🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

(death of René LAFORGUE, this night)…

By gathering together the difficult thoughts to which we are led, on which I left you last time,
by beginning to approach through privation what concerns the most central point of the structure of the subject’s identification,
by gathering together these thoughts I found myself starting again from some introductory remark – it is not my custom
to resume absolutely ex abrupto on the interrupted thread – this remark echoed some of those strange
characters I spoke to you about last time, whom people called ‘the philosophers’, great or small.

This remark was roughly as follows: as far as we are concerned, that the subject is mistaken is certainly there,
for all of us, analysts as much as philosophers, the inaugural experience. But that it interests us, us,
is manifestly and, I would say, exclusively in this: that he can say it. And saying it proves infinitely fruitful,
and more especially fruitful in analysis than elsewhere, at least one likes to suppose so.

Now let us not forget that the remark has been made by eminent thinkers that if what is at stake in the matter is the real,
the so-called path of rectifying the means of knowledge might well – to say the least – distance us indefinitely
from what is at issue in reaching, that is to say the absolute.

For if it is a matter of the real tout court, it is a matter of this: it is a matter of attaining what is aimed at as independent of all our moorings

• in the search for what is aimed at, this is what is called absolute – cast off everything at the end, every overload therefore. It is always a more overloaded way that the criteria of science tend to establish, in the philosophical perspective I mean…
  I am not speaking of those scientists who, they, far from what one believes, hardly doubt at all.
  It is to that extent that we are most certain that they at least approach the real
  …in the philosophical perspective of the critique of science, we must – we – make some remarks,
  and specifically the term we must mistrust most, in order to advance in this critique, is the term
  appearance, for appearance is very far from being our enemy, at least when it is a matter of the real.

It is not I who had what I am telling you embodied in this simple little image:

it is indeed in the appearance of this figure that the reality of the cube is given to me, that it leaps to my eyes as reality.
By reducing this image to the function of an optical illusion, I simply turn away from the cube, that is to say from the reality
that this artifice is made to show you.

It is the same with the relation to a woman, for example. Every scientific deepening of this relation will in the end go
to formulas, like that famous one you surely know, of Colonel BRAMBLE, which reduces the object at issue,
the woman in question, to what she is precisely from the scientific point of view: an agglomerate of albuminoids, which obviously
is not very well attuned to the world of feelings attached to the said object.

It is all the same entirely clear that what I shall call, if you permit me, ‘the object-vertigo in desire’: this sort of idol, of adoration that can make us prostrate ourselves, or at least bend us, before a hand as such.
Let us even say, to make ourselves better understood on the subject of what experience delivers to us, that it is not because it is
her hand, since in a place even less terminal, a little higher up, some down on the forearm can suddenly take on for us that unique savor which in some way makes us tremble before this pure apprehension of her existence.

It is quite evident that this has more relation to the reality of the woman than any elucidation whatever of what is called sexual attraction, insofar of course as elucidating sexual attraction posits in principle that the point is to call its lure into question, whereas this lure is its very reality. Therefore, if the subject is mistaken, he may be quite right from the point of view of the absolute,
it still remains – and even for us who deal with desire – that the word error keeps its meaning.

Here allow me to give what I for my part conclude, namely to give you as completed the fruit on this point of a reflection whose continuation is precisely what I am going to advance today. I will attempt to show you
its well-foundedness: namely that it is possible to give a meaning to this term ‘error’…
in every domain and not only in ours, this is a bold assertion, but it supposes that I consider that

• to use an expression to which I shall have to return in the course of my lesson today –
  I have indeed gone all around this question
  …it can only be a matter, if this word error has a meaning for the subject, of an error in his count.

In other words, for any subject who does not count, there could be no error. This is not self-evident: one must have felt one’s way in a certain number of directions to realize that one believes – this is where I am, and I ask you to follow me –
that only this opens up the impasses, the side-passages into which one has entered around this question.
This of course means that this activity of counting, for the subject, begins early.

I have done an extensive rereading of someone for whom everyone knows I do not have affine inclinations,
despite the great esteem and respect his work deserves, and in addition the undeniable charm his person radiates,
I mean monsieur PIAGET, this is not to advise anyone against reading him!
So I reread The Child’s Conception of Number.

It is staggering that one can believe one can detect the moment when the function of number appears in a subject
by asking him questions which, in a way, imply their answer, even if these questions are put
through material that one perhaps imagines excludes the directed character of the question.

