Lacan Jacques. Seminar of January 14, 1975

What I say interests--you are the proof of it--everyone. It interests me, but not as it does
everyone, and this is felt in what I say--which is why it interests everyone.
Why is this felt? Because what I say is a clearing of the way concerning my practice, and
it takes its departure from this question--which I would not ask if I did not have the answer in my
practice--what implies that psychoanalysis works?
You see here (fig. 1) a nice little four-looped Borromean knot. It is Borromean since it
suffices to cut any one of these three rounds of thread for the other three to be freed. Nothing
prevents you from making a Borromean knot as long as you like. Notice however that as it is
drawn here the number of rounds is not homogeneous, and that one can distinguish a first and a
last. The last--let us say that it is the round to the extreme right--is that which holds together the
whole chain, and makes it so that we have four there. If I proceed by the same model to make a
five-looped knot, I will have to give this last round another way of being knotted, since it will
hold one more.
In making use of rounds of thread in composing these Borromean chains, I illustrate
something that is not without relation to the sequence of numbers.
You know how, by means of some axioms, Peano articulates it. It is the function of the
successor, of the n + 1, that he stresses as structuring the whole number--which supposes
nonetheless to start with one that is not the successor of any, which he designates by zero. All
that these axioms produce will be from then on, conforming to the arithmetic requirement,
homologous to the series of whole numbers.
The knot is something else. Here in fact the function of the plus-one is specified as such.
Suppress the plus-one, and there is no more series--by the sole fact of the sectioning of this one-
among-others, the others are liberated, each as one. This could be a wholly material way of
making you feel that One is not a number, although the sequence of numbers is made of ones.
It must be admitted that there is in this sequence of numbers a consistency such that one
has the greatest of difficulties not holding it as constituant of the real. All approach to the real is
woven for us by the number. But to what is owed this consistency that there is in the number? It
is not natural at all, and it is indeed this that makes me approach the category of the real as
knotted to what I am also lead to give a consistency, the imaginary and the symbolic.
If I make use of the knot, it is because in these three something that I originate of the
symbolic, of the imaginary, and of the real, has the same consistency. It is on this basis that I
produce the Borromean knot, and this to justify my practice.
Isolating consistency as such, one has never done this. Me, I isolate it, and to illustrate it
I give you the cord.
This is to make an image. For I do not deprive myself of making images. What do we
have there on the board if not images?--the most astonishing thing about which is that you find
your bearings there. That these lines are continuous or broken, depending on whether they pass
above or below, is already miraculous. But how far do you see into this? Would you know to
say that this knot here (fig. 1) is the same as this (fig. 2)? Take it upon yourselves to fiddle with
the thing. With a chain of three, it is impossible to pass from one disposition to the other. This
could work however--but beginning with how many rounds? I will leave it to you to search for
the rule.
And I will return to consistency. Consistency is subjacent to all that we say. Is it because
of what one calls non-contradiction? I say no, and I illustrate it with these figures. They have a
consistency that I am indeed forced to call real, and which is that of the cord. It is supposed that
a cord that holds.
A metaphor? One never thinks of what there is of metaphor in the term consistency. And
what is still stronger is that I communicate this real consistency by way of an intuition that I can
call imaginary, since I make use of images.
We have here in, in our hands, with this cord, a supposed foundation of consistency,
which is indeed something other than the line.
This distinction does not however go by itself. How do we detach ourselves from the
idea that the geometric line is not without some thickness? By what could its continuity be
supported?--if not by some consistency, that is, by something that would make a cord. This idea
is at the basis of the mirages mathematicians have been fighting over for a long time. For
example, in the first dust in the eyes that the functions called continuous have been given. It
seemed that one could not construct a line which does not have somewhere a tangent, straight
line or curve. And it took time for mathematicians to awaken to this: that one could make a 16
perfectly continuous line which had no tangent. This is to say the importance, the pregnancy of
the image of the cord.
But is this indeed an image? It is not for nothing that I say to you: Hold well to the cord.
In fact, when the other end of a cord is knotted, on can hold on to it. This has to do with the real.
It is here that I have chosen to remind you that in the tenth of those good Rules for the
Direction of the Spirit, Descartes did not believe it superfluous to remark, "As all spirits are not
equally carried to spontaneous discovery by their own powers . . . we should not immediately
occupy ourselves with more difficult and arduous things, but we must first delve into the less
important and more simple arts; those above all where order reigns more, like those of the
artisans who make canvas and carpets, or those of the women who embroider or make lace, as
well as all the combinations of numbers and all the operations that relate to arithmetic and other
similar things."
There is not the least suspicion that Descartes, in saying this, had the feeling that there is
a relation between arithmetic and the fact that women make lace, even that carpet makers make
knots. Never, in any case, is he in the least occupied with knots. We already had to be quite far
into the 20th century for something to be outlined that could be called knot theory.
Knot theory is in its infancy. There are cases where it does not at all permit us to prove
whether, yes or no, the tangle you have traced is a knot. And this despite the conventions that
you might be given in advance to account for the knot as such.
To what is our maladresse with knots owed? Is it to intuition? Is it because vision
always more or less makes a surface? I demonstrate to you, these knots render tangible, that this
goes much farther than that. It is that, fundamentally, the being who speaks (and what can you
say of the others? Not much. We must wait until we have advanced farther into their sounds)--
the being who speaks is always somewhere, badly situated, between two and three dimensions.
This is why you have heard me produce this, which is the same thing as my knot: an
equivoke on the word dimension, which I write dit-mension, mension [lying] of the dit [said].
One doesn't know very well if we indeed have three dimensions in the dire, if we find it so easy
to move around there.   --assuredly we are  there, we walk. But we must not
imagine that walking has the least relation with space in three dimensions.
There is little doubt that our body has three dimensions, however much we mash it up
(créve la boudouille), but this does not prevent what we call space from always being more or
less flat. All space is flat--there are mathematicians who have made this very explicit (l'avoir
écrit en toutes lettres). All manipulation of a real is situated from there on in a space of which it
is a fact that we know very badly how to manage it outside of techniques that impose giving it
three dimensions. I add that it is striking that there is a technique--analysis--that one can reduce
it to what it apparently is, to wit, chatter, which forces my hand, forces me to weigh the question
of space as such.
In treating of space in the same fashion as is imposed by the fact of the technique, does
not science encounter a paradox? We might have the suspicion--does not matter create a
problem at every instant? A problem, as defense against advancing, is something to crush before
coming to see what it defends.