🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

There is the double cut [inner eight]:

that which makes two turns around that famous point of the projective plane: two ears crossing through each other, the first being able to move without moving the point [a].

Here are three figures:

fig.1 fig.2 fig.3

Figure 1 corresponds to the simple cut, insofar as the projective plane could not tolerate more than one without being divided.
That one does not divide; it opens. This opening is interesting to show in this form because it allows us to visualize, to materialize for ourselves, the function of the point.

Figure 2 will help us understand the other one. It is a matter of knowing what happens when the cut designated here has opened the surface.
Of course, what is involved here is a description of the surface linked to what are called its extrinsic relations, namely the surface
insofar as we are trying to insert it into three-dimensional space. But I told you that this distinction between the intrinsic properties of the surface and its extrinsic properties was not as radical as is sometimes insisted upon
out of a concern for formalism, because it is precisely with regard to its embedding in space, as they say, that certain of the
intrinsic properties of the surface appear in all their consequences. I am only pointing out the problem to you.

Everything I am going to tell you, in fact, about the projective plane, the privileged place occupied there by the point, what we shall call
‘the point,’ which is here represented in the cross-cap, here [fig.1], terminal point of the line of pseudo-penetration of the surface into itself,
this point, you can see its function in this open form [fig.2] of the same object described in figure 1.

fig.2

If you open it along the cut, what you will see appear is a bottom [fig.2: a] that is below, that of the hemisphere.
Above, it is the plane of this anterior wall [fig.2:b] insofar as it continues as a posterior wall [fig.2: c]
after having penetrated the plane that is, so to speak, symmetrical to it in the composition of this object.

Why do you see it thus laid bare all the way to the top?

Because once the cut has been made, since these two planes, which cross like this at the level of the line of penetration,
do not really cross, since it is not a real penetration but a penetration necessitated only by
the projection into space of the surface in question, we can at will raise back up, once a cut has dissolved
the continuity of the surface, one of these planes through the other since, after all, not only is it not important
to know at what level they pass through one another, which points correspond in the passage-through, but on the contrary it is expressly appropriate not to take into account this coincidence of the levels of the points insofar as the penetration could
render them, at certain moments of the reasoning, superposable. On the contrary, it is appropriate to mark that they are not.

The anterior plane of figure 1, which passes to the other side, has been lowered toward the point that we henceforth call
‘the point’ pure and simple, while above we see this occur: a line that goes up to the top of the object and that,
behind, passes to the other side. When we make, in this figure, a passage-through, we obtain something
that presents itself as a hollow open toward the front:

The dotted line will pass behind this sort of ear and finds an exit on the other side, namely the cut
between this edge here and what, on the other side, is symmetrical to this sort of basket, but at the rear. One must consider
that behind there is an exit. There is figure 3, which is an intermediate figure.

Here you still see the intercrossing at the upper part of the anterior plane, which becomes posterior and then returns.
And you can raise that indefinitely, I pointed this out to you. That is indeed what happened at the extreme level.
It is the same thing as that edge which you find described in figure 1. This part that I designate in figure 1,
we are going to call A. That is what is maintained at this place in figure 2. The continuity of this edge:

is effected with what, behind the surface in some way oblique thus freed, folds back to the rear once you have begun to let the whole thing go, so that if they were glued back together, this would join up as in figure 3. That is why I indicated it in blue on my drawing [blue arrows]. Blue is, in short, everything that perpetuates the cut itself.

What results from this?

It is that you have a hollow, a pocket into which you can introduce something.
If you pass your hand through, it passes behind this ear, which is in continuity at the front with the surface. What you encounter behind is a surface corresponding to the bottom of the basket, but separated from what remains on the right, namely this surface that comes forward there and folds back at the rear in figure 2. Following a path like that, you have
a solid arrow, then dotted because it passes behind the ear that corresponds to A. It comes out here because that is
the part of the cut that is behind. That is the part I can designate by B. The ear that is drawn here by the limits
of this dotted line in figure 2 could be on the other side.