One can say only one thing, that in the end it is much rather a lure that is at issue in this way of proceeding.
What the child appears not to recognize, it is not at all certain that this is not at all due to the very conditions of the experiment.
But the force of this field is such that one cannot say there is not much to learn, not so much in the little
that is finally gathered concerning the alleged stages of the acquisition of number in the child, as in the fundamental reflections of M. PIAGET,
who is certainly a much better logician than psychologist, concerning the relations of psychology and logic.

And specifically this is what makes a work, unfortunately unfindable, published by VRIN in 1942, called
Classes, Relations and Numbers, a very instructive work, because there the structural, logical relations
between class, relation and numbers are brought out, namely everything that one later or earlier claims to find again in the child which is manifestly already constructed a priori, and quite rightly experience shows us there only what one organized
in order to find it in the first place.

This is a parenthesis confirming this: that the subject counts, well before applying his talents to any collection whatsoever, although, of course, it is one of his first concrete, psychological activities, to constitute
collections. But he is implicated as subject in the so-called relation of computus [reckoning/counting] much more radically constitutive than one wants to imagine, on the basis of the functioning of his sensorium and his motricity.

Once again here, FREUD’s genius surpasses the deafness, if I may say so, of those to whom he addresses himself, by the whole extent precisely of the warnings he gives them, and which go in one ear and out the other. This no doubt justifies
the appeal to the mystical third ear of monsieur Theodor REIK, who on that day was not at his best,
for what use is a third ear if one hears nothing with the two one already has!

The sensorium in question, for what FREUD teaches us, what is it for? Does this not mean to tell us that it serves
only for that, only to show us that what is already there in the subject’s calculation is indeed real, does indeed exist? In any case, that is what
FREUD says: with him the judgment of existence begins; it serves to check the accounts, which is all the same
a strange position for someone linked in a direct line to the positivism of the 19th century.

So, let us take things up again where we left them, since it is a matter of calculation, and of the basis, and the foundation of calculation
for the subject: the unary trait. For of course, if the function of counting begins so early, let us not go too fast as to what
the subject can know of a higher number.

It seems scarcely thinkable that 2 and 3 do not come quickly enough, but when we are told that certain so-called ‘primitive’ tribes,
near the mouth of the Amazon, were able only recently to discover the virtue of the number 4 and erected altars to it, it is not the picturesque side of this story of savages that strikes me, it even seems self-evident to me,
for if the unary trait is what I tell you, namely difference, and difference not only which supports, but which supposes
the subsistence alongside it of 1 + 1 + 1, the + is in fact there only to mark well the radical subsistence of this difference,
where the problem begins is precisely that one can add them, in other words, that 2, that 3 have a meaning.
Taken from this end, it gives a lot of trouble, but one must not be surprised at that.

If you take things in the opposite direction, namely if you start from 3, as John Stuart MILL does,
you will never again manage to recover 1, the difficulty is the same. For us here – I note this to you in passing, with our way of questioning the facts of language in terms of the effect of the signifier, insofar as that signifying effect, we are accustomed to recognizing it at the level of metonymy – it will be simpler for us than for a mathematician to ask our student
to recognize in every meaning of number an effect of metonymy virtually arising from nothing more,
and as from its elective point, than from the succession of an equal number of signifiers.

It is insofar as something happens that makes sense from the sole succession of extent X of a certain number
of unary traits, that the number 3, for example, can make sense. Namely that it makes sense, whether it has any or not.

That writing the word anden in English [Lacan’s pun: anden is written with three letters in English as ‘and’], this is perhaps, again, the best way we have to show the emergence
of the number 3, because there are three letters.

Our unary trait, we for our part do not need to ask so much of it, for we know that at the level
of the Freudian succession, if you permit me this formula, the unary trait designates something that is radical
for this originary experience: it is the uniqueness as such of the turn in repetition.

I think I have sufficiently marked for you that the notion of the function of repetition in the unconscious is absolutely distinguished from every natural cycle in this sense that what is accentuated is not its return, it is that what is sought
by the subject is its signifying uniqueness. And insofar as one of the turns of repetition, if one may say so, has marked the subject
who sets himself to repeating what he can of course only repeat, since it will never be anything but a repetition,
but with the aim, with the design, of making the primitive unary of one of its turns re-emerge.

