🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

I was informed this morning while I was working…
as always, for everyone: at the last moment, while I am working
…I was informed that June 12…
June 12 which is not, although it is the second Tuesday, which is not
in principle the one on which I was hoping to give you an appointment
…I was informed that on June 12 the room would be occupied by what are called oral exams,
and that consequently one could not assure me of this, that it would be free at such and such an hour,
given that oral exams, one does not know how they extend, how they end, nor when.

In any case I had no intention, as I have just told you, of giving you an appointment on June 12
since it is the Tuesday of Pentecost[Laughter]. I did, however, intend to give you an appointment on June 19, the 3rd Tuesday. On June 19 the exams will continue[Laughter].

So I cannot foresee…
despite the fact that I raised, well… some objection to this system
…I cannot foresee, then, whether on June 19 I will be able to continue what I am setting forth for you this year.
You will do as you wish, you will take the chance, you will make a petition, I don’t know,
you will do what pleases you. So that is the point.

It is evident that, as it was this very morning that I was informed of it, I was not able to stew things in such a way
that I would make my conclusion today, if indeed in any of my years there is, properly speaking, a conclusion, since necessarily what I set forth for you can only ever remain up to a certain point open,
it is not my privilege; things, as each year, remain open on a certain number of points left pending.
Moreover, that will be precisely what today I will have ample occasion to develop.

I dreamed last night that when I came here, there was nobody[Laughter]. That is where the wish-character of the dream is confirmed. Although, of course, I was…
since I had already worked during the night
…I was rather outraged, since I also remembered in my dream that I had worked at four-thirty in the morning, I was rather outraged that all that should be of no use, but it was all the same the satisfaction of a wish,
namely that, from then on, I had nothing left to do but twiddle my thumbs. There!
[what fills the room is a saying, what would empty the room is that ‘everything’ had been said, that Lacan’s said had closed → wish of the dream]

I will say…
I will say, it is my function…
I will say it once again, I repeat myself…
I will say once again what pertains to my saying, and which is enunciated as ‘there is no metalanguage’.

[repetition of ‘say’→ the saying must always be taken up again → it can never close in a definitive said: there is no metalanguage].

When I say that, I am apparently speaking ‘the language of being’[Parmenides: to think is to be].
Except, of course, that, as I pointed out last time, what I am saying is what there is not.

[there is ‘saying’ only of lack]

‘Being is… – as one says -… non-being is not’[Parmenides].
There is, or there is not: for me it is only a fact of said.
One supposes being to certain words, ‘individual’ for example, or ‘substance’,
it is even made to say that: that one supposes being to the individual, among others.

[the said-mension of being is the inscription of what has been lost → non-being (the symbolic as support of the ex-sistence of a saying)] [wordplay: ‘dit-mension’ = ‘dit’ (said) + ‘dimension’]

The word ‘subject’ that I employ…
you will see, I will return to it
…obviously takes on a different accent by virtue of my discourse[discourse A].
To say everything[wish of the dream], I warn you: I distinguish myself from ‘the language of being’.
This implies that there can be ‘word-fiction’, I mean: starting from the ‘word’

[the said-mension offers the subject the structure of fantasy: S◊a, the fiction of words].
And as some perhaps remember, it is from there that I began when I spoke of Ethics.
It is not because I wrote things that function as forms of language[formalization] that I guarantee the being of metalanguage.
For that being, I would have to present it as subsisting by itself, by itself alone: language of being.

[formalization in mathemes does not resolve into a metalanguage that would make it possible to ground being, to say its substance]

Mathematical formalization…
which is our aim, our ideal—why?—because only it is a matheme,
that is to say, capable of being transmitted integrally
…mathematical formalization is writing, and it is within that that I will try to advance today.
Now it subsists, this mathematical formalization, only if, in presenting it, I use the language I use.
That is where the objection[to metalanguage] lies: no formalization of language is transmissible without the use of language itself.

[there is no metalanguage that would give the exhaustive formal principle of language, because even mathematics requires language in order to take on meaning]

It is by my saying that this formalization[cf. the α,β,γ,δ, of ‘The Purloined Letter’]—ideal metalanguage—I make it ex-sist (ex hyphen sister).
It is thus that the symbolic does not merge—far from it—with being, but that it subsists as ex-sistence of the saying.

