🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

The teaching to which I am leading you is governed by the paths of our experience. It may seem excessive, if not troublesome, that these paths give rise in my teaching to a form of detours, let us say unusual ones, which, on that account, may appear, properly speaking, exorbitant. I spare you them as much as I can. I mean that, by means of examples tied as tightly as possible to our experience, I sketch a kind of reduction, if one may say so, of these necessary paths.

You nevertheless must not be surprised that there are implicated in our explanation fields, domains, such as, for example this year, topology, if in fact the paths we have to traverse are those which, calling into question an order as fundamental as the most radical constitution of the subject as such, thereby concern everything one could call a kind of ‘revision of science’.

For example, this radical supposition that is ours, which places the subject in its constitution in dependence, in a secondary position with respect to the signifier, which makes of the subject as such an effect of the signifier: this cannot fail to rebound from our experience, however incarnated it may be, into the domains of thought that are in appearance the most abstract.

And I believe I am forcing nothing in saying that what we elaborate here could be of the highest interest to the mathematician. For example—as was recently observed on looking at it, I believe, fairly closely—in a theory which, for the mathematician, at least for a time, posed a major problem: a theory like that of the transfinite, whose impasses are certainly greatly illuminated by our bringing out the function of the unary trait, insofar as what grounds this theory of the transfinite is a return, a grasping of the origin of counting before number, I mean of that which precedes all counting and comprehends it, and supports it, namely one-to-one correspondence, ‘trait for trait’.

Of course, those detours can be for me a way of confirming the breadth, the infinity, and the fecundity of what it is absolutely necessary for us to construct, for our part, from our experience. I spare you them.

If it is true that things are thus, that analytic experience is the one that leads us through the incarnated effects of what is—of course from always, but the fact that we notice it only now is the new thing—the incarnated effects of this fact of the primacy of the signifier over the subject, it cannot be that every kind of attempt to reduce the dimensions of our experience to the already constituted point of view of what is called ‘psychological science’…
in the sense that no one can deny, cannot fail to recognize, that it was constituted on premises that neglected—and for good reason, because it was elided—this fundamental articulation on which we are placing the emphasis, this year only in a manner even more explicit, tighter, more knotted
…it cannot be, I say, that every reduction to the point of view of ‘psychological science’ as it has already been constituted, while preserving as hypothesis a certain number of points of opacity, of elided points, of major points of unreality, does not necessarily lead to formulations that are objectively lying, I do not say misleading, I say ‘lying’, falsified, which determine something that always manifests itself in the communication of what one may call ‘an incarnated lie’.

The signifier determines the subject, I tell you, insofar as necessarily: that is what psychoanalytic experience means. But let us follow the consequences of these necessary premises. The signifier determines the subject, the subject takes from it a structure: it is the one I have tried to demonstrate to you, to show you, in the support of the graph.

This year, concerning identification, that is to say concerning that something which focuses our experience on the very structure of the subject, I am trying to make you follow more intimately this link from the signifier to subjective structure. What I am bringing you to under these topological formulas, of which you have already sensed that they are not purely and simply that intuitive reference to which the practice of geometry has accustomed us, is to consider that these surfaces are structures, and I had to tell you that they are all structurally present in each of their points, if indeed we are to use this word ‘point’ without reserving what I am going to bring to it today.

By my preceding statements, I have brought you to this, that it is now a matter of setting up in its unity: that the signifier is cut, and this subject and its structure, it is a matter of making it depend on that. This is possible in this, that I ask you to admit and to follow me for at least a time, that the subject has the structure of a surface, at least topologically defined.

It is therefore a matter of grasping—and this is not difficult—how the cut engenders the surface. That is what I began to exemplify for you the day when, sending you, like so many little shuttlecocks for I know not what game, my Möbius surfaces, I also showed you that these surfaces, if you cut them in a certain way, become other surfaces, I mean topologically defined and materially graspable as changed, since they are no longer Möbius surfaces, solely by virtue of this median cut that you carried out, but a band a little twisted on itself but very much a band, what one calls a band, such as this belt that I have here around my waist. This was to give you the idea of the possibility of the conception of this engendering, in some way inverted with respect to a first obviousness.

