment of words that don’t originally belong to it? It leaves me entirely indifferent! All the more so because I absolutely cannot find a way to translate it, and it is a term, in English, of extraordinary pertinence.

I point this out in passing, for the reason that in my view it is, in a certain way, if one may say so, a confirmation of something. Namely, that if the authors… and I’m not going to give you the history of the authors who introduced it, because time is pressing… if the authors made use of “acting out,” of the English term acting out, well, they knew very well what they meant, and I’m going to provide you the proof.

Not by using what I might have believed I could find in an excellent fundamental philological dictionary that I, of course, have at home in thirteen volumes: the New English Oxford Dictionary: not a trace of act out. But it was enough for me to open Webster’s… which is also an admirable instrument—though only in a single volume—and which is published in America… to find under to act out, the following definition, which I hope to find again… Here it is! To… I apologize for my… for my English… for my articulation, my inadequate “spelling” in English… to represent (in parentheses: as a play, story, and so on) in action—thus: to represent like a play on stage, a story in action, as opposed—as opposed to reading. For example: to act out a scene one has read. So, act out—I’m not saying: to play, since it’s act out, isn’t it, it’s not play—a scene one has read. So there are two stages.

You have read something: you read RACINE, but you read it badly, of course—I mean: you read it aloud in a dreadful way—someone who is there wants to show you what it is: he performs it. That is what to act out is.

I suppose the people who chose this term in English literature to designate acting out knew what they meant. In any case, it fits perfectly. I act out something because it was read to me, translated, articulated, signified insufficiently, or “off the mark.”

I would add that if you ever find yourself in the situation I just imagined, namely that someone wants to give you a better presentation of RACINE, it’s not a great starting point; it will probably be just as bad as your way of reading. In any case, it will already begin from a certain imbalance: there is already something off-center, even muted, in the acting out introduced by such a sequence. That is the remark around which I intend to approach what I am only putting into question today.

To speak of the logic of the fantasy, it is indispensable to have at least some idea of where the psychoanalytic act is situated. This will compel us to take a small step back. Indeed, one can observe—it goes without saying, but even better to say it—that the psychoanalytic act is not a sexual act.

It is not at all possible to make them interfere. It is quite the opposite. But to say “the opposite” does not mean the contradictory, since we are doing logic! And to make this felt, I only need to evoke “the analytic couch.” It still has something to do with it! In the topological order, there is something I noticed—but it really is a problem—that myths hardly ever speak of, and yet “the bed” is something that concerns the sexual act.

The bed is not simply what ARISTOTLE talks to us about—for, I remind you, to designate in this context the difference between phusis (ϕύσις) and technè (τέχνη). And to present to us a wooden bed as though, at any moment, it might start to bud again! I searched thoroughly, and in ARISTOTLE there is no trace of the bed being considered as… I don’t know… what I would call, in my own language—and which is not very far from ARISTOTLE’s—the place of the Other!

He had a certain sense of topos (τόπος), he too, when it came to the order of nature. It’s quite curious—having spoken… in Book Eta, if memory serves, of the Metaphysics, but I won’t swear to it… of that bed so properly, he never considers it as topos (τόπος) of the sexual act.

We say “child of a first bed.” That too should be taken literally. Words are not said or joined together by chance. Under certain conditions, the fact of entering the space of the bed can perhaps qualify an act as having a certain relation to the sexual act, as in: “faire les ruelles” of the Précieuses.

So “the analytic bed” signifies something: a space not without a certain relation to the sexual act, a relation that is, strictly speaking, one of opposition—namely, that nothing of the sort can take place there. It nonetheless remains a bed and thereby introduces the sexual under the form of an empty field or an empty set, as is said somewhere.

And so, if you refer to my little structural diagram, since it is there that we already placed it—the sexual Other—it is also there that the analytic act, in no case, has anything to do.