This possibility of two ears is what you will find when you have carried out the double cut and isolate in the cross-cap something that is fabricated here. What you see in this central piece thus isolated in figure 4

fig.4

is, in short, a plane such that you now erase the rest of the object, so that you will no longer have to put dotted lines here, nor even any passage-through. Only the central piece remains. What do you then have? You can imagine it easily.
You have a sort of plane which, by warping, comes, at a certain moment, to recut itself along a line that then passes behind.

So here too you have two ears: a strip in front, a strip in back. And the plane passes through itself along
a line strictly limited to a point. It could be that this point were placed at the extremity of the posterior ear:
that would be, for the plane, a way of recutting itself that would be just as interesting in certain respects,
since that is what I realized in figure 5:

to show you in a moment the way in which the structure of this point should be considered…
I personally know that you have already been concerned about the function of this point, since one day you
privately asked me why always, both I myself and the authors, represent it in this form, indicating at the center a sort of small hole. It is quite certain that this small hole gives one pause for thought.
And it is precisely on this that we are going to insist, because it delivers the quite particular structure of this point
which is not a point like the others. This is what I am now going to be led to explain
…its somewhat oblique, twisted shape is amusing, for the analogy is striking with the helix¹, the antihelix² and even the lobule
of the form of this cut projective plane, if one considers that one can recover this form, which fundamentally is drawn
toward the form of the Möbius strip; it is found again much more simplified in what I once called ‘the arum’
or else ‘the donkey’s ear.’

This is done only to draw your attention to this evident fact that nature seems in some way drawn into these structures, and in particularly significant organs, those of the bodily orifices that are in some way left
apart, distinct from the analytic dialectic. To these bodily orifices, when they show this sort of resemblance,
there could be attached a sort of consideration, a connection to the Naturwissenschaft of this point,
which indeed must border on it there, be reflected there, if it actually has some value.

The striking analogy of several of these drawings I have made with the figures you find on every page of embryology books also deserves attention.

When you consider what happens, scarcely beyond the stage of the germinal plate, in the egg of snakes or fish,
insofar as this is what comes closest, in an examination that is not absolutely complete in the current state of science,
to the development of the human egg, you find something striking: the appearance on this germinal plate,
at a given moment, of what is called the primitive streak, which is likewise terminated by a point, Hensen’s node, which is a point
quite significant and truly problematic in its formation, insofar as it is linked by a sort of correlation to the formation of the neural tube: it comes in some way to meet it through a process of folding of the ectoderm. It is, as you are well aware, something that gives the idea of the formation of a torus, since at a certain stage this neural tube remains open like a trumpet on both sides.

By contrast, the formation of the chordal canal which occurs at the level of this Hensen’s node, with a way of propagating laterally, gives the idea that there occurs there a process of intercrossing whose morphological aspect cannot fail to recall
the structure of the projective plane, especially if one thinks that the process realized from this point called Hensen’s node is in some way
a regressive process. As development advances, it is in a line, in a posterior recession of Hensen’s node,
that this function of the primitive streak is completed, and that here there occurs this opening toward the front, toward the endoblast, of this canal which,
in sauropsids, presents itself as the homologue – without being at all identifiable with the neuroenteric canal found in batrachians – namely what puts into communication the terminal part of the digestive tube and the terminal part of the neural tube.

In short, this point so highly significant for conjoining the cloacal orifice, this orifice so important in analytic theory,
with something that is found, in front of the lowest part of the caudal formation, to be what specifies the vertebrate
and the pre-vertebrate more strongly than any other character, namely the existence of the notochord of which this primitive streak
and Hensen’s node are the point of departure.