It is the surface, you will think, that allows the cut, and I tell you: it is the cut that we can conceive, if we take the topological perspective, as engendering the surface. And this is very important, for in the end it is there perhaps that we are going to be able to grasp the point of entry, of insertion, of the signifier into the real, to observe in human praxis that it is because the real presents to us, if I may say so, natural surfaces that the signifier can enter there.

Of course, one can amuse oneself by making this genesis with ‘concrete’ actions, as they are called, in order to recall that man cuts, and God knows that our experience is indeed one in which the importance of this possibility of cutting with a pair of scissors has been brought out. One of the fundamental images of the first analytic metaphors—the two little thumbs that jump under the snapping of scissors—is, of course, there to incite us not to neglect what there is of the concrete, of the practical: the fact that man is an animal that extends himself with instruments, and the pair of scissors in the foreground.

One could amuse oneself by remaking a natural history: what results from it for the few animals that have the pair of scissors in the natural state? That is not where I am leading you, and for good reason: what the formula ‘man cuts’ leads us to is much rather its semantic echoes: that he cuts himself off, as they say, that he tries to cut out of it [to get away with it / slip out of it]. All that is otherwise to be gathered around the fundamental formula of castration: ‘we’ll cut it off for you!’

An effect of the signifier, the cut was first for us, in the phonematic analysis of language, that temporal line, more precisely the successive line of signifiers that I have until now accustomed you to calling the signifying chain. But what is going to happen if now I incite you to consider the line itself as original cut?

These interruptions, these individualizations, these segments of the line which were called, if you wish, on occasion ‘phonemes’, which therefore presupposed being separated from the one that precedes and the one that follows, making a chain at least punctually interrupted, that ‘geometry of the sensible world’ to which, last time, I incited you to refer with the reading of Jean NICOD and the work thus entitled, you will see in a central chapter the importance that this analysis of the line has insofar as it can be—I may say—defined by its intrinsic properties, and what ease would have been given to it by the radical placing in the foreground of the function of the cut, for the theoretical elaboration that he must scaffold with the greatest difficulty and with contradictions that are nothing other than the neglect of this radical function, if the line itself is cut, each of its elements will therefore be section of cut.

And that is, in sum, what introduces this lively element, if I may say so, of the signifier that I called the inner eight:

namely precisely the loop:

The line recuts itself. What is the interest of this remark? The cut brought to bear on the real manifests there—in the real—what is its characteristic and its function, and what it introduces into our dialectic—contrary to the use made of it—that the real is the diverse—the real, I have from the beginning made use of this original function to tell you that the real is what introduces the same, or more exactly: ‘The real is what always returns to the same place’.

What does that mean, if not that the cut-section, in other words the signifier, being what we have said: always different from itself—A is not identical to A—there is no way to make the same appear except on the side of the real. In other words the cut, if I may express myself thus: at the level of a pure subject of cut, the cut can only know that it has closed, that it passes back through itself, because the real, insofar as distinct from the signifier, is the same. In other words: only the real closes it. A closed curve is the real revealed, but as you see, most radically: the cut has to recut itself, if nothing already interrupts it. Immediately after the trait, the signifier takes this form:

which is, properly speaking, the cut. The cut is a trait that recuts itself. It is only afterwards that it closes:

on the basis that—in cutting itself—it has encountered the real, which alone allows one to connote as the same, respectively, what is found under the first, then the second loop.

There we find the knot that gives us a recourse at the point of what constituted the uncertainty, the wavering of the whole identificatory construction—you will grasp it very well in the articulation of Jean NICOD—it consists in this: must one wait for the same in order for the signifier to consist, as one has always believed, without stopping sufficiently at the fundamental fact that the signifier, to engender the difference of what it signifies originally, namely: ‘The time’, that time there which, I assure you, cannot be repeated, but which always obliges the subject to find it again, that time there therefore requires, to complete its signifying form, that at least once the signifier be repeated, and this repetition is nothing other than the most radical form of the experience of demand. What the signifier is—incarnated—is all the times that demand repeats itself.

And if precisely demand did not repeat itself in vain, there would be no signifier, because no demand. If what demand encloses in its loop, you had it: no need for demand. No need for demand if need is satisfied. A humorist once cried out:

‘Long live Poland, Gentlemen, because if there were no Poland, there would be no Poles!’