With what I have just told you, I do not need to put the emphasis on this, namely that this is already at play before the subject knows how to count properly. In any case, nothing implies that he needs to count very far the turns of what he repeats,
since he repeats without knowing it. It is no less true that the fact of repetition is rooted in this originary unary,
that as such this unary is closely stuck to and coextensive with the very structure of the subject insofar as he is thought
as repeating in the Freudian sense.

What I am going to show you today – by an example and with a model that I am going to introduce – what I am going to show you today is this: that there is no need at all for him to know how to count for one to be able to say and demonstrate with what constituting necessity of his function as subject he is going to make an error of counting. No need at all that he know, nor even that he seek
to count, for this counting error to be constitutive of him, subject. As such, it is the error.

If things are as I tell you, you must be saying to yourselves that this error can last a long time, on such bases,
and that is quite true. It is so true that it is not only in the individual that it bears in its effect, it bears
its effects in the most radical characters of what is called ‘thought’.

Let us take for a moment the theme of thought, on which there is all the same reason to use some caution

• you know that on that score I am not lacking in it – it is not so certain that one can validly refer to it in a way
  that is to be considered a strictly generic dimension. Let us nevertheless take it as such:
  ‘the thought of the human species’.

It is quite clear that it is not for nothing that more than once I have been led, inevitably, to call into question here, since the beginning of my discourse this year, the function of the class and its relation with the universal, to the point that it is
in some way the reverse and the opposite of all this discourse that I am trying to carry through before you.

At this point, just remember what I was trying to show you concerning the little exemplary dial on which
I tried to rearticulate before you the relation of the universal to the particular and of propositions, respectively affirmative and negative.

Unity and totality appear here in the tradition as solidarized, and it is not by chance that I always return to them
in order to burst apart the fundamental category. Unity and totality, both solidarized, linked to one another in this relation
that one may call a relation of inclusion, totality being totality in relation to units, but unity being [also] that which founds
totality as such by drawing unity toward this other sense, opposed to the one I distinguish from it, of being the unity of a whole.

It is around this that this misunderstanding continues in the so-called logic of classes: this secular misunderstanding of extension
and intension of which it seems that the tradition indeed always makes more and more account, if it is true

• taking things in the perspective for example of the middle of the 19th century, under the pen of a HAMILTON[1805-1865] –
  if it is true that it was only frankly articulated starting from DESCARTES and that the Port-Royal Logic,
  you know, is modeled on the teaching of DESCARTES. Besides, that is not even true! For it is there
  for a long time already, and since ARISTOTLE himself, this opposition of extension and intension.
  What one can say is that it creates for us, concerning the handling of classes, difficulties ever more unresolved,
  whence all the efforts logic has made to go place the nerve of the problem elsewhere, in propositional quantification,
  for example. But why not see that in the structure of the class itself, as such, a new departure
  is offered to us, if to the relation of inclusion we substitute a relation of exclusion, as the radical relation?

In other words, if we consider as logically original with regard to the subject this – which I do not discover, which is within reach of a mediocre class logician – namely that the true foundation of the class is neither its extension, nor its intension:
that class always supposes classification. In other words, mammals for example, to light my lantern at once,
are what one excludes from vertebrates by the unary trait mamma. What does that mean?

It means that the primitive fact is that the unary trait can be missing, that there is first absence of mamma, and that one says:
there it can only be that mamma is missing. That is what constitutes the class ‘mammals’.

Look closely at things with your back to the wall, that is to say reopen the treatises to go around those thousand little aporias
that formal logic offers you, to perceive that this is the only possible definition of a class, if you want
to assure it truly of its universal status insofar as it constitutes at once, on one side the possibility of its nonexistence,
its possible nonexistence with this class, for you can just as validly, failing the universal,
define the class that contains no individual at all, it will nonetheless be a universally constituted class,
with the reconciliation, I say, of this extreme possibility with the normative value of every universal judgment,
insofar as it can only transcend all inductive inference, namely issuing from experience. That is the meaning of the little dial I had represented to you concerning the class to be constituted among the others, namely the vertical trait.

The subject, first, constitutes the absence of such-and-such trait. As such, he himself is the upper-right quadrant.
The zoologist, if you permit me to go that far, does not carve the class of mammals out of the assumed totality
of the maternal breast, it is because he detaches himself from the breast that he can identify the absence of breast.