That is what I underlined…
in the text called ‘L’étourdit’: d – i – t
…that is what I underlined, to say that the symbolic supports only ex-sistence.
[of that lost jouissance that founded being, only the ex-sisting trace remains, supported by the symbolic]

In what way? I recalled it last time, it is one of the important things I said in this exercise
that, as usual, I do, more or less in order to manage to make myself heard,
but it would perhaps all the same be important that you remember the essential.

The essential, I recalled it to you once again with regard to the unconscious: the unconscious is distinguished…
among everything that had been produced up to then of discourse
…in that it enunciates this, which is the bone of my teaching, that:
– I speak without knowing it.
– I speak with my body and this without knowing it.
– I therefore always say more than I know about it.

That is where I arrive at the sense of the word ‘subject’ in this other discourse[discourse A]:
what speaks without knowing it makes ‘I’, ‘subject’[subject → subjected], subject of the verb[being] certainly, but that is not enough to make me ‘be’.
It has nothing to do with what I am forced to put into being enough knowledge to hold, but not a drop more. And that is what up to then one called ‘form’.
In Plato, form is that knowledge that fills being.

Form knows no more than it says. [identity of being with itself (consistency) → ‘everything can be said’]
It is real—have I just said—in the sense that it holds being in its grip, but right up to the brim[nothing is lost: no remainder].
It is the knowledge of being. The discourse of being[Parmenides] supposes that being knows, and that is what holds it[discourse M: S2 holds a].

There is a relation of being that cannot be known; it is that whose structure, in my teaching,
I question insofar as that knowledge—as I have just said—impossible, is thereby ‘inter-dit’.
[discourse A: the S1, asemantic signifiers, are cut off from knowledge: S1◊S2]

And it is here that I play on equivocation, on the equivocation that, from that impossible knowledge, tells us that it is ‘censored’, ‘forbidden’.
It is not[censored, forbidden], if you properly write this inter-dit, with a hyphen between the inter and the dit,
it is that it is said ‘between’ the words[ex-sistence], between the lines, and that is what it is a matter of enunciating:
to what sort of real it gives us access.

It is a matter of showing where its forming goes, this metalanguage that is not, and that ‘I’[subject of discourse] make ex-sist[through discourse]. What cannot be demonstrated suggests something that can truly be said about the subject,
for example—among other things—about the undemonstrable.

Thus opens this sort of truth, the only one accessible to us[to the analyst], and which bears, for example,
on not-knowing-how-to-do. I don’t know how to go about it—why not say it—with truth any more than with woman, since I said that the one and the other, at least for man, were the same thing, it makes the same embarrassment.
It happens—it is accidental—that I have a taste for the one as well as for the other, despite everything that is said about it[Laughter].
This discordance of knowledge and being[discourse A: S1◊ S2], that is our subject.

That does not prevent one from also saying that there is no discordance as to what runs the show,
according to my title this year, ‘Encore’. It is the insufficiency of knowledge by which we are still caught,
and it is by that that this game of ‘en-corps’ is conducted, not that knowing more would lead us better,
but perhaps there would be better jouissance, an accord of jouissance and its end. [wordplay: ‘Encore’ (again/still) echoed in ‘en-corps’ (in-body)]

Now ‘the end of jouissance’…
that is what everything Freud articulates teaches us, from what he thoughtlessly calls ‘partial drives’
…‘the end of jouissance’ is ‘beside’ what it comes to, namely that we reproduce ourselves.

The ‘I’ is not a being; it is a ‘supposed to what speaks’.[S: subject, subjectum: sub-posed, ὑποχείμενον: upokeimenon]
‘What speaks’ has to do only with solitude[i.e. the ex-sistence::§, what speaks does not find the Other but objects(a)] at the point of the relation[sexual],
which I can define only by saying, as I did: that it cannot be written[‘what does not cease not to be written’].

This solitude, it, of rupture of knowledge, [the ex-sistence::§, S1 does not find the Other → cut off from knowledge S2] not only can it be written, but it is even what is written par excellence: what from a rupture of being leaves a trace.[division of ‘being’ between S and a: S◊a]
That is what I said in a text, certainly not without imperfections, that I called ‘Lituraterre’:

‘The cloud of language—did I express myself metaphorically—makes writing.’

