🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

Last time, we heard Madame AULAGNIER speak to us about anxiety.
I paid all the tribute it deserved to her discourse, the fruit of work and reflection that were altogether well oriented.
At the same time, I pointed out how a certain obstacle – which I located at the level of communication – is always the same one, the one that arises each time we have to speak about language.

Certainly, the sensitive points, the points which, in what she told us, deserve to be rectified are precisely those where, placing the accent on what exists as unsayable, she makes of it the index of a heterogeneity of what she is aiming at precisely as the ‘unable to be said’, whereas what is at stake in this matter, when anxiety occurs, is precisely to be grasped in its link with the fact that there is ‘saying’ and ‘what can be said’.

Thus she cannot give its full value to the formula: ‘Man’s desire is the desire of the Other’.
It is not by reference to a third party that would be reborn, the more central subject, the subject identical to itself, the Hegelian self-consciousness that would have to operate the mediation between two desires that it would in some way have before itself:
its own, as an object, and the desire of the Other. And even in giving primacy to this desire of the Other, it would have
to situate, to define its own desire in a sort of reference, of relation or non-relation of dependence to this desire of the Other.

Of course, at a certain level where we can always remain, there is something of that order, but that something is precisely what enables us to avoid what is at the heart of our experience and what is to be grasped. And that is why, for that reason, I am trying to forge a model for you of what is to be grasped. What is to be grasped is that the subject that interests us is desire. Of course, this only takes on its sense from the moment we have begun to articulate,
to situate at what distance, through what intermediary, which is not an intermediate screen but constitution, determination, we can situate desire.

It is not that demand separates us from desire – if it were only a matter of setting demand aside in order to find it! – its signifying articulation determines me, conditions me as desire. That is the long path I have already made you travel. If I made it
so long, it is because it had to be so in order that the dimension this presupposes might make you undergo, as it were, the mental experience of apprehending it.

But this desire, thus borne, deferred into a distance, articulated as such, not beyond language as because of an impotence
of that language, but structured as desire by that very power, it is this that must now be reached so that I may succeed
in making you conceive, grasp. And there is in grasping, in the Begriff, something sensible, something of a transcendental aesthetics that must not be the one received up to now, since it is precisely from that one received up to now that the place of desire has until now withdrawn.

But this is what explains to you my attempt – which I hope is to succeed – to lead you along paths that are also
of aesthetics insofar as they try to seize something that has not been seen in all its relief, in all its fecundity
at the level of intuitions not so much spatial as topological. For our intuition of space clearly cannot exhaust everything that is of a certain order, since, after all, those very people who deal with it with the highest qualification,
mathematicians, are trying on all sides – and succeed – to go beyond intuition.

In the end I lead you on this path in order to say things with words, with words that are watchwords:
it is a matter of escaping the preeminence of the intuition of the sphere insofar as, in some way, it commands very intimately,
even when we are not thinking about it, our logic. For of course, if there is an aesthetics called ‘transcendental’
that interests us, it is because it is what dominates logic. That is why to those who say to me:

‘Could you not really tell us things, make us understand what happens in a neurotic
and in a pervert, and how it is different, without going through your little tori and other detours?’

I will answer that this is nonetheless indispensable, just as indispensable and for the same rea-son, because it is the same thing
as doing logic, for the logic at issue is not an empty thing. Logicians – like grammarians – dispute,
and these disputes, insofar as of course we can only, upon entering their field, evoke them with discretion
so as not to lose ourselves there…

But all the confidence you place in me rests on this: that you give me credit for having made some effort
not to take the first path that came along and for having eliminated a certain number of them. But still, to reassure you, it occurs to me to point out that it is not indifferent to place in the foreground, in logic,
the function of hypothesis for example, or the function of assertion. In the theater, in what is called ‘an adaptation’,
people make Ivan KARAMAZOV say: ‘If God does not exist, then everything is permitted’.

You refer back to the text, you read:
and besides, if my memory is good, it is Alyosha who says this, as if by chance
…‘Since God does not exist, then everything is permitted’.

Between these two terms, there is the difference from ‘if’ to ‘since’, that is to say from a hypo-thetical logic to an assertoric logic.
And you will say to me: ‘A logician’s distinction, in what way does it interest us?’ It interests us so much that it is in order to represent things in the first way that at the final term, the Kantian term, we are made to maintain the existence of God.

Since, after all, everything is there: as it is clear that not everything is per-mitted, then in the hypothetical formula it imposes itself as necessary that God exists. And that is why your daughter is mute and how, in the teaching articulation of free thought, the existence of God is maintained at the heart of the articulation of all valid thought as a term without which
there would not even be a way to advance something in which the shadow of a certainty could be grasped. And you know – what I thought
I should remind you a little about on this subject – that DESCARTES’s procedure cannot pass by other paths.