The subject as such on this occasion is -1. It is from there, from the unary trait insofar as excluded, that he decrees that there is a class
where universally there cannot be absence of breast: –(–1). It is from this that everything is ordered, specifically in
particular cases, in the run of things, there is some [+1] or there is none [quadrant 4 : –1].

A contradictory opposition is established diagonally, and it is the only true contradiction that remains at the level of the establishment
of the universal-particular, negative-affirmative dialectic: by the unary trait. Everything is thus ordered in the run of things
at the lower level: there is some or there is none, and this can exist only insofar as there is constituted, by the exclusion
of the trait, the level of the all-valid or of what holds as all at the upper level.

It is therefore the subject – as was to be expected – who introduces privation, and by the act of enunciation which is formulated essentially thus:

‘Could it be that there is no breast?…’

ne which is not negative, ne which is strictly of the same nature as what is called expletive in French grammar.

‘Could it be that there is no breast? Not possible… nothing, perhaps’,

That is the beginning of every enunciation of the subject concerning the real.

In the first quadrant [1], the point is to preserve the rights of ‘nothing’ above, because it is this that creates below
the ‘perhaps’, that is to say possibility. Far from one’s being able to say as an axiom – and there lies the astonishing error of all
the abstract deduction of the transcendental – far from one’s being able to say that every real is possible, it is only from the ‘not possible’
that the real takes its place.

What the subject seeks is this real precisely as ‘not possible’, it is the exception. And this real exists, of course.
What one can say is that there is precisely only ‘not possible’ at the origin of every enunciation, but this is seen
from the fact that it starts from the statement of ‘nothing’. This, to tell the truth, is already reassured

What I would like to underscore is that here, this torus, I am speaking of it in the strict geometrical sense of the term, that is to say that according to the geometrical definition, it is a surface of revolution, it is the surface of revolution of this circle around an axis, and what is generated is a closed surface. This is important because it joins something I announced to you, in a conference—outside the series in relation to what I am saying to you here but to which I have referred since—namely regarding the emphasis I intend to place on the surface in the function of the subject. [J. Lacan: Of What I Teach, conference of 23-01-1962]

In our time, it is fashionable to envisage all sorts of spaces in multitudes of dimensions. I must tell you that, from the point of view of mathematical reflection, this requires that one not believe in it without reservation. The philosophers, the good ones, those who trail behind them a good smell of chalk like monsieur ALAIN, will tell you that already the third dimension, well, it is quite clear that from the point of view I put forward a moment ago—that of the real—it is quite suspect. In any case for the subject two are enough, believe me. This explains my reservations about the term ‘depth psychology’ and will not prevent us from giving a meaning to this term.

In any case, for the subject as I am going to define it, do understand that this infinitely flat being—which, I think, was the delight of your mathematics classes when you were in philosophy—‘the infinitely flat subject,’ said the teacher…
As the class was rowdy—and I was myself—one did not hear everything.

It is here… Well it is here that we are going to advance into ‘the infinitely flat subject’ as we can conceive it if we want to give its true value to the fact of identification as FREUD promotes it for us. And this will still have many advantages, you will see, because after all, if it is expressly to the surface that I ask you here to refer, it is for the topological properties that it will be able to demonstrate to you.

It is a good surface, you see, since it preserves, I would say necessarily… it could not be the surface it is if there were not an interior. Consequently be reassured, I am not subtracting volume from you, nor the solid, nor that complement of space of which you surely need in order to breathe.

I simply ask you to notice that if you do not forbid yourselves to enter this interior, if you do not consider that my model is made to serve only at the level of the properties of the surface, you are going, so to speak, to lose all its savor, for the advantage of this surface lies entirely in what I am going to show you of its topology, of what it brings that is topologically original in relation, for example, to the sphere or to the plane.

And if you set about braiding things inside, having to carry lines from one side to the other of this surface—I mean insofar as it seems to oppose itself to itself—you are going to lose all its topological properties. From these topological properties you are going to get the nerve, the piquancy and the savor.

They consist essentially in a support-word that I allowed myself to introduce in the form of a riddle at the conference I was speaking of a moment ago, and this word, which could not then appear to you in its true sense, is lacs [French lacs = loop/noose/lacing; echoes lacune]. You see that as we advance, I reign over my words, for a certain time I drummed your ears with lacune, now lacune is reduced to lacs.