Who knows whether the fact that we can read these rivulets that I was looking at, on the way back from Japan, over Siberia [cf. 12-05-1971]
as a metaphoric trace of writing, is not linked…
‘lier’ and ‘lire’, they are the same letters, pay attention to it [wordplay: in French, ‘lier’ (to link) and ‘lire’ (to read) share the same letters]
…is not linked to something that goes beyond the effect of rain, which there is no chance the animal reads as such?

Rather, is it not linked to this form of ‘idealism’[fiction of words] that I would like to get into your head:

– not, certainly, the one Berkeley speaks of, living in a time when the subject had taken its independence[discourse M→H],
– not that everything we know is representation,

…but rather this idealism that pertains to the impossible of inscribing the sexual relation between two bodies of different sexes.

[fiction of words, said-mension, such as ‘sexual relation’, relation not to the Other but to the same, to ‘partial objects’: object(a)]

It is through that[the object(a)] that the opening is made by which it is ‘the world’ that comes to make itself our partner.
It is the speaking body insofar as it can only manage to reproduce itself thanks to a misunderstanding about its jouissance,
and that is to say that it reproduces itself only thanks to a failure of what it wants to say.

For what it wants to say[i.e. to catch, to seize by speech the speaking body of the object(a), that ‘thing of jouissance’ (lost) heterogeneous to any language],
as French says well: its sense, is its effective jouissance, and it is by missing it, that is, by fucking,
for that is precisely what it does not want to do, in the end[cf. also ‘courtly love’].

The proof is that, when one leaves it all alone, it sublimates all the time like mad: it sees Beauty, the Good,
not counting the True; it is still there, as I have just said, that it is closest to what is at issue.

But what is true is that the partner of the other sex remains the Other,
so it is by missing it that it succeeds in still being[and en-corps] reproduced, without knowing anything of what reproduces it.

[‘what reproduces it’: the en-corps of reproduction,
‘what reproduces it’: the ‘encore’ of the reiteration of the saying → ‘seize’ the impossible to ‘seize’]

Notably…
this is in Freud perfectly perceptible,
of course it is only a stammering but we cannot do better
…he does not know whether what reproduces him is life[‘the being of jouissance’: existence] or death[‘the being of the symbolic’ (writing): ex-sistence].
I did not say: ‘what he…’, q.u. apostrophe i.l.; I said: ‘what reproduces him’, words separated.

Yet I must say ‘what there is of’ metalanguage, and in what it merges with the trace left by language.
[through language, a trace is written (α,β,γ,δ) of each of the object identifications, this trace that ex-sists founds a combinatorics: ‘lalangue’→ what there is of ‘metalanguage’]

It is by that that it returns to the revelation of the correlate of language, that knowledge in excess[S2] of being, its little chance of going to the Other, of which I nevertheless pointed out last time—and that is the other essential point—that it is, that knowledge in excess, passion of ignorance
and that precisely it is of that that he wants to know nothing: of the being of the Other[a] he wants to know nothing.
[discourse (H): S2◊a, knowledge inter-dit, discourse (A): S1◊ S2, ignored knowledge].

That is precisely why the two other passions are those called:

– love, which has nothing to do—contrary to what philosophy has concocted—with knowledge,
[philosophy aims at the Other, S(A), which it seeks to complete, but it reaches only a in place of S(A)]

– and hate, which is indeed what has the most relations with being, what comes closest to it, that I call ex-sisting. Nothing concentrates more hate than that ‘saying’ where what I call ex-sistence is situated.

Writing is a trace in which an effect of language is read…
when you scribble something—me too, I certainly don’t deprive myself of it:
it is with that that I prepare what I have to say, and it is remarkable that, of writing, one must make sure
…it is not metalanguage, although one can make it fulfill a function that resembles it, but which nonetheless remains…
with respect to the Other, where language is inscribed as truth
…which nonetheless remains entirely secondary.

For nothing of what I could write on the board—general formulas that link, at the point we are at, energy to matter…
for example the latest formulas of Heisenberg
…nothing of all that will hold, if I do not support it
– by a saying that is that of the language,
– and by a practice that is that of people who give orders in the name of a certain knowledge[discourse U].