It remains that it is not necessarily by pinning on it the term atheist that one will best define our project, which is perhaps to try to make pass through something else the consequences entailed in fact, for us in experience, by there being the permitted.
‘There is the permitted because there is the forbidden’, you will tell me – all pleased to find there the opposition of A and non-A,
of white and black. Yes… But that does not suffice, because far from exhausting the field, the permitted and the forbidden, what is at issue
to structure, to organize, is how it is true that the one and the other determine each other, and very closely, while leaving
an open field which, not only is not excluded by them, but makes them meet, and in this movement of torsion,
if one may say so, gives its form properly speaking to what supports the whole, that is to say the form of desire.

To put it plainly: that desire institutes itself in transgression. Everyone senses, everyone clearly sees, everyone has experience of this,
which does not mean – cannot even mean – that this is only a question of boundary, of a drawn limit,
that it is beyond the crossed boundary that desire begins. Of course, this often seems the shortest path,
but it is a desperate path. The path of passage is made elsewhere.

Yet the boundary, that of the forbidden, does not mean either that we bring it down from the sky and from the existence of the signifier.
When I speak to you of the Law, I speak of it to you as FREUD does, namely that if one day it emerged, no doubt the signifier had to stamp it at once with its mark, its punch, its form, but it is nonetheless from something that is an original desire that the knot could be formed so that these might be founded together: the Law as limit and desire in its form.

That is what we are trying to figure in order to enter even into the detail, retrace this path which is always the same,
but which we tighten around an increasingly central knot whose umbilical figure I do not despair of showing you.
We take up the same path and we do not forget that what is least situated for us in terms of references
that would be: legalist, formalist, or naturalist, is the notion of (a) insofar as it is not the imaginary other that it designates – the imaginary other insofar as with it we identify in ego-misrecognition – it is i(a).

And here too we find this same internal knot which makes what seems to be quite simple: that the other is given to us
under an imaginary form, not so, in this that this other is precisely what is at issue when we speak of the object.
Of this object, it is not at all to be said: that it is simply the real object, that it is precisely the object of desire
as such, no doubt original, but that we can only say it as such, from the moment when we shall have grasped,
understood, apprehended what it means that the subject – insofar as it constitutes itself as dependence on the signifier,
as beyond demand – is desire.

Now it is this point of the loop that is not yet secured and it is there that we are advancing, and that is why
we recall the use we have made of (a) up to now. Where have we seen it? Where are we first going to designate it?
In fantasy! Where obviously, it has a function that has some relation to the imaginary. Let us call it ‘the imaginary value in fantasy’. It is altogether other than simply projectable in an intuitive way into the function of lure
as it is given to us in biological experience, for example, by the innate releasing mechanism.

It is something else, and this is what remind you:
– and the formalization of fantasy as constituted in its support by the set: barred S desire of a [S◊a],
– and the situation of this formula in the graph which shows homologously, by its position on the upper level which makes it the homologue of the i(a) of the lower level: insofar as it is the support of the ego, little m here, just as barred S desire of a [S◊a] is the support of desire.

What does that mean? It means that fantasy [S◊a] is there where the subject grasps itself, in what I pointed out to you as being
in question on the 2nd floor of the graph, under the form taken up at the level of the Other, in the field of the Other, at this point here [A] of the graph, of the ques-tion ‘What does it want?’, which is equally well the one that will take the form ‘What does he want?’ [Che vuoi?], if someone
has known how to take the place – projected by the structure – of the locus of the Other, namely – of this locus – the one who is its master and guarantor.

This means that in the field and along the course of this question fantasy has a function homologous to that of i(a), of the ideal ego, of the imaginary ego on which I rely, that this function has a dimension – no doubt sometimes pointed out
and even more than once – whose role it is for me here to remind you that it anticipates the function of the ideal ego, as the graph indicates to you by this: that it is by a sort of ‘return’ which nonetheless permits a short-circuit with respect to the intentional leading
of discourse considered as constituting – on this first level – the subject, that here, before, signified and signifier
crossing again, it has constituted its sentence, the subject imaginarily anticipates the one it designates as ‘me’ [S →i(a)→m].

It is indeed this same one no doubt that the ‘I’ of discourse supports in its function as shifter. The literal ‘I’ in discourse is no doubt nothing other than the subject itself that speaks, but the one that the subject designates here as its ideal support
is in advance, in a future anterior, the one that it imagines will have spoken: ‘He will have spoken’. At the very core of fantasy
there is likewise a ‘He will have wanted’. I do not pursue further here this opening, nor this remark, nor this reminder:
that at the start of our path in the graph I held a dimension of temporality to be implicated.