Demand is the Poland of the signifier.

That is why I would be rather inclined today, parodying this accident of the theory of abstract spaces whereby one of these spaces—and there are now more and more of them, which I do not believe I am obliged to interest you in—is called ‘Polish space’, let us today call the signifier a Polish signifier…
that will spare you from calling it the lacs [lacings/loops; also punningly close to Lac-], which would seem to me a dangerous encouragement to the use that one of my fervent followers recently thought he ought to make of the term lacanism! I hope that at least as long as I live, this term, manifestly appetizing, after my second death, will be spared me!
…thus what my Polish signifier is destined to illustrate is the relation of the signifier to itself, that is to say to lead us to the relation of the signifier to the subject, insofar as the subject can be conceived as its effect.

I have already remarked that apparently: ‘there is no signifier except every surface on which it is inscribed being presupposed’.
But this fact is in some way imaged by the whole system of the Fine Arts which illuminates something that introduces you to interrogating architecture, for example under this bias that makes appear to you why it is irreducibly trompe-l’œil [cf. lure], perspective.

And it is not for nothing that I also placed the emphasis, in a year whose concerns seem to me very far from properly aesthetic concerns, on anamorphosis, that is to say—for those who were not there before—the use of the vanishing of a surface to make an image appear, which certainly, when spread out, is unrecognizable, but which, from a certain point of view, gathers itself and imposes itself.

This singular ambiguity of an art as to what appears of its nature, of being able to be attached to solids and volumes, to I know not what completeness, which in fact always reveals itself as subject to the play of planes and surfaces, is something as important, as interesting, as also seeing what is absent from it.

Namely all sorts of things that the concrete use of extension offers us, for example knots, quite concretely imaginable to realize in an architecture of underground passages, as perhaps the evolution of times will let us know. But it is clear that no architecture has ever thought of composing itself around an arrangement of elements, rooms and communications, even corridors, as something that, within itself, would make knots.

And why not, however? It is precisely why our remark: ‘that there is no signifier except a surface being presupposed for it’ is reversed in our synthesis which goes to seek its most radical knot in this: that the cut—in fact—commands, engenders the surface, that it is what gives it, with its varieties, its constituting reason.

It is indeed thus that we can grasp, homologate this first relation of demand to the constitution of the subject insofar as these repetitions, these returns in the form of the torus, these loops that renew themselves by making what, for us, in the imagined space of the torus, presents itself as its contour, this return to its origin allows us to structure, to exemplify in a major way a certain type of relations of the signifier to the subject that allows us to situate in its opposition the function D of demand and that of (a), the object of desire: (a), the object of desire D, the scansion of demand.

You may have noticed that in the graph, you have the following symbols:
– s(A), A, on the upper level: S(A), S◊D [barred S cut of D],
– on the two intermediate levels: i(a), m, and on the other side: S◊a the fantasy, and d.

Nowhere do you see D and (a) conjoined. What does that translate? What does that reflect? What does that support?
It supports first of all this, that what you find instead is S◊D, and that these elements of the signifying treasury at the level of enunciation, I teach you to recognize them, this is what is called the Trieb, the drive.

Thus I formalize it for you: the first modification of the real into subject under the effect of demand is the drive. And if, in the drive, there were not already this effect of demand, this effect of signifier, the latter could not be articulated in a schema so manifestly grammatical. I am expressly alluding to the fact that here I suppose everyone to be well versed in my earlier analyses; as for the others, I refer them to the article Trieb und Triebschicksale, which here is translated bizarrely as ‘avatars’ of the drives, no doubt by a kind of confused reference to the effects that the reading of such a text produces on the initial obtuseness of psychological reference.

The application of the signifier that we call today, to amuse ourselves, ‘the Polish signifier’, to the surface of the torus, you see it here:

it is the simplest form of what can occur in a way infinitely enriched by a series of wound contours—the coil properly speaking, that of the dynamo—insofar as in the course of this repetition the turn is made around the central hole. But in the form in which you see it drawn here, simpler, this turn is also made—I stress it, this cut is the simple cut—in such a way that it does not recut itself.