It stops there, at that point [Lacan points to the A on the right]: both the little (a), and their relation… I mean the Other (capital A), from which, after all, I would sometimes like to elide the heavy connotations. But still, for those who are deaf, who have never heard me before, this concerns the field of the Other, inasmuch—not so much as it redoubles—but as it splits in such a way that precisely within it—within its interior—there is a question of an Other as the field of the sexual act.

And since this Other here, which clearly cannot go without, and which is this field of the Other (of alienation), this field of the Other that introduces to us the Other of the A, which is also the field of the Other where truth presents itself to us, but in this broken, fragmented, partial manner, which properly constitutes it as an intrusion into knowledge.

Before even daring to raise the questions concerning this: “where is the psychoanalyst?”, we must recall what is at stake regarding the status of what is designated here: the segment little (a). You have, I think, already sensed that it is quite clear there is a relation between this (a) here [in yellow] and that capital A there [in green], that they even have the same function in relation to two different things.

The little (a)… a closed form, a form given at the outset of the analytic experience, under which the subject presents himself, a production of his history, and we can even say more: waste product of that history, a form that is the one I designate by the name of object (a)… has the same relation to the A of the sexual Other as this A of truth, of the field of intrusion of that something which limps, which falters in the subject, under the name of symptom—the same relation that this field little (a) has, with what? With the whole!

Any cut made in this field… and that does not mean that the analyst who proceeds with it is to be identified with this field of the Other… as one might, of course, be tempted to do: the crude analogies between the analyst and the father, for instance, since it could also be there that operates this measure destined to determine all the relations of the whole and notably those of the little (a) with the field of the sexual A. Let us not rush, I beg you, into such hastily drawn formulas, all the more so as they are false.

…this does not prevent the fact that there is the closest relationship between the field of the capital A of the truthful intervention and the way the subject comes to presentify the little (a), if only… as you just saw, in appearance, in the example borrowed from Ernst KRIS… as a form of protest to a premature cut.

There is only one unfortunate thing: namely that this is precisely not where KRIS’s intervention took place; it took place in this field here:

insofar as in analysis—I say: in analysis, all the more so as it is a desexualized field. I mean that in subjective economy, it is on the desexualization of the field proper to the sexual act that the economy, and thus the reverberations that other sectors of the field will have upon one another, depend.

That is why this is worth… before I go further—which will only happen after the Easter holidays, because the next of our sessions, which will be the last before, I will reserve for someone who asked me to respond to what I have put forward, at least since the beginning of January, concerning this topology, the one that includes both the four terms of alienation and those of repetition… it is worth, in these conditions, lingering over what this field consists in, inasmuch as, in analysis, it is there that the place of the sexual act is reserved.

I return to the foundation of the satisfaction of the sexual act, insofar as it is also what gives the status of sublimation. I return to it so as, for this year, not to have to push further what I have introduced on this point.

What about the satisfaction of the sexual act? It falls under this, which we know from analytic experience: that there is, not from one partner to another, but from any of the partners to the idea of the couple as “One”:

– this lack, which we can define in different ways: lack of being, lack in the jouissance of the Other
– this lack, this non-coincidence of the subject as product, inasmuch as he advances into this field of the sexual act, for at that moment he is nothing other than a product.

He has no need to be, nor to think, nor to have his slide rule… He enters into this field and believes himself equal to the role he has to play in it. This applies whether he is man or woman. In both cases, the phallic lack, whether it is called castration in one case, or Penisneid in the other, is that which symbolizes the essential lack. That is what is at stake.

And why is it the penis that ends up symbolizing it? Precisely because it is that which… in the form of detumescence, materializes this flaw, this lack in jouissance… materializes the lack that derives from, or more exactly that appears to derive from, the law of pleasure.