So when you scribble, well, as one says it is always on a page and it is with lines.
And there we are plunged right away into the history of dimensions.

– As what cuts a line is the point, and the point has 0 dimension, the line will be defined as having two[lapse]. As what cuts… The line will be defined as having 1!

– As what the line cuts is a surface, the surface will be defined as having 2.

– As what the surface cuts is space, space will have 3.

Only it is there that the little sign I wrote on the board takes on its value.

I mean the one that I must distinguish from the one that I wrote below it; they are separate.

You can note that it is something that has all the characteristics of writing; it could just as well be a letter. Only, since you write cursively, it does not occur to you to stop the line before it meets
another one, to make it pass under, to suppose it passes under, because in writing it is a matter of something quite other
than three-dimensional space. This line cut here, I said, means that it passes under the other,
here it is above, because it is the other that is interrupted.

That is what produces—even though there is here only one line—this thing that is distinguished from what would be a simple circle,
a string circle if that existed; it is distinguished in this sense that although there is only one string, it makes a knot.

It is nevertheless quite something else—this line—than the definition we gave of it a moment ago
with respect to space, that is, in sum, a cut: what makes a hole, an inside, an outside of the line.

This other line, this string as I called it, does not become embodied so easily in space.
The proof is that the ideal string, the simplest, would be a torus.

And it took a very long time to realize, thanks to topology, that what is enclosed in a torus
is something that has absolutely nothing to do with what is enclosed in a bubble[sphere].

It is not a matter of cutting the torus, for whatever you do with the surface of a torus, you will not make a knot.
But, on the other hand, with the place of the torus, as this demonstrates to you, you can make a knot.
That is why, allow me to tell you: the torus is reason[Laughter], it is what makes the knot possible.

That is indeed why what I am showing you, this twisted torus, is the image, as simple, as bare as I can give it to you, that I evoked the other day as the trinity: 1 and 3 in a single stroke.

→

It nonetheless remains that it is by remaking three tori, by the little trick that I have already shown you under the name
of ‘Borromean knot’, that we will be able to operate, to say something about what it is to use the first knot.

Naturally, there are some who were not there when I spoke—last year, around February—of the Borromean knot.
We will try today to make you feel the importance of this story,
and in what it has to do with writing insofar as I defined it as ‘what language leaves as a trace’.

The Borromean knot consists in this: we are dealing with what is seen nowhere, namely a true string circle. Because imagine that when one traces a string, one never manages to have its trace join its two ends.
For you to have a string circle, you have to make a knot, preferably a sailor’s knot.[Laughter]

I don’t know what that does to you… Ah, let’s make the sailor’s knot… if you think it’s easy[Laughter], try it yourself,
it always causes a certain embarrassment.[Laughter]
Well, anyway, I tried these days to get used to it[Laughter], and there is nothing easier than missing it[Laughter]. There![Laughter and applause]

Thanks to the sailor’s knot, you have there a string circle.

The problem posed by the Borromean knot is this: how to do, when you have made your string circles,
so that… so that something like what you see at the top, namely a knot,
so that these three string circles hold together and in such a way, in such a way that if you cut one,
they are all free, I mean the three?
The three, which is nothing, for the problem is to make it so that with any number, any number of string circles, when you cut one, all the others, without exception, are henceforth free, independent.

Here, for example, is the case. I already, last year, put that on the board. Naturally, I made a small mistake[Laughter]…
It is not entirely satisfactory but it is going to become so; nothing is easier in this order than making a mistake. Another mistake… As you see it there, as you see it there inscribed, it is easy for you to see
that since these two string circles are constructed in such a way that they are not knotted to one another,
it is only by the 3rd that they hold.

That is what, curiously, I did not manage to reproduce with my string circles[Laughter]. But thank God,
I nevertheless have another way of doing it than reproducing what I did on the board, namely missing it.
I will immediately give you the means, in a completely rational and understandable way…
There! So here is a string circle. Here is another.
You pass the second circle through the first, and you fold it like this:

It will then suffice that, from a third circle you take the second, for these three to be knotted, and knotted in such a way that it obviously suffices that you cut one of the three for the other two to be free.[Laughter]

Suppose, suppose dear friend[Lacan addresses the person handling the string circles] that I take away this one from you.
It is that one you want? It is exactly the same thing for the simple reason that that one,
which I represented to you as folded and which in sum has two ears, through which the 3rd passes,
it is absolutely symmetric on the other side, namely that with respect to the 3rd, it also has two ears that take the 1st.