There is certainly a whole series of directions of research which, I believe, would deserve attention. In any case, if I have not insisted on it, it is surely because that is not the direction in which I wish to engage. If I am speaking of it now, it is both to awaken in you a little more interest in these structures so captivating in themselves, and also to authenticate a remark made to me about what embryology would have to say here, at least by way of illustration. This will allow us to go further

• and immediately – on the function of this point. A very tight discussion on the level of the formalism of these topological constructions
  would only drag on endlessly and perhaps might tire you.

If the line that I trace here [line of penetration], in the form of a sort of intercrossing of fibers, is something whose
function in this cross-cap you already know, what I mean to point out to you is that the point that terminates it, of course,
is a mathematical point, an abstract point. We therefore cannot give it any dimension.
Nevertheless we can think it only as a cut to which we must give paradoxical properties: first from the fact that we can conceive it only as punctiform, and on the other hand it is irreducible.

In other words, for the very conception of the surface we cannot consider it as filled in:
it is ‘a point-hole,’ if one may say so. Moreover, if we consider it as ‘a point-hole,’ that is to say made of the joining together of two edges, it would be in some way unseverable in the direction that passes through it, and this can indeed be illustrated by this type
of unique cut [1] that one can make in the cross-cap. There are some made conventionally to explain the functioning of the surface, in the technical books devoted to it.

[1][2]

If there is a cut [2] that passes through this point, how are we to conceive it? Is it in some way the homologue, and only the homologue, of what happens when you pass one of these lines higher up,
crossing the structural line of false penetration? That is to say, in some way: if something exists that we can call a ‘point-hole,’ such that the cut, even when it approaches it to the point of coinciding with this point,
goes around this hole?

That is indeed what must be conceived, for when we trace such a cut, this is what we arrive at:

→
fig.1fig.3
Take, if you wish, figure 1, transform it into figure 3, and consider what is involved between the two ears that remain
there, at the level of A, and of B which would be behind: it is something that can still spread apart indefinitely, to the point that the whole takes on this aspect [fig. 5]:

These two parts of the figure represent the folds, anterior and posterior, that I drew in figure 4.
Here, at the center, this surface that I drew in figure 4 appears here also in figure 5. It is indeed there, behind.
It remains that at this point something must be maintained which is in some way the beginning of the mental fabrication
of the surface, namely in relation to this cut which is that around which it is really constructed.

For this surface that you want to show, it is appropriate to conceive it as a certain way of organizing a hole.
This hole, whose edges are here [fig. 5], is the beginning and the point from which one must start so that there may be made,
in a way that effectively constructs the surface in question, the edge-to-edge joinings that are drawn here,
namely that this edge here, after of course all the modifications necessary for its descent through the other surface,
and this edge here come to join with the one we have brought into this part of figure 5: a with a’.
The other edge, by contrast, must come to join, according to the general direction of the green arrow, with that edge there: d with d’.

It is a joining-together that is conceivable only on the basis of the beginning of something that signifies itself as the covering-over, as punctual as you please, of this surface by itself at one point, that is to say of something that is here,
at a small point where it is split and where it comes to cover itself.

[b]

It is around this that the process of construction operates. If you do not have that, if you consider that the cut b
that you make here passes through the point-hole not by going around it like the other one-turn cuts, but on the contrary
by coming to cut it here, in the manner in which in a torus we can consider that a cut is produced thus,
what does this figure become? It takes on another and entirely different aspect. Here is what it becomes.

It becomes purely and simply the most simplified form of the folding forward and backward of the surface of figure 5:

fig.5

That is to say that what you saw, in figure 5, organized according to a form that comes to intercross edge to edge according to four segments: segment a joining segment a’, it is a segment that would bear no. 1 in relation to another that would bear
no. 3 in relation to the continuity of the cut thus drawn, then segment no. 2 with segment no. 4.

Here – last figure – you have only two segments. We must conceive them as adjoining one another
through a complete inversion of one with respect to the other.

fig. 6

It is very difficult to visualize, but the fact that what is on one side in one direction must join to what,
on the other side, is in the opposite direction, shows us here the pure structure, though non-visualizable, of the Möbius strip.
The difference between what occurs when you make this simple cut on the projective plane and the projective plane itself is that you lose one of the elements of its structure; you make of it only a pure and simple Möbius strip, except for this:
you do not see appearing anywhere what is essential in the structure of the Möbius strip, an edge.