The graph is made to show already this type of ‘knot’ that we are for the moment seeking at the level
of identification. The two curves crossing in opposite directions, showing that synchronism is not simultaneity,
already indicate, in the temporal order, what we are trying to knot in the topological field.
In short, the movement of succession, signifying kinetics, that is what the graph supports.

I recall it here to show you the scope of the fact that I have not made so much doctrinal use of this temporal dimension, of which contemporary phenomenology makes great capital, because, in truth, I believe there is nothing
more mystifying than talking about ‘time’ at random. But still – here I take note of it in order to indicate it to you – it is there that we shall have to return in order to constitute from it, no longer a kinetics, but a temporal dynamics,
which we can only do after having crossed what for the moment must be done, namely:
the spatializing topological locating of the identificatory function.

This means that you would be wrong to stop at anything that I have already formulated, that I thought I should formulate
in an equally anticipatory way, on the subject of anxiety – with the supplement that Mme AULAGNIER kindly added to it the other day – so long as there has not effectively been restored, related, brought back into the field of this function,
what I have already indicated from the beginning – I can say from the article on Le stade du miroir [Écrits p.93] – which distinguished
the relation of anxiety from the relation of aggressivity, namely temporal tension.

Let us return to our fantasy and to (a), in order to grasp what is at issue in this imagification proper to its place in fantasy.
It is of course the case that we cannot isolate it without its correlative of S [S◊a], from the fact that the emergence of the func-tion of the object
of desire as (a) in fantasy is correlative with this sort of ‘fading’, of ‘vanishing of the symbolic’ which is the very thing
I articulated last time – I think in responding to Mme AULAGNIER, if my mem-ory is good – as the exclusion determined by the subject’s very dependence on the use of the signifier.

That is why it is insofar as the signifier has to redou-ble its effect in wanting to designate itself that the subject arises as exclu-sion
from the very field that it determines, then being neither the one who is designated, nor the one who designates. But with this reservation, which is the essential point, that this only occurs in relation to the play of an object, first as alternation of a presence and an absence.

What does the conjunction S and (a) first mean formally? It means that in fantasy, under its purely formal aspect, radi-cally the subject makes itself –(a), absence of (a) and nothing but that, before the (a) at the level, if you will, of what
I called ‘identification with the unary trait’.

Identification is introduced, takes place, purely and simply only in this product of –(a) by (a),
and it is not difficult to see in what way…
not simply as by a mental game, but because we are brought back to it
by something that is, for us, our mode of something that legitimately receives its formula there
…the –(a)2 = 1 that results from it introduces us to what there is of fleshly, of implicated, in this mathematical symbol of √–1.
Of course, we would not stop at such a game if we were not brought back to it by more than one route in a convergent way.

For the moment let us resume our march in order to try to designate what commands for us, in the drawing of the structure,
the necessity of accounting for the form to which desire leads us. Let us not forget it, unconscious desire as
we have to account for it, is found in the repetition of demand, and after all, from the origin of what FREUD modulates for us, it is what motivates it.

I see someone telling me ‘Well yes, of course one never speaks of that!’, with this reservation that for us desire is not justified only by being a ‘tendency’: it is something else. If you hear, if you follow what I mean to signify to you by ‘desire’: it is that we do not content ourselves with the opaque reference to ‘a repetition automatism’, we have perfectly identified it: it is the search, at once necessary and condemned, for a unique, qualified, pinned-down occurrence, as such
by this unary trait, that very one which cannot be repeated, except always by being another.

And from then on, in this movement, this dimension appears to us by which desire is what supports the movement,
no doubt circular, of demand always repeated, but of which a certain number of repetitions can be conceived

• that is the use of the topology of the torus – as completing something: the spool movement of the repetition of demand
  closes somewhere, even virtually, defining another loop that is completed by this very repetition,
  and that draws – what? – the object of desire!

What is necessary for us to formulate in this way, insofar as equally at the outset what we institute as the very basis of all our apprehension of analytic signification is essentially this: that no doubt we speak
of an oral object, anal object, etc., but that this object matters to us, this object structures what for us is fundamental in the subject’s relation to the world, in this that we always forget: this object does not remain an object of need:
it is by being caught in the repetitive movement of demand, in the repetition automatism, that it becomes an object of desire.