Not only this, do not think, you know, that it is useless, is it, all these little botchings,
it is not so familiar that the way I managed to explain it, precisely with failures,
would not be what can get it into your head, because I have to show it to you because after all,
it is only like that that it can get in!

After the first folding, you can with the third—provided here you make a knot—make a new folding,
and to this one a fourth, a fourth which is like the first, being added. You see that it remains just as true with four as with three, that it suffices to cut one of these knots for all the others to be free among themselves.

You can put an absolutely infinite number of them, it will always be true.

Nevertheless, this story, which makes the Borromean knot simple in the sense that here, for example, you can perfectly touch in what way it is the two parts of this element that make ‘ears’, this one and this one,
and that, in sum, by pulling it with the other, it is this circle that folds in two; here and here pass, are the two ears,
so that that circle there, which will go there, leaving the one that we can on this occasion, but only on this occasion, call first, which will remain in the state of a circle, a ‘support’ circle, first folded circle.

With this, in a way, sensible intuition of the function of the circles, you can observe that it suffices to cut
any one whatsoever—whether it is one in the middle or one of the two ends—for everything there is of folded knots,
at the same time, to be freed from among themselves.

The solution is therefore absolutely general. That does not mean that, for any number whatsoever of string circles,
one will be able to make a disposition as… well, relatively elegant by its relative symmetry, as the one I made
on the board, namely that these three circles are strictly, relative to one another, of an equivalent form;
it will certainly be more complicated—and this as soon as we have reached four; this will very often show us
the effects of twisting that do not allow us to maintain them in the state of a circle.

Nevertheless, what I want to make you feel on this occasion is that starting from the circles,
we are dealing with something that is distinguished only by being the One. It is very precisely, moreover, in that respect that
a true string circle without a knot is very difficult to make, but it is certainly the most eminent representation
of something that is supported only by the One, very precisely in the sense that it encloses nothing but a hole!

And why did I, in former times, bring in the Borromean knot?
It is very precisely in order to translate the formula:

• I ask you—what?[oral object(a): H]
• to refuse what—what?[anal object(a): M]
• what I offer you[scopic object(a): U] »
  …that is to say something that, with respect to what is at issue…
  and you know what it is: namely the object(a)
  …the object(a) is no being.

The object(a) is what a demand supposes as empty, a demand that, in the end, it is only by defining it as situated by metonymy, that is to say by the pure continuity assured from the start to the beginning of the sentence,
that we can imagine what it can be for a desire that no being supports,
I mean that is without any other substance than that which is ensured by the knots themselves.

And the proof is that, enunciating this sentence ‘I ask you to refuse what I offer you…’, I could only motivate it by this:
‘it is not that’ that I spoke of, that I took up again last time, and which means that in the desire of every demand,
there is only the request for that something which, with respect to jouissance that would be satisfying,
which would be the Lustbefriedigung supposed in what is called—also improperly in psychoanalytic discourse—‘the genital drive’, the one in which a relation would be inscribed that would be the full relation, the writable relation,
between what pertains to the One and what remains irreducibly the Other.

That is why I insisted on this: that the partner of this ‘I’ which is the ‘subject’, subject of every sentence of demand,
that this partner is not the Other, but that something which comes to substitute for it in the form
of this cause of desire[(a) semblance of sexual relation], which I thought I could diversify—not without reasons—into 4,
insofar as they are constituted according to the Freudian discovery, insofar as they are constituted diversely:
– of the object of sucking,
– of the object of excretion,
– of the gaze,
– and likewise of the voice.
It is insofar as substitutes for what pertains to the Other that these objects are claimed, are made the cause of desire.

As I said a moment ago, it seems that the subject represents inanimate objects to itself,
very precisely as a function of this, that there is no sexual relation.
There are only speaking bodies—I said—that make themselves an idea of the world as such.