Now this edge is entirely essential in the Möbius strip. Indeed, in surface theory – I cannot expand on it
in an entirely satisfactory way – in order to determine properties such as genus, number of connections, characteristic, everything that makes the interest of this topology, you must take into account that the Möbius strip has an edge
and has only one, that it is constructed on a hole.

It is not for the pleasure of paradox that I say that surfaces are organizations of the hole. Here then, if it is a matter
of a Möbius strip, that means that, although nowhere is there any need to represent it, the hole must nevertheless remain. For it to be a Möbius strip, you will therefore place a hole there. However small it may be, however punctiform it may be, it will topologically fulfill exactly the same functions as the complete edge in this something that you can draw when you draw a Möbius strip, that is to say roughly something like this:

As I pointed out to you, a Möbius strip is as simple as that. A Möbius strip has only one edge.
If you follow its edge, you have gone around everything that is edge on this strip, and in fact it is only one hole,
a thing that can appear as purely circular.

By emphasizing the two sides, inverting, one with respect to the other, adjoining them, it would still remain that it would be necessary, for it truly to be a Möbius strip, that we preserve in as reduced a form as possible the existence of a hole.
That is indeed what indicates to us the irreducible character of the function of this point.

And if we try to articulate it, to show its function, we are led, in designating it as the point-origin of the organization of the surface on the projective plane, to find there properties that are not completely those of the edge of the Möbius surface, but that are nevertheless something that is so much a hole that if one intends to
suppress it by this operation of section, by the cut passing through this point, it is in any case a hole that one makes appear in the most incontestable way.

What does that mean further?

For this surface to function with its complete properties, and particularly that of being one-sided,
like the Möbius strip, namely that an infinitely flat subject moving on it can, starting from any exterior point
of its surface, return by an extremely short path, and without having to pass by any edge, to the reverse point of the surface from which he started, for this to occur, there must be somewhere in the construction of the apparatus that we call
the projective plane, however reduced you suppose it, this sort of bottom that is represented here:

The rear end of the apparatus, the part not structured by the intercrossing, a little piece of it must remain, however small, without which the surface becomes something else, and specifically no longer represents this property of functioning as one-sided. Another way of bringing out the function of this point: the cross-cap cannot be drawn purely and simply as something that would be divided in two by a line where the two surfaces intercross [a].

There must remain here [b] something that, beyond the point, surrounds it: something like a circumference, however reduced it may be, a surface that allows communication between the two upper lobes, so to speak, of the surface thus structured. This is what shows us the paradoxical and organizing function of the point.

– But what this allows us to articulate now is that this point is made of the joining together of two edges of a cut, a cut which itself could in no way be passed through again, be severable,
– a cut that you see here, in the way I have pictured it for you, as deduced from the structure of the surface, and such that one can say that if we arbitrarily define something as interior and as exterior, by putting for example: in blue on the drawing what is interior and in red what is exterior, at one of the edges of this point the other would present itself thus, since it is made of a cut – however minimal you may suppose it – the surface that comes to superpose itself on the other. In this privileged cut, what will confront one another without joining will be an exterior with an interior, an interior with an exterior.

Such are the properties I am presenting to you; one could express this in a learned form, more formalist,
more dialectical, in a form that seems to me not only sufficient, but necessary in order then to picture
the function that I intend to give it for our use.