This is what I wanted to show you the day when, for example, taking the breast as signifier of oral demand,
I showed you that precisely because of this, eventually – it was what I had that was simplest in order to let you touch it with your finger – it is precisely at that moment that the real breast becomes, not an object of nourishment, but an erotic object, showing us once again that the function of the signifier excludes the signifier being able to signi-fy itself [S1→S2→a↓].

It is precisely because the object becomes recognizable as the signifier of a latent demand that it takes on the value of a desire that is of another register. Libidinal signification, into which people began to enter in analysis as marking all human desire, means only this, can only mean this. That does not mean that it is not necessary to recall it.

It is the factor of this transmutation that must be grasped. The factor of this transmutation is the function of the phallus, and there is no way to define it otherwise. The function of the phallus is what we are going to try to give a topological support to.
The phallus, its true form, which is not necessarily that of a penis, although it resembles it a great deal,
is what I do not despair of drawing for you on the board.

If you were capable, without succumbing to vertigo, of contemplating with some continuity the said penis I was speaking of, you might perceive that with its foreskin, it is remarkably made. That might perhaps help you notice that topology is not
the tissue-paper thing you imagine, as you will certainly have the occasion to realize.

That being said, it is doubtless not for nothing that across centuries of art history there are only representations
that are really so lamentably crude of what I call ‘the penis’. Finally, let us begin by recalling this nonetheless

• because one must not go too fast – this phallus is never so much there, and that is where one must begin, as when it is absent.
  Which is already a good sign for presuming that it is the pivot, the turning point of the constitution of every object as an object of desire.

That it is never so much there as when it is absent, it would be unfortunate if I needed to remind you of it with more than an indi-cation, if it were not enough for me to evoke for you the equivalence ‘Girl = phallus’, to put it plainly, that the omnipresent silhouette
of Lolita can make you feel. I do not need Lolita all that much; there are people who know very well how to feel
what the mere appearance of a bud on a small tree branch is. That is obviously not the phallus,
for all the same, the phallus is the phallus, it is nonetheless its presence precisely there where it is not. That even goes very far.

Mme Simone DE BEAUVOIR made a whole book in order to recognize Lolita in Brigitte BARDOT. The distance there is
between the completed blossoming of feminine charm and what is properly the spring, the erotic activity of Lolita,
seems to me to constitute a total gap, the easiest thing in the world to distin-guish.

The phallus, when did we begin here to concern ourselves with it in a way that was somewhat structuring and fruitful?
It is obviously in connection with the problems of feminine sexuality. And the first introduction of the difference in structure between demand and desire, let us not forget, is in connection with the facts discovered in all their original relief by FREUD
when he approached this subject, that is to say which are articulated in the most tightly knit way in this formula:
that it is because it has to be demanded where it was not, the phallus – namely in the mother, from the mother, by the mother, for the mother –
that through that passes the normal path by which it can come to be desired by the woman.

If indeed it happens to her that it can be constituted as an object of desire, analytic experience emphasizes this:
that the process must pass through a primitive demand with all that it carries in the occasion of something absolutely phantasmatic, unreal, contrary to nature. A demand structured as such, and a demand that continues to convey its marks
to the point that it appears inexhaustible.

And that all the emphasis of what FREUD says does not mean, that it suffices for Mr. JONES him-self to hear it,
it means that it is insofar as the phallus can continue to remain indefinitely an object of demand to the one who cannot
give it on that plane, that precisely all the difficulty rises as to its even reaching what would seem even…
if indeed God had made them ‘man and woman’, as the atheist JONES says,
so that they might be for one another as thread is for the needle
…what would nevertheless seem natural: that the phallus should first be an object of desire. It is through the entrance door, and the difficult entrance door, and the entrance door that twists the relation to it, that this phallus enters, even where it seems to be the most natural object, into the function of the object.

The topological schema that I am going to form for you consists, with respect to what at first presented itself to you
under this form of the inverted eight, it is intended to warn you of the problematic of every limitative use of the signi-fier,
insofar as through it a limited field cannot be iden-tified with that pure and simple one of a circle.

The field marked on the inside is not as simple as that, here, as what marked a certain signifier on the outside.
There is necessarily somewhere – from the fact that the signifier is redoubled, is called to the function of signifying itself –
a produced field which is one of exclusion and through which the subject is rejected into the outer field.

I anticipate and declare that: the phallus in its radical function is the only signifier, but, although it can signify itself,
it is unnameable as such. If it is in the order of the signifier, for it is a signifier and nothing else, it can be posited without differing from itself.
How can it be conceived intuitively? Let us say that it is the only name that abolishes all other nominations and that this is why
it is unsayable. It is not unsayable since we call it the phallus, but one cannot at once say the phallus
and continue to name other things.