The torus has this considerable advantage, over a surface nevertheless very good to savor which is called the sphere, or quite simply the plane, of not being at all homogeneous with respect to lacs, whatever they may be—lacs, that is lacings—which you can trace on its surface. In other words you can, on a torus as on any other surface, make a little circle, and then, as they say, by progressive shrinkings reduce it to nothing, to a point. Observe that, whatever the lacs you situate thus in a plane or on the surface of a sphere, it will always be possible to reduce it to a point.

And insofar—as KANT tells us—that there is a transcendental aesthetic. I believe in it, I simply believe that his is not the right one, because precisely it is a transcendental aesthetic of a space which is not One to begin with, and secondly where everything rests on the possibility of the reduction of whatever is traced on the surface, which characterizes this aesthetic, in such a way as to be able to be reduced to a point, in such a way that the totality of the inclusion that a circle defines can be reduced to the vanishing unity of any point around which it gathers itself.

From a world whose aesthetic is such that, everything being able to fold back onto everything, one always believes one can have the whole in the hollow of one’s hand. In other words: that whatever one draws there, one is in a position to produce there this sort of collapse which, when it is a matter of signifiers, will be called tautology.

Everything entering into everything, consequently the problem arises: how can it be that with purely analytical constructions one can arrive at developing an edifice that competes with the real as well as mathematics does?

I propose that one admit that—in a way no doubt involving concealment, something hidden that will have to be relocated, rediscovered everywhere—one posit that there is a topological structure whose being in what way it is necessarily that of the subject it will be a matter of demonstrating, and which entails that there be some of its lacs that cannot be reduced.

It is the whole interest of the model of my torus that, as you see, merely by looking at it, there is on this torus a certain number of traceable circles, that one [1], insofar as it would close upon itself, I shall call simply, for purposes of denomination, full circle. No hypothesis about what pertains to its interior: it is a simple label which I believe, my God, no worse than another, all things considered. I weighed this at length while speaking of it with my son: why not name it… one could call this the generating circle, but God knows where that would lead us!

But let us suppose then that every enunciation, of those called synthetic…
because one is especially astonished by this: although one can enunciate them a priori, they seem, one does not know where, one does not know what, to contain something, and this is what is called intuition, whose foundation one seeks in transcendental aesthetics
…let us suppose then that every synthetic enunciation—there are a certain number of them at the principle of the subject, and in order to constitute it—
well then, unfolds along one of these circles, called full circle, and that this is what best images for us what, in the loop of this enunciation, is tightened as irreducible.

I am not going to limit myself to this simple little pleasantry, because I could have been content to take an infinite cylinder, and then because if it stopped there, it would not go very far. Intuitive, geometrical metaphor, let us say. Everyone knows the importance of the whole battle among mathematicians, it rages only around elements of this species.

POINCARÉ and others maintain that there is an irreducible intuitive element, and the whole school of axiomaticians claims that we can entirely formalize from axioms, definitions and elements, the whole development of mathematics, that is to say tear it away from all topological intuition. Fortunately monsieur POINCARÉ sees very well that, in topology, that is indeed where one finds the sap of the intuitive element, and that one cannot resolve it.
And I shall even say more: outside intuition one cannot do this science called ‘topology’, one cannot begin to articulate it, because it is a great science.

There are major first truths attached around this construction of the torus and I am going to let you touch with your finger something: on a sphere or on a plane, you know that one can draw any map, however complicated it may be, called geographical, and that it is enough, in order to color its regions in a way that allows none to be confused with its neighbor, to use four colors.

If you find a very good demonstration of this truly first truth, you may bring it to the proper authority because you will be awarded a prize, the demonstration not having yet to this day been found. On the torus—it is not experimentally that you will see it, but it can be demonstrated—to solve the same problem seven colors are needed.
In other words, on the torus you can, with the point of a pencil, define up to—but not one more—seven domains, these domains each being defined as having a common boundary with the others. Which is to tell you that if you have a little imagination to see them quite clearly, you will draw these hexagonal domains.

It is very easy to show that you can on the torus draw seven hexagons and not one more, each having a common boundary with all the others…
This—I apologize for it—is to give a little consistency to my object. It is not a bubble, it is not a breath, this torus, you see how one can speak of it, although entirely, as they say in classical philosophy, as a construction of the mind, it has all the consistency of a real
…seven domains.