I pointed out to you that the double cut [inner eight] is the first form of cut that introduces, into the surface
defined as the cross-cap of the projective plane, the first cut, the minimal cut that obtains the division of this sur-face.
Last time I already indicated to you what this division leads to and what it meant. I showed it to you
in very precise figures that you have, I hope, all taken down in your notes, and which consisted in proving to you
that this division has precisely the result of dividing the surface into:

1. a Möbius surface, that is to say a one-sided surface of the type of the figure shown here:

This one retains, if one may say so, within itself only a part of the properties of the surface called cross-cap, and precisely that particularly interesting and expressive part which consists in the one-sided property, and in the one that I have always emphasized since I circulated among you little Möbius ribbons of my own making, namely that it is a skew surface, that it is – let us say in our language – speculariz-able [i.e., mirrorable in a way that reveals non-superposability], that its image in the mirror
cannot be superposed on it, that it is structured by a fundamental dissymmetry.

2. And this is the whole interest of this structure that I am demonstrating to you, namely that the central part, on the contrary:

what we shall call the central piece, isolated by the double cut, while being manifestly the one that carries with it the true structure of the whole apparatus called cross-cap. It is enough to look at it, I would say, to see it. It is enough to imagine that, in some way, the edges join here at the points of correspondence they present visually, for the general form of this projective plane or cross-cap to be immediately reconstituted.

But with this cut, what appears is a sur-face having this aspect which you can, I think, now regard as something that, for you, has reached sufficient familiarity for you to project it into space, this surface that passes through itself along a cer-tain line that stops at a point.

It is this line, and above all this point, that give the double-turn form of this cut its privileged significance
from the schematic point of view, because it is to that one that we are going to entrust ourselves in order to give ourselves a schematic representation, schematic of what the relation S cut of (a) [S◊a] is, what we do not manage to grasp at the level of the structure of the torus,
namely something that allows us to articulate schematically the structure of desire, the structure of desire insofar as formally we have already inscribed it in that something of which we say that it allows us to conceive
the structure of fantasy: S◊a.

We shall not exhaust the subject today, but we shall try today to introduce for you that this figure,
in its schematic function, is exemplary enough to allow us to find the relation of S cut of (a) [S◊a],
the for-malization of fantasy in its relation with something that is inscribed in what remains of the so-called surface
of the projective plane, or cross-cap, when the central piece [a] is in some way enucleated from it.

It is a specularizable structure, fundamentally dissymmetrical, which will allow us to localize the field of this dissymmetry of the subject with respect to the Other, especially concerning the essential function played there by the specular image.
For here indeed is what is at stake: the true imaginary function, if one may say so, insofar as it intervenes at the level of desire, is a privileged relation with (a), object of desire, terms of fantasy. I say terms since there are two, S and (a), linked by the function
of the cut. The function of the object of fantasy, insofar as it is a term of the function of desire, this function is hidden.

What is most efficient, most effective in the relation to the object as we understand it in the currently accepted vocabulary of psychoanalysis, is marked by a maximum veiling. One can say that libidinal structure,
insofar as it is marked by the narcissistic function, is what for us covers over and masks the relation to the object.

It is insofar as the narcissistic relation, secondary narcissistic, the relation to the image of the body as such, is linked
by something structural to that relation to the object which is that of the fundamental fantasy, that it takes on its full weight.
But this something structural of which I speak is a complementary relation: it is insofar as the relation of the subject marked by the unary trait finds a certain support, which is lure, which is error, in the body-image as constitutive
of specular identification, that it has its indirect relation with what is hidden be-hind it, namely the relation to the object,
the relation to the fundamental fantasy.

There are therefore two imaginaries, the true and the false, and the false is sustained only in that sort of subsistence to which all the mirages of ‘knowing-myself’ remain attached. I have already introduced this pun ‘mis-recognition’ [mé-connaissance / méconnaissance]: the subject misrecognizes himself
in the mirror relation. This mirror relation, to be understood as such, must be situated on the basis
of that relation to the Other which is the foundation of the subject, insofar as our subject is the subject of discourse, the subject of language.