To picture things, in real space, the one you can visualize: you see it up to here, on this surface presented to you, this face of the torus toward you, it then disappears on the other face, which is why it is dotted, to come back on this side. Such a cut grasps, if I may say so, absolutely nothing.

Carry it out on an inner tube, and in the end you will see the inner tube opened in a certain way, transformed into a surface twice twisted on itself, but not cut in two at all.

It renders, if I may say so, graspable—in a signifying and pre-conceptual way, but one that is not without characterizing a kind of grasp in its own fashion—this radical thing: of the flight, if one may say so, the absence of any access to grasping at the place of its object, at the level of demand.

For if we have defined demand in this, that it repeats itself and that it repeats itself only as a function of the inner void that it circumscribes…
this void that supports and constitutes it, this void which entails, I point out to you in passing, no sort of ethical play, nor pleasantly pessimistic, as if there were a worse beyond the ordinary of the subject, it is simply a necessity of elementary logic, if I may say so
…every graspable satisfaction—whether one situates it on the side of the subject or on the side of the object—is lacking to demand.

Simply, for demand to be demand—that is to say, for it to repeat itself as signifier—it must be disappointed. If it were not, there would be no support for demand. But this void is different from what is at issue concerning (a), the object of desire. The advent constituted by the repetition of demand, the metonymic advent, what slides and is evoked by the very sliding of the repetition of demand, (a) the object of desire, can in no way be evoked in this void circumscribed here by the loop of demand. It is to be situated in this hole that we shall call ‘the fundamental nothing’ in order to distinguish it from the void of demand, the nothing in which is called to advent: the object of desire.

What is at issue for us to formalize with the elements I bring you is what makes it possible to situate in fantasy the relation of the subject as S, of the subject informed by demand, with this (a), whereas at this level of signifying structure…
that I demonstrate to you in the torus, insofar as the cut creates it in this form…this relation is an opposite relation: the void that supports demand is not the nothing of the object that it circumscribes as object of desire; it is this that this reference to the torus is destined to illustrate for you.

If that were all you could draw from it, it would be quite an effort for a short result, but as you are going to see, there are many other things to draw from it. Indeed, to go quickly and without, of course, making you cross the different steps of topological deduction that show you the internal necessity commanding the construction that I am now going to give you, I am going to show you that the torus allows something which, certainly, you will be able to see, the cross-cap, for its part, does not allow. I think that those least inclined to imagination see, through the topological windings, what is at issue at least metaphorically:

The term ‘chain’, which implies concatenation, has already entered language sufficiently for us not to dwell on it. The torus, by virtue of its topological structure, implies what we may call a complementary, another torus that can come to concatenate with it.

Let us suppose them as entirely in conformity with what I ask you to conceptualize in the use of these surfaces, namely that they are not metric, that they are not rigid, that they are rubber. If you take one of those rings used in the game of that name, you will be able to observe that if you grasp it in a firm and fixed way by its circumference, and you make turn upon itself the body of what has remained free.

You will obtain very easily, and in the same way as if you used a curved rod, twisting it thus on itself, you will bring it back to its first position without the torsion being, so to speak, inscribed in its substance. Simply, it will have returned to its original point. You can imagine that by a torsion which would therefore be this one: of one of these tori on the other, we proceed to what one may call a tracing of whatever would already be inscribed on the first, which we shall call the 1.

And let us posit that what is at issue is—what I ask you to refer simply to the first torus—this curve insofar as not only does it encompass the thickness of the torus, and not only does it encompass the space of the hole but also traverses it, which is the condition that can allow it to encompass both at once, void and nothing:
and what is here in the thickness of the torus, and what is here at the center of the knot.

It can be demonstrated—but I spare you the demonstration, which would be long and would require effort from you—that by proceeding thus, what will come onto the second torus will be a curve superposable on the first if one superposes the two tori.
What does that mean? First that they might not be superposable. Here are two curves:

They look as though they are made in the same way, yet they are irreducibly non-superposable. That implies that the torus, despite its symmetrical appearance, includes possibilities of bringing to light, by the cut, one of those torsion effects that allow what I shall call radical dissymmetry, that whose presence in nature you know is a problem for every formalization, that which makes it so that snails have in principle a direction of rotation such that those that have the contrary direction are a very great exception.