Indeed, it is to the extent that pleasure has a limit, that too much pleasure is displeasure, that it stops there and that it seems as if nothing is missing. Well, that is a miscalculation! Exactly the same kind we would make… and I can slip this past you like one slips nutmeg into a dish: I assure you that if I go through a certain number of little equations involving this a, this 1 + a, this 1 – a which is equal to a² and everything that follows from that, I could pass off as nothing the transformation of this 2 + a that you see here in the form of this a there and those others which are each worth 1…

… I could of course transform it into a 2a + 1, without you even seeing the trick [Laughter]. I don’t have the time today—if you want me to do it next time, when we have a small debate together, it will be easy to do, and actually very amusing. There is nothing more entertaining than this very lovely function called the Golden Ratio.

The 1 – a that is here and which can easily be shown to be equal to a², that is what is satisfying about the sexual act, namely that in the sexual act, one does not notice what is lacking. That is the entire difference with sublimation. Not that in sublimation one always knows it, but that one obtains it as such in the end—if indeed there is an end to sublimation—that is what I will try to materialize for you by means of what is involved in this relation called “mean and extreme ratio.”

What happens in sublimation? Far from the lack that is here under the function of (a), in relation to this little (a) which has just been placed here on the 1, in the way you saw above. The interest of this relation, as I told you last time, is the capacity to proceed by successive reduction, which unfolds as follows: you fold down here the a² and obtain, concerning what remains—namely the a here—another subtraction of a, that is a – a², which turns out—it’s easy to demonstrate, just as a² was equal to 1 – a—to be equal to a³, which is placed here.

So here is what you obtain, by always taking the remainder, and not, of course, what you have already reproduced from a².

If you fold down a³ in the same way, you obtain here a sector which has the value a⁴. Then you fold it again and you have here a⁵. You therefore have all the even powers on one side, all the odd powers on the other. It is easy to see that they will, so to speak, meet each other halfway, until they total into 1, but that the point where the cut occurs between the odd powers and the even powers is easy to calculate: this point is precisely one that can be determined by the fact that it is equal to the a² that appeared here at the start. You only need to play a little with these proportions on a blank sheet for you to be able to verify it yourselves.

What does this give as a structure for the sublimatory function? First of all, that unlike the simple and pure sexual act, it starts from the lack and it is with the help of this lack that it constructs what is its work, which is always the reproduction of this lack. Whatever it may be, in whatever form it is taken, the work of sublimation is by no means necessarily a work of art. It can be many other things still, including what I am doing here with you, which has nothing to do with a work of art.

This reproduction of lack, which goes so far as to tighten around the point where its final cut strictly equals the initial lack a², that is what is at stake in any completed work of sublimation. This, of course, implies a repetition within the act: it is only by reworking the lack in an infinitely repeated way that the limit is reached that gives the entire work its measure.

Of course, for this to function, the measure must be correct from the start. Because observe something: that with the measure little (a), which we have given as being a particularly harmonic measure, you have the following formula: 1 + a + a² + … etc. (to infinity in terms of the invoked powers) is equal to: 1 + 1 / 1 – a

This is not only true for a of the correct measure, the one of the Golden Ratio: a, insofar as it serves us as an image, of the subject’s measure in relation to sex in an ideal case—this functions for any x, of any value, on the sole condition that this x lies between 0 and 1. That is, that it also involves, in relation to the 1, some flaw or some lack. But of course, the manipulation will not be as easy when it comes to the repetitive function of sublimation.

It is indeed the question of what is at stake, from the outset, with this “a” that concerns us: the “a” is not related, in the subject, solely to the sexual function—it is even anterior to it; it is purely and simply linked to repetition itself. The relation of (a) to the barred S [S], insofar as the S strives to be precisely situated with respect to sexual satisfaction, is what is properly called the fantasy, and this is what, this year, we desire to deal with.

But before seeing how we access it—namely, in the analytic act—it was necessary that I articulate for you in a way that, certainly, may seem far removed from the facts—it is not, you will see, nearly as much as you might believe—by joking about whether or not you have your slide rule in your pocket…

You will see, on the contrary, that it is by introducing these novelties into the structural order that many of the confusions, collapses, and entanglements of theory can be clarified in a way that finds its validation in the order of effectiveness.