And at this point one can say it: the tale, the world as such, the world of being full of knowledge, is only a dream,
a dream of the body insofar as it speaks: there is no knowing subject.
There are subjects who give themselves correlates in the object(a), correlates of jouissant speech insofar as jouissance of speech.

What else does it jam, what other Ones?
For I pointed it out to you a moment ago, it is clear that this ‘bi-lobulation’, this transformation of the string circle into ears, can be done in a strictly symmetrical way. It is even what happens as soon as one reaches the level of 4,
that is to say that the two circles that my fingers represent at the end of these would be in function; there would be 4.

Reciprocity, to say everything, between the subject and the object(a) is total. For every speaking being, the cause of its desire is strictly, as to structure, equivalent, if I may say, to its fold, to what I called its division of subject.
And that is indeed what explains to us that for so long the subject could believe that the world knew as much as it did,
it is that it is symmetrical, it is that the world, what I called last time thought,
is the equivalent, is the mirror image of thought.

That is indeed why the subject, insofar as it fantasizes, there has been…
up to the advent of the most modern science
…there has been nothing but fantasy as to knowledge.

And that is indeed what made possible this ‘scale of beings’, thanks to which there was supposed, in a being called ‘supreme being’,
what was ‘the good of all’.
Which is likewise the equivalent, the equivalent of this, that the object(a) can be said—as its name indicates:
– write the a in parentheses: (a),
– put sexed after: (a)sexed,
– and you have that the Other presents itself to the subject only under an (a)sexed form.

That is to say that everything that has been the support, the support-substitute, substitute of the Other under the form of the object of desire,
everything that has been made of this order is (a)sexed. And it is very precisely in that the Other as such remains…
not without our being able to advance a little further into it
…remains in doctrine, Freudian theory, a problem, the one that was expressed in what Freud repeated:
‘What does the woman want?’ The woman being, on the occasion, the equivalent of truth.
That is why this equivalence that I produced is justified.

Can we not nevertheless by this route, this route of what I distinguished as the One to be taken as such, in the sense that there is nothing else in this figure of the string circle, which nevertheless has its interest in offering us,
in offering us the something that writing no doubt reaches.

The requirement, indeed, that I produced under the name of Borromean knot, namely to find a form,
this form supported by this mythical support that is the string circle.
Mythical, I said, for one does not make a closed string circle; that is a completely important point.

What is this requirement that I enunciated under the name of Borromean knot?
It is very precisely this that distinguishes what we find in language, in ordinary language,
and that supports the very widespread metaphor of ‘the chain’. Contrary to string circles, chain elements are forged.

[The chain: each ring comes to fill the emptiness of the ring that precedes it and thus plug the hole with ‘an object of the world’.
The Borromean knot: the three rings knot without any one coming to plug the hole, but the knot is knotted]

It is not very difficult to imagine how it is done: one twists metal until the moment one can manage
to weld it, and the chain is thus something that can have its function to represent the use of language.
No doubt it is not a simple support; one would have to, in this chain, make links that would go and hook
onto another link a little further on, with two, three floating intermediate links,
and also understand why a sentence has a limited duration.
Now all this, the metaphor cannot give it to us.

It is nevertheless striking that in taking the supports of string circles that I told you, there were all the same,
in what I made sensible to you, a first and a last. This first and this last were simple circles
that crossed, pierced, if I may say, the two that I call…
you see the difficulty of speaking of these things
…what I call ‘ear lobes’, folded circles; they were therefore two simple knots, which in the end turned out
to make something like the beginning and the end of the chain.

This remains, this remains: that these two circles, initial and terminal, nothing would prevent us from conflating them,
namely that, having undone them…
‘undone’ is imaginary: to unmake them
…to have just one pass through, taking the four lobes thus summed up in a case where there are only two,
but the situation would be exactly the same if there were an infinite number.

A thing to note: we would not—to put it quickly—we would in this case still nevertheless have a difference.
It is not because we would have joined the last two knots that all the articulations would be the same,
for here they are opposed two by two, so there are four strands to knot, whereas here, taking my single circle, you would have the support of this circle and four strands to pass, which would make an opposition not of 2 to 2 that make 4, but of 4 to 1 that make 5.