A whole crowd of phenomena are of this order, up to and including chemical phenomena that are expressed in the so-called effects of ‘polarization’. There are therefore structurally surfaces whose dissymmetry is elective, and which involve the importance of the direction of rotation: dextrorotatory or levorotatory. You will see later the importance of what that means.

Simply know that the phenomenon, if one may say so, of transfer by tracing of what occurred as a component, as encompassing the loop of demand with the loop of the central object, this transfer onto the surface of the other torus—of which you sense that it is going to allow us to symbolize the relation of the subject to the big Other—will yield two lines which, with respect to the structure of the torus, are superposable.

I ask your pardon for making you follow a path that may seem arid to you; it is indispensable that I make you feel its steps in order to show you what we can draw from it. What is the reason for this? It can be seen very well at the level of the so-called fundamental polygons. This polygon being thus described, you suppose opposite it its tracing which is inscribed thus [fig.2]:

fig.1 fig.2 fig.3

The line in question on the polygon projects here [fig.1: a] as an oblique, and will continue on the other side on the tracing, inverted [fig.2: b]. But you must notice that by tilting this fundamental polygon by 90° [fig.2 → fig.3], you will reproduce exactly, including the direction of the arrows, the figure of this one [fig.1], and that the oblique line will be in the same direction, this tilting representing exactly the complementary composition of one of the tori with the other.

Now make on the torus, no longer this simple line, but the repeated curve whose function I taught you a moment ago:

Is it the same? I spare you the hesitations: after tracing and tilting, what you will have here is symbolized as follows:

What does that mean? It means, in our signified transposition, in our experience, that the subject’s demand, insofar as here it repeats itself twice, inverts its relations D and (a), demand and object at the level of the Other:
– that the subject’s demand corresponds to the Other’s object (a),
– that the subject’s object (a) becomes the Other’s demand.
This relation of inversion is essentially the most radical form we can give to what happens in the neurotic:
– what the neurotic aims at as object is the Other’s demand,
– what the neurotic demands, when he demands to grasp (a), the ungraspable object of his desire, is (a), the Other’s object.
The accent is placed differently according to the two slopes of neurosis:
– for the obsessional, the accent is placed on the Other’s demand, taken as the object of his desire,
– for the hysteric, the accent is placed on the Other’s object, taken as the support of her demand.

What this implies, we shall have to go into in detail insofar as what is at stake for us here is nothing other than access to the nature of this (a). We shall grasp the nature of (a) only when we have structurally elucidated by the same path the relation of S to (a), that is to say the topological support that we can give to fantasy.

Let us say, to begin illuminating this path, that (a), the object of fantasy, (a), the object of desire, has no image and that the impasse of the neurotic’s fantasy is that, in his quest for (a), the object of desire, he encounters i(a)—such as it is the origin from which the whole dialectic begins into which, from the beginning of my teaching, I have been introducing you—namely that the specular image, the understanding of the specular image, consists in this, and I am astonished that no one has thought to gloss the function I give it: the specular image is an error.

It is not simply an illusion, a lure of the captivating Gestalt whose aggressivity has marked the accent, it is fundamentally an error insofar as the subject ‘mis-knows’ himself there [mé-connait: pun joining méconnaître (misrecognize) and me (me)], if you will allow me the expression, insofar as the origin of the ego and its fundamental misrecognition are here gathered together in the spelling. And insofar as the subject is mistaken, he believes that he has his image before him. If he knew how to see himself, if he knew—what is the simple truth—that there are only the most deformed relations, in no way identifiable, between his right side and his left side, he would not think of identifying himself with the mirror image.

When, thanks to the effects of the atomic bomb, we shall have subjects with a right ear as large as an elephant’s ear and, in place of the left ear, a donkey’s ear, perhaps relations to the specular image will be better authenticated! In fact, many other conditions, more accessible and also more interesting, would be within our reach. Let us suppose another animal, the crane, with one eye on each side of the skull. It seems a mountain [a huge challenge] to know how the visual planes of the two eyes can indeed be composed in an animal whose eyes are thus arranged. One does not see why this opens more difficulties than for us. Simply, for the crane to have a view of its images, one must place for it two mirrors, and it will not risk confusing its left image with its right image.