Last marker: in our pointings-out, at the beginning of one of our scien-ti-fic days, someone [Favez] tried to articulate
in a certain way the most radical transferential function occupied by the analyst as such.
It is certainly an approach not to be neglected that he came to articulate quite bluntly, and indeed that one may have the feeling that it is something rather bold, that the analyst in his function has the place of the phallus,
what can that mean?

It means that the phallus of the Other is very precisely what incarnates, not the desirable, the ἐρώμενος [eromenos],
although its function is that of the factor by which any object whatsoever is introduced to the function of object of desire,
but that of the desiring one, of the ἐρῶν [eron].

It is insofar as the analyst is the support-presence of an entirely veiled desire that he is this incarnated ‘Che vuoi ?’.
I was recalling just now that one may say that the factor ϕ has a phallic value constitutive of the very object of desire:
it supports it and incarnates it, but it is a function of subjectivity so formidable, problematic, projected into
an alterity so radical… And that is precisely why I led you and brought you back to this crossroads, last year,
as being the essential spring of the whole question of transference: what must it be, this desire of the analyst?

For the moment, what is proposed to us is to find a topological model, a model of transcendental aesthetics
that allows us to account at once for all these functions of the phallus. Is there something that resembles that, which like that, is what is called in topology a closed surface, a notion that takes its function, to which we have
the right to give a homologous value, an equivalent value of the function of signifiance, because we can
define it by the function of the cut.

I have already referred to it sev-eral times. The cut, understand it with a pair of scissors on a rubber balloon,
an inner tube, so as to inhibit the fact that – through habits that may indeed be qua-lified as secular – in many cases
a host of problems that arise do not leap to the eyes.

When I thought I was telling you very simple things about the inner eight on the surface of a torus

and then I unrolled my torus believing that it went without saying, that I had long since explained to you that there was a way of opening the torus with two snips of scissors, and when you open the torus across you have an open belt, the torus is reduced to this:

And at that moment it is enough to try to project onto this surface the rectangle, which we would have done better to call ‘quadrilateral’, to apply onto it what we previously desi-gnated under this form of inverted eight, in order to see what happens and to what something is effectively limited, something can be chosen, distinguished between a field limited
by this cut and, if you like, what is outside, which does not go so much without saying, does not leap to the eyes.

Nevertheless, this little image that I represented to you seems to have, for some, at first impact, posed a problem.
So it is not all that easy. Next time I shall have, not only to return to it, but to show you
something of which I have no reason to make a mystery beforehand, for after all, if cer-tain wish to prepare themselves, I indicate to them
that I shall speak of another mode of surface, defined as such and purely in terms of surface,
whose name I have already pronounced and which will be very useful to us.

It is called in English – where the works are the most numerous – a cross-cap, which means something like
‘crossed cap’. It has been translated into French on certain occasions by the term ‘mitre’, with which indeed it may have a crude resemblance. This form of defined topological surface certainly carries in itself a purely speculative and mental attraction which, I hope, will not fail to hold you.

I shall take care to give you figural representations of it, which I have made numerous, and especially from angles,
which are not of course those under which they interest mathematicians or those under which you will find them represented in the few works concerning topology. My figures will retain all their original function,
given that I do not give them the same use and that they are not the same things I have sought.

Know nevertheless that what it is a matter of forming in a sensible way, in a perceptible way, is intended to include as support a certain number of reflections, and others that are expected to follow – yours on the occasion – to include
a value, if I may say so, mutative, that allows you to think the things of logic, by which I began,
in another way than the famous EULER circles keep them moored for you.

Far from this inner field [x] of the [inner] eight being necessarily, and for an entire field, excluded, at least in one topological form – a fact more perceptible and among the most repre-sentable, and the most amusing of the cross-caps in question – insofar as far from this field being a field to exclude, it is on the contrary perfectly to be kept.

Of course, let us not get carried away: there would be a way entirely simple to image it in a way that keeps it.
It is not very difficult, you need only take something that has a somewhat appropriate shape, a soft circle and, twisting it in a certain way and folding it back, to have before you a strip whose lower part would be in continuity with the rest of the edges. Only there is still this, that it is never anything but an artifice, namely that this edge is effectively always the same edge.

That is indeed what is at issue: it is a matter of knowing – very differently – whether this surface, which is in dispute for us, which comes to symbolize, aesthetically, intuitively, another possible scope of the signifying limit of the marked field, is realizable in a different way and in some sense immediate to obtain, by simple application of the properties of a surface
with which you have not, up to the present, had the habit.

That is what we shall see next time.