And so one could say that even what would then—since here you have only two elements—the 3rd element,
the 3rd element in its topological relation, would not have the same relation with the other two as the other two have between themselves, and as such—by simple inspection of the knots in junction—the 3rd element would be distinguished from the others.

I think I have said enough about the symmetry of the relations of the 1st and the 2nd, since the last I called 3rd.
This symmetry still holds, this symmetry still holds if you unify the 3rd circle with any one of the other two,
simply you will then have a figure like this, the one that opposes a simple circle to what I call the inner eight.

You will therefore have had the vanishing of the Other, but at the price of the arising of something that is the inner eight
and which—as you know—is that in which I support the Möbius strip. In other words, that in which
—in a strict support of this route that I am trying to clear for you of the function of the knot—is expressed by the inner eight.

I can here only set it in motion—why?—because I still have to advance something that seems to me, before
I leave you, crucial. If I gave you the solution of Borromean knots by this threading of chains, in the form
of these circles that become totally independent provided you cut just one, what can this be used for?
Contrary to what you see in language, namely what is very simply materialized for you,
and what is also not very difficult… not very difficult to find an example of—and not for nothing—in psychosis.

Remember what hallucinatorily populates Schreber’s solitude: ‘Nun will ich mich…’,
which I translate: ‘now I am going to…’—it is a future. Or again ‘Sie sollen nämlich…’: ‘you, for your part, must…’.
These interrupted sentences that I called code messages, these interrupted sentences leave suspended I know not what substance.

What can serve us in this requirement of a sentence whatsoever, which is such that, having sectioned the One,
that is to say removed the One from each of its links, all the others at the same time are free. Is that not
the best support we can give for what proceeds by this language that I called ‘mathematical’?

The proper thing of mathematical language, once it is sufficiently tightened as to its requirements of pure demonstration, is very precisely this: that everything that advances in it…
advances in it not so much in spoken commentary, but in the handling of letters
…supposes this: that it suffices that one does not hold for all the rest, all the rest of the other letters,
not only to constitute by their arrangement nothing valid, but to disperse.

And it is very precisely in this that the Borromean knot can serve us as a better metaphor as to what it is with a requirement that is this: that we proceed only from the One. The One generates science, not in the sense
[End of the recording] in which anything is measured by it[the ‘1’ unit of measure]; it is not what is measured in science, contrary to what one believes, that is important.

What makes the original nerve, what distinguishes science—modern science—
from the science of reciprocity between νοῦς[nouss] and the world, between ‘what thinks’ and ‘what is thought’,
is precisely this function of the One, insofar as the One is there, we can suppose, only to represent
– what pertains precisely to the fact that the One is alone,
– that the One truly knots with nothing that resembles the sexual Other,
contrary to the chain between ones that are all made in the same way, of being nothing other than the One.
When I said there is One and I insisted on it, that I really trampled on it like an elephant throughout all last year, you see what I am clearing and what I am introducing you to.

How then somewhere to posit as such the function of the Other, how…
if up to a certain point it is simply knots of the One
that support what remains—when it is written—of all language
…how to posit a difference? For it is clear that the Other does not add to the One; the Other only differs from it.

If there is something by which it[the Other] participates in the One, it is that, far from adding,
what is at issue concerning the Other is…
as I already said, but it is not certain you heard it
…that the Other is the One less.

That is why in every relation of a man with a woman, the one who is at issue is under the angle of the One less that she must be taken. I had already indicated that to you a little with regard to Don Juan, but of course
there is only one person, I think—my daughter, namely—who noticed it.

Nevertheless, simply today to set in motion what else I could tell you, I am going to show you something. For it is not enough to have found a general solution as to what the problem is for an infinite number
of Borromean knots; we would have to have the means to show that it is the only solution.

Now we are at this: that to this day there is no knot theory.
What does that mean? It means this: that very precisely, to the knot there applies to this day
no mathematical formalization that would allow…
apart from a few small fabrications, small examples such as those I showed you
…to foresee that a solution, the one I have just given, is not simply an ex-sisting solution,
but that it is necessary, that it does not cease—as I say to define the necessary—that it does not cease to be written.

Now it suffices that right away I show you something that of course I could not write on the board,
because you don’t know the fuss it gives me to put all that on paper in a way that I keep at your disposal, which will likewise be photographed in a forthcoming article, but which demands a certain[fuss].