This function of the specular image, insofar as it refers to the misrecognition of what I called a moment ago ‘the most radical dissymmetry’, is the very one that explains the function of the ego in the neurotic. It is not because he has a more or less twisted ego that the neurotic is subjectively in the critical position that is his. He is in this critical position by reason of a radical structuring possibility of identifying his demand with the object of the Other’s desire or of identifying his object with the Other’s demand, a form which is, properly speaking, the lure-effect of the signifier on the subject, even though an exit from it is possible, precisely when next time I shall show you how, in another reference of the cut, the subject insofar as structured by the signifier can become the cut itself. But that is precisely what the neurotic’s fantasy does not attain, because he seeks its ways and paths through an erroneous passage.

Not that the neurotic does not know very well how to distinguish, like every subject worthy of the name, i(a) from (a), because they do not at all have the same value, but what the neurotic seeks—and not without basis—is to arrive at (a) through i(a): the path in which the neurotic persists—and this is perceptible in the analysis of his fantasy—is to arrive at (a) by destroying i(a) or by fixing it.

I said first by destroying it, because that is the most exemplary: it is the obsessional’s fantasy insofar as it takes the form of the sadistic fantasy, which it is not. The sadistic fantasy…
as the phenomenologist commentators do not fail for an instant to stress,
with all the excess of the overflows that allows them to settle forever in the ridiculous
…the sadistic fantasy is supposedly the destruction of the Other.

And since phenomenologists are, let us say—serves them right!—not authentic sadists but simply have the most common access to the perspectives of neurosis, they indeed find every appearance for supporting such an explanation. It suffices to take a sadistic, or Sadean, text for this to be refuted: not only is the object of sadistic fantasy not destroyed, but it is literally resistant to every test, as I have emphasized many times.

As to what the properly Sadean fantasy is—understand clearly that I do not mean to enter into it here yet, as I probably may do next time—what I only want to punctuate here is that what one might call ‘the impotence of sadistic fantasy’ in the neurotic rests entirely on this: that there is indeed a destructive aim in the obsessional’s fantasy, but this destructive aim, as I have just analyzed it, has the sense, not of the destruction of the other, object of desire, but of the destruction of the image of the other in the sense in which I situate it for you here, namely that precisely it is not the image of the other, because the other, (a) object of desire—as I shall show you next time—has no specular image.

That is indeed a proposition, I admit, that abuses things a little. I believe it not only entirely demonstrable, but essential for understanding what happens in what I shall call the neurotic’s going astray in the function of fantasy. For, whether he destroys it or not, in a symbolic or imaginary way, this image i(a), that is not what will ever make him authenticate, by any subjective cut, the object of his desire, for the good reason that what he aims at, whether to destroy it or to support it—i(a)—has no relation—for the sole reason of the fundamental dissymmetry of i(a), the support—with (a) which does not tolerate it.

What the neurotic moreover does in fact arrive at is the destruction of the Other’s desire. And that is precisely why he is irremediably led astray in the realization of his own. But what explains it is this: namely that what makes the neurotic, if one may say so, symbolize something on this path that is his own—aiming in fantasy at the specular image—is explained by what I materialize for you here: the dissymmetry that appears in the relation of demand and object in the subject, in relation to demand and object at the level of the Other.

This dissymmetry, which appears only from the moment when there is, properly speaking, demand, that is to say already two turns, if I may express myself thus, of the signifier, and seems to express a dissymmetry of the same nature as that supported by the specular image: they have a nature which, as you see, is sufficiently illustrated topologically, since here the dissymmetry that would be what we would call specular would be this [a] with this [b].

[a][b]

It is from this confusion through which 2 different dissymmetries come, for the subject, to serve as support for what is the subject’s essential aim in his being, namely the cut of (a)—the true object of desire where the subject himself is realized—it is in this misguided aim, captured by a structural element tied to the effect of the signifier itself on the subject, that there resides not only the secret of the effects of neurosis, namely: that the so-called relation of narcissism, the relation inscribed in the function of the ego, is not the true support of neurosis, but for the subject to realize its false analogy, the important thing—even though already the tightening, the discovery of this internal knot is crucial for orienting us in neurotic effects—is that it is also the only reference that allows us to radically differentiate the structure of the neurotic from neighboring structures: namely from that which is called perverse, and from that which is called psychotic