It is by situating what S cut of (a) [S◊a] is…
with respect to the fundamental deficiency of the Other as locus of speech, with respect to what is the only definitive answer at the level of enunciation, the signifier of A, of the universal witness insofar as it is lacking
and at a given moment has no more than a function of false witness
…it is by situating the function of (a) at this point of failure, by showing the support the subject finds in this (a)…
which is what we aim at in analysis as object having nothing in common
with the object of classical idealism, having nothing in common with the object of the Hegelian subject
…it is by articulating this (a) in the most precise way at the point of lack in the Other…
which is also the point where the subject receives from this Other, as locus of speech, his major mark,
that of the unary trait, the one that distinguishes our subject, from the transparent knowingness of classical thought, as a subject entirely attached to the signifier insofar as this signifier is the turning point of his rejection,
he the subject, outside all signifying real-ization
…it is by showing, starting from the formula S◊a as the struc-ture of fantasy, the relation of this object (a) with the lack in the Other,
that we see how at a certain moment everything recoils, everything is effaced in the signi-fying function before the rise, the irruption of this object.

That is what we can move toward, although it is the most veiled zone, the most difficult to articulate
of our experience. For precisely we have control of it in this, that by these paths which are those of our experience, paths that we traverse, most habitually those of the neurotic, we have a structure that it is not at all a matter
of laying on the backs of scapegoats: at this level, the neurotic, like the pervert, like the psychotic himself,
are only faces of normal structure.

I am often told after these lectures: when you speak of the neurotic and of his object which is the demand of the Other,
unless his demand is the object of the Other, why do you not speak of normal desire! But precisely, I speak of it all the time:

– The neurotic is the normal, insofar as for him the Other, with a capital A, has all the importance.

– The pervert is the normal insofar as for him the phallus, the capital Φ, which we are going to identify with this point that gives the central piece of the projective plane all its consistency, the phallus has all the importance.

– For the psychotic the own body, which is to be distinguished in its place in this structuration of desire, the own body has all the importance.

And these are only faces where something is manifested of this element of paradox which is the one I am going to try to articulate before you at the level of desire. Already last time, I gave you a foretaste of it, by showing you
what can be distinct in the function insofar as it emerges from fantasy, that is to say from something that the subject foments, tries to produce in the blind place, in the masked place which is the one of which this central piece gives the schema.

Already concerning the neurotic – and precisely the obsessive – I was indicating to you how it can be conceived that the search for the object is the true aim, in obsessive fantasy, of that always renewed and always powerless attempt
at that destruction of the specular image insofar as it is that which the obsessive aims at, which he senses as an obstacle
to the realization of the fun-damental fantasy.

I showed you that this sheds much light on what happens at the level of fantasy – not sadistic – but Sadian,
that is to say the one that I had the occa-sion to spell out before you, for you, with you, in the seminar on Ethics,
insofar as, realization of an inner experience that one cannot entirely reduce to the contingencies of the knowable framework of an effort of thought concerning the relation of the subject to nature, it is in the injury to nature
that SADE tries to define the essence of human desire.

And that is indeed whereby, already today, I could, for you, introduce the dialectic at issue.
If somewhere we can still preserve the notion of knowledge, it is assuredly outside the human field.
Nothing prevents us from thinking – we positivists, Marxists, whatever you like – that nature, for its part,
knows itself. It surely has its preferences; it does not, for its part, take just any material. That is indeed what has left us for some time the field, us, to find heaps of others, and funny ones, which it had quite amusingly left aside! In whatever way it knows itself, we see no obstacle there.

It is quite certain that the whole development of science, in all its branches, takes place for us in a way that makes the notion of knowledge clearer and clearer. Connaturality with whatever means in the natural field
is what is most foreign, ever more foreign, to the development of this science.

Is it not precisely that which makes it so timely that we advance into the structure of desire such as our experience – precisely, effectively – makes us feel it every day? The nucleus of unconscious desire and its relation of orientation, of magne-tization so to speak, is absolutely central with respect to all the paradoxes of human misrecognition.
And does not its first foundation lie in this: that human desire is a fundamentally ‘acosmic’ function?

