The Topological
Dénouement of the Cure
Underconstruction
The
following article was rejected for publication by
the Buffalo Center of Psychoanalysis as being "incomprehensible"
to the audience of their journal Umbra (which we
were informed addresses a type of understanding peculiar to
students of critique and literature). Be that as it may,
others less hampered by such strictures will find below, for
the first time in the English language, an introduction to Lacan's
generalization and extension of the psychoanalytic cure. R.G.
Historical Background
If Jacques Lacan had been
interrogating the limits of Freudian psychoanalysis
from the beginning, it was not until 1956 with D’une
question préliminaire a' tout traitement possible de
la psychose ( Of A Preliminary Question To Any Possible Treatment
of Psychosis) that he showed the necessity of reformulating
the problem in a topological presentation that went beyond
an "abstract theory of the faculties of the subject"
1 .
Although Lacan continued
to purify what he called the "ideology of psychoanalysis"
through a topology of surfaces, it was not until February
9th 1972, in his seminar Ou Pire, that he changes
to a theory of knots and announces his discovery of the Borromean
Rings. What remains invariant in this transformation is the
insistence that the use of such topological structures consists not
in illustrating the theory of psychoanalysis, but of initiating
a practice of psychoanalysis itself:
For is not structuralism
what permits us to pose our experience as the field
where it speaks? If yes, "the distance to experience" of structure
disappears since it [the structure] operates not as a theoretical
model, but as the original machine which puts in scene the subject.
(Remarques Sur La Rapport De Daniel Lagache, Lacan, 1958-60)
By the time of R.S.I.,
Lacan corresponds the three closed chords of the Borromean
Lock to the Real, Symbolic, and the
Imaginary, while noting this tertiary grouping
of rings was only a minimum and required a fourth ring
∑ (in black) that was only implicitly indicated
in Freud's use of the term psychic reality 2.
Further still, by explicitly equating this fourth ring with
the Nom-du-Pere and the Oedipus complex Lacan isolates it as what
analysis comes to operate on: "To be knotted otherwise, this is what
is essential to the Oedipus Complex and it is precisely on what analysis
operates." (R.S.I., January 14th 1975)
∑
fig. 1
Four Ring Borromean
Lock
Previously, Lacan had noted
that the ethics of psychoanalysis would depend on introducing
something 'useful' precisely at the point not only of
the failures of his Ecole, but analysis itself
(Preliminary to the Seminar of R.S.I., November
9th 1974). By doing so, Lacan began not only to render account
of the ideals of psychoanalysis (its possibilities and
psychotherapies) and its closures (its applications and
techniques in the Heideggerian sense), but to open up a place
for the treatment of the aporias of its cure.
Statement of the
Problem: From Aporia to Structure
In the contemporary scene of Lacanian psychoanalysis, we are faced
with a double obstacle of a too contextual understanding
of psychoanalysis and a completely de-contextualized understanding
of its relation to topology.
On one hand, we have the infinite psychoanalytic histories describing
the nature of its aporias - the incomplete nature of Freud's
analysis of neurosis, the impossibility of analyzing psychosis
and perversion, negative therapeutic reaction, etc.- and
the repetitive epistemological investigations into the nature
of its impostures, immaturity, and psuedