Identification 128

Identification 128

Jacques Lacan
雅克 拉康

11.4.62 XVII 211

When one of my obsessionals, quite recently again after having
developed all the subtlety of the science of his exercises with
respect to feminine objects to whom, as is common among other
obsessionals, he remains attached, as I might say, by what one
can call a constant infidelity: at once the impossibility of
leaving any of these objects and the extreme difficulty of
(12) maintaining them all together, and that he adds that it is
quite clear that in this relationship, in this so complicated
relationship which requires this high degree of technical
subtlety, as I might say, in the maintaining of relationships
which in principle must remain outside one another, impermeable
as one might say to one another and nevertheless linked, that, if
all of this, he tells me, has no other purpose than to leave him
intact for a satisfaction which he himself here comes to grief
on, it must therefore be found elsewhere, not just simply in a
future that is always put off, but manifestly in another space
since as regards this intactness and its purpose he is incapable
when all is said and done of saying at what this could end up in
terms of satisfaction.


We have all the same here in a tangible way, something which can
pose for us the question of the structure of desire in the most
day-to-day fashion.


Let us come back to our torus and let us inscribe on it our
Eulerian circles. This is going to necessitate – I apologise for
it – a tiny little twist which is not, even though it might
appear so to someone who comes into my seminar today for the
first time, a geometrical twist – it will be that perhaps right
at the end but very incidentally – which is properly speaking
topological. There is no need for this torus to be a regular
torus nor a torus on which we could make measurements. It is a
surface constituted according to certain fundamental
relationships that I am going to be led to remind you of, but
because I do not want to appear to go too far from what is the
field of our interest I am going to limit myself to things that I
have already initiated and which are very simple.


As I pointed out to you: on a surface like this, we can describe
this type of circle which is the one that I have already connoted
(13) for you as reducible, one which if it is represented by a
little string which passes at the
end through a buckle, I can by
pulling on the string reduce to a
point, in other words to zero. I
pointed out to you that there are
two other kinds of circle or loop
whatever size they may be because
for example this one here could
just as well have that shape there:


That means a circle which goes through the hole whatever may be
its more or less tight more or less loose shape. This is what
defines it: it goes through the hole it passes to the other side
of the hole. It is represented here in dots while the 2 is
represented in full.


This is what that symbolises: this circle
is not reducible, which means that if you suppose it to be
realised by a string still passing through this little arch which
would allow us to tighten it we cannot reduce it to something
like a point; whatever its circumference may be, there will
always remain at the centre, the circumference of what one could
call here the thickness of the torus.


If from the point of view
which interested us earlier, namely the definition of an inside
and an outside, this irreducible circle shows from one side a
particular resistance, something which with respect to other
circles confers on it an eminent dignity, on this other point
here suddenly it is going to appear singularly deprived of the
properties of the preceding one; because if you materialise this
circle that I am talking to you about for example by a cut with a
pair of scissors, what will you obtain?


Absolutely not, as in
the other case, a little piece which disappears and then the
remainder of the torus. The torus will remain entirely intact in
the form of a pipe or of a sleeve if you wish.


If you take on the other hand another type of circle, the one
that I already spoke to you about, the one which does not go
through the hole, but goes around it, this one finds itself in
the same situation as the preceding one as regards


It also finds itself in the same situation as
the preceding one as regards the fact that it is not sufficient
to define an inside or an outside. In other words that if you
follow this circle and if you open the torus with the help of a
pair of scissors, you will finally get what?


Well, the same
thing as in the preceding case: this has the shape of a torus but
it is a shape which presents only an intuitive difference, which
is altogether essentially the same from the point of view of
(14) structure. You always have after this operation, as in the
first case, a sleeve, simply it is a very short and a very wide
sleeve, you have a belt if you wish but there is no essential
difference between a belt and a sleeve from the topological point
of view, again you can call it a strip if you wish.



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