That is why, when I try for you to foment these plastic images, it may seem to you that you are seeing an updating of old imaginary techniques, those which I taught you to read under the form of the sphere in PLATO.
You could tell yourselves that.

This little double point, this punch-mark [poinçon also evokes the lozenge operator ◊], shows us that there is the field in which is circumscribed what is the true spring of the relation between the possible and the real. What made all the charm, all the long-pursued seduction of classical logic, the true point of interest of formal logic – I mean that of ARISTOTLE – is what it supposes and what it excludes
and which is truly its pivot-point, namely the point of the impossible insofar as it is that of desire. And I shall return to it.

So you could tell yourselves that everything I am in the process of explaining to you there is the continuation of the preceding discourse.
It is – let me use this formula – it is ‘Theo tricks’ [‘trucs à théo’ = a joking phrase sounding like cheap tricks / theology tricks], for in the end it is fitting to give it a name,
to this God with whom we gargle our throats a little too romantically under this proclamation that we would have pulled off
a fine stroke by saying that God is dead.

There are gods and gods. I have already told you that there are some that are quite real. We would be wrong to misrecognize their reality.
The god at issue, and whose problem we cannot elude as a problem that is our business,
a problem in which we have to take sides, that one, for the distinction of terms, echoing BECKETT
who one day called him GODOT, why not call him by his true name: the Supreme Being? If I remember correctly, moreover, ROBESPIERRE’s good lady friend had that as her proper name: I believe she was called Catherine THÉOT.

It is quite certain that a whole part of analytic elucidation, and to tell the truth the whole history of the father in FREUD,
is our essential contri-bution to the function of Theo in a certain field, very precisely in this field that finds
its limits at the edge of the double cut, insofar as it is this that determines the structuring characters,
the fundamental nucleus of fantasy in theory as in practice.

If something can be articulated that weighs the domains of Theo against one another, which turn out not to be so totally reduced,
nor reducible since we busy ourselves with them so much, except that for some time we have been losing, so to speak, their soul, their sap, and the essential. We no longer know quite what to say; this father seems to be reabsorbed into an ever more receding cloud,
and at the same time to leave singularly suspended the bearing of our practice; that there is indeed some historical correlative there, it is not at all superfluous that we evoke it when it is a matter of defining what we are dealing with
in our field: I believe the time has come.

The time has come because already, under a thousand concretized, articulated, clinical and practitionerly forms, a certain sector is emerging in the evolution of our practice, one that is distinct from the relation to the Other – capital A – as fun-damental, as structuring of the whole experience whose foundations we have found in the unconscious.

But its other pole has all the value I called just now comple-mentary:

– that without which we drift, I mean that without which we return, as a retreat, an abdication, to that something which was the ethic of the theological era,

– that whose origins I made you feel, certainly retaining all their worth, all their value, in that original freshness preserved for them by PLATO’s dialogues.

What do we see after PLATO, if not the promotion of what now perpetuates itself under the dusty form
of this distinction – of which it is truly a scandal that one can still find it under the pen of an analyst –
of the ‘ego-subject’ and the ‘ego-object’!

Talk to me about the rider and the horse, the dialogue of the soul and desire. But precisely it is a matter of this soul and of this desire,
this referral of desire to the soul at the very moment when precisely it was a matter only of desire, in short, everything I showed you last year in the Symposium. It is a matter of seeing this more essential clarity that we, for our part, can bring to it:
it is that desire is not on one side.

If it seems to be that unmanageable thing that PLATO describes in so pathetic, so moving a way and that the higher soul is destined to dominate, to captivate, of course it is because there is a relation, but the relation is internal, and dividing it is precisely
to let oneself go to a lure, to a lure that stems from the fact that this image of the soul – which is nothing other than the central image
of secondary narcissism, such as I defined it earlier and to which I shall return – functions only as an access route – a deceptive access route but an access route, oriented as such – to desire.