For most of you, not possible. As long as I have not shown it to you, you are entitled to oppose to me this not possible: why not six, why not eight? Now let us continue. It is not only that loop there that interests us as irreducible, there are others that you can draw on the surface of the torus and whose smallest is what is what we can call the most internal of those circles that we shall call empty circles[2].
They go around this hole. One can do many things with them. What is certain is that it is apparently essential.
Now that it is there, you can deflate your torus, like a balloon, and put it in your pocket, for it does not belong to the nature of this torus that it always be nice and round, nicely even. What is important is this holed structure.
You can reinflate it whenever you need it, but it can—like little Hans’s little giraffe that tied a knot in its neck—twist itself.

There is something I want to show you right away. If it is true that synthetic enunciation insofar as it maintains itself in one of the turns, in the repetition of this one, does it not seem to you that this will be easy to figure?
I have only to continue what I had first drawn for you in a solid line, then in dotted lines, this is going to make a coil.

There then is the series of turns which make in unary repetition that what returns is what characterizes the primary subject in his signifying relation of repetition automatism. Why not push the winding to the end,
until this little coil-serpent bites its tail?

It is not an image to be studied as an analyst, which exists under the pen of monsieur JONES.
What happens at the end of this circuit? It closes. There we find, moreover, the possibility of reconciling
what there is of the supposed, implied eternal return, in the sense of Naturwissenschaft, with what I stress concerning
the necessarily unary function of the turn.

It does not appear to you here, as I represent it to you, but already there at the beginning, and insofar as the subject traverses
the succession of the turns of his demand, he has necessarily made a mistake of 1 in his count, and we see here reappear
the unconscious –1 in its constitutive function. This for the simple reason that the turn he cannot count,
is the one he made in going around the torus, and I am going to illustrate it for you in an important way by what is of a nature
to introduce you to the function we are going to give to the two types of irreducible lacs, those that are full circles
and those that are empty circles, of which you can guess that the second must have some relation to the function of desire.

For, in relation to these successive turns—succession of full circles—you must perceive that the empty circles,
which are in some way caught in the rings of these loops and which unite among themselves all the circles of demand,
there must indeed be something there that has a relation to little (a), object of metonymy, insofar as it is that object.

I did not say that desire is symbolized by these circles, but the object as such that is proposed to desire. This is to show you
the direction in which we shall advance thereafter. It is only a very small beginning. The point on which
I want to conclude, so that you may well feel that there is no artifice in this sort of skipped turn that I seem
to be making you pass through as if by conjuring, I want to show it to you before leaving you. I want to show it to you
before leaving you with respect to a single turn on the full circle. I could show it to you by making a drawing on the blackboard.
I can trace a circle such that it is ready to go around the full of the torus. It will stroll around the outside of the central hole,
then return from the other side. A better way to make you feel it, you take the torus and a pair of scissors,
you cut it along one of the full circles, there it is unfolded like a sausage open at both ends. You take the scissors again
and cut lengthwise, it can open completely and spread out:

It is a surface that is equivalent to that of the torus, it is enough for this that we define it thus, that each of the points
of its opposite edges has an equivalence implying continuity with one of the points of the opposite edge. What I have just drawn for you
on the unfolded torus is projected thus:

Here is how something that is nothing but a single lacs will present itself on the torus suitably cut by these two scissor-cuts.
And this oblique line defines what we can call a third species of circle, but which is precisely the circle that interests us, concerning this sort of possible property that I am trying to articulate as structural of the subject: that although he has made only a single turn,
he has nonetheless indeed made two, namely the turn of the full circle of the torus, and at the same time the turn of the empty circle,
and that as such, this turn that is missing from the count, is precisely what the subject includes in the necessities of his own surface
of being infinitely flat that subjectivity cannot grasp, except by a detour, the detour of the Other.

This is to show you how one can imagine it in a particularly exemplary way thanks to this topological artifice, to which,
do not doubt it, I grant a little more weight than merely that of an artifice, likewise, and for the same reason, because it is the same thing as, answering a question put to me concerning √–1 as I introduced it into the function of the subject:

– ‘In articulating the thing thus—someone asked me—do you mean to manifest something other than a pure and simple symbolization replaceable by anything else whatever, or something that bears more radically on the very essence of the subject?’
– ‘Yes—I said—it is in this sense that what I developed before you must be understood’

And this is what I intend to continue to develop with the form of the torus.