It suffices that I do this to you:

eh, annoying that the others, the other knots, are there
…look at this: I have just passed two of these circles through one another, in such a way that they make here,
not at all the folding that I showed you a moment ago, but simply a sailor’s knot.

As they are by that very fact…
since I have just arranged them closed
…as they are by that very fact perfectly separable from one another, you must think that, if simply…
which is just as possible for me
…I make—with a circle that follows—the same sailor’s knot, it suffices that I bring close to those another…
there is the sailor’s knot
…here I can do the same thing with a 3rd circle, I will still have a sailor’s knot.

It does not matter whether it is face to face with the 1st or whether it is strictly in the line, that is to say that what passes in front passes in front also of the next—I can make an infinite number of them and even close the circle that that will make,
close it simply for the last.

For the last, of course, it will not be separable; I will have to pass this last one between the two at the end
of what I will already have constructed, and pass it by making a knot,
and not by introducing it as I have just done for those two.

It will nevertheless remain that here is another solution just as valid as the 1st,
for if I section any one whatsoever of those that I will have arranged thus, all the others at the same time will be free,
and yet it will not be the same sort of knot.

I passed you, on the occasion, this: that a moment ago, for the knot that I showed you thus,
by telling you that likewise there was some necessity that the one in which I joined the 1st and the last circle,
some necessity of a difference, there is, in reality, none.

For I point it out to you, at the moment when I have just shown you the others,
namely what I called the shaping of sailor’s knot, you see very well from this that even the last…
this last that I told you that the confrontation was of 1 to 4,
and that at the same time there were 5 strands in play
…that even the last I can make exactly similar to all those, that there is no difficulty in that,
and that thus I will also in this way have resolved, without introducing any privileged point, the question of the Borromean knot, for a number x and likewise infinite of string circles.

Is it not in this possibility of difference…
For you feel well that there is no topological analogy
between one and the other of these ways of knotting string circles
…is it in this different topology…
one that we can express here with respect to sailor’s knots as a topology of twisting, let us say,
as compared with the others that would be simply of bending
…is it that we can use this for…
for it would not be contradictory even to take this in a sailor’s knot; it is very easy to do,
try it, exactly here is the way the bent thing is taken as a sailor’s knot
…where to put the limit of this use of knots to arrive at the solution that this, the section of any one whatsoever
of these string circles entails the freeing of all the others, that is to say gives us the model of what it is
starting from this mathematical formalization, the one that substitutes for the function of any number whatsoever of Ones
what one calls ‘a letter’. For mathematical formalization is nothing else.

That you write that something, that you write that something, that energy is 1/2mv2.
What does that mean? That means that whatever the number of Ones you put under each of these letters, you are subject to a certain number of laws that are group laws such as addition, multiplication…

That is the question I open and which is made to announce to you—if possible, which I hope—
what I can possibly transmit to you concerning what is written.
– What is written, in sum—what would that be?—the conditions of jouissance,[the letter]
– and what is counted—what would that be?—the residues of jouissance![(a)]

For likewise this a, a-sexed, is it not by joining it with what she has most of jouir, being the Other…
of being able to be said only Other
…that woman offers it under the species of the object(a)?

Man believes he creates…
believe that I do not say that at random
…he believes, believes, believes, well, he creates, creates, creates, and he creates, creates, creates woman.

Yeah! In reality he puts her to work, but to the work of the One[The Woman → Lfemme → (a)] and that is indeed wherein this Other…
insofar as the articulation of language is inscribed there, that is to say truth
…the Other can be barred, barred by this that I qualified a moment ago as ‘the 1 less’,
where the S of A, of A insofar as it is barred[S(A)], that is indeed what that means,
and that is how we come to pose the question of making of the One something that holds,
that is to say that is counted without being. [‘…qualify as the One[…] what has 0 dimension, that is to say what does not exist.’ S20 p. 119]

Mathematization alone reaches a real…
and that is how it is compatible with our discourse, analytic discourse,
…a real that precisely escapes[ex-sists], that has nothing to do with what traditional knowledge has supported,
that is to say not what it believes: reality, but indeed fantasy.

The real is the mystery of the speaking body, it is the mystery of the unconscious.