It is certain that PLATO was not unaware of it. And what makes his enterprise all the more strangely per-verse
is that he masks it from us. For I shall speak to you of the phallus in its double function, the one that allows us to see it
as the common point of eversion, if I may say so, of ‘evergence’ [a coined term, built as the reverse of convergence] – if I may venture this word as constructed backwards
from that of convergence – if, this phallus, I think I can articulate for you on the one hand its function at the level of the S of fantasy
and at the level of the (a) that for desire it authenticates.

As of today I shall indicate to you the kinship of paradox with this very image given to you by this schema of figure 4, since here nothing other than this point ensures for this surface thus cut out its charac-ter as a one-sided surface, but ensures it entirely, truly making of S the cut of (a), but let us not go too fast: (a), it assuredly, is the cut of S.

The sort of reality that we aim at in this objectality, or this objectivity, that we alone define,
is truly for us what unifies the subject. And what did we see in SOCRATES’ dialogue with ALCIBIADES?
And what is this comparison of this man, raised to the pinnacle of passionate homage, with a box?

This marvelous box, as always it has existed everywhere man has known how to construct objects for himself, figures of what for him is the central object, that of the fundamental fantasy. It contains what, says ALCIBIADES to SOCRATES? The ἂγαλμα [agalma]!
We are beginning to glimpse what this ἂγαλμα [agalma] is, something that must not have a slight relation with
this central point that gives its accent, its dignity to object (a).

But things, in fact, are to be inverted at the level of the object. This phallus, if it is so paradoxically constituted that one must always be very careful about what is the enveloping function and the enveloped function, I believe that it is rather in the heart of the ἂγαλμα that ALCIBIADES seeks what there he appeals to, at that moment when the Symposium ends, in that something
that we alone are capable of reading – though it is obvious – since what he seeks, before what
he prostrates himself, to what he was making that impu-dent appeal, is to what? SOCRATES as desiring, whose avowal he wants.

At the heart of the ἂγαλμα, what he seeks in the object manifests itself as being the pure ἐρῶν [eron], for what he wants is not to tell us that SOCRATES is lovable, it is to tell us that what he desired most in the world was to see SOCRATES desiring.

This most radical subjective impli-cation at the very heart of the object itself of desire – where I think that all the same
you find yourselves a little, simply because you can fit it into the old drawer of man’s desire
and the desire of the Other, is something that we shall be able to point out more precisely.

We see that what organizes it is the punctual, central function of the phallus. And there, we have our old enchanter, rotting or not, but an enchanter assuredly, the one who knows something about desire, who sends our ALCIBIADES
packing [sur les roses] by telling him what? To take care of his soul, of his ego, to become what he is not, a neurotic,
for the centuries later, a child of Theo.

And why? What is this referral by SOCRATES to a being as admirable as ALCIBIADES?
In that the ἂγαλμα, it is manifestly he who is it, as I believe I demonstrated before you, it is purely
and mani-festly that, the phallus, ALCIBIADES is it. Simply, no one can know whose phallus he is. To be phallus in that state, one must have a certain stuff – he certainly did not lack it – and SOCRATES’ charms
remain on that score without hold on ALCIBIADES, without any doubt.

He passes across the centuries that followed, from theological ethics toward that enigmatic and closed form, but which the Symposium nevertheless indicates to us at the point of departure and with all the necessary complements, namely that ALCIBIADES, manifesting
his appeal to the desiring one at the heart of the privileged object, does there nothing other than appear in a position of unbridled seduction with respect to the one I called ‘the fundamental cunt’ [‘con’ is vulgar French; also echoes ‘con’ as fool, but here sexual/vulgar force is primary], which for the crowning irony PLATO connoted with the proper name of the ‘Good’ itself, AGATHON. The Supreme Good has no other name in his dialectic.

Is there not something there that shows sufficiently that there is nothing new in our inquiry?
It returns to the point of departure in order – this time – to understand everything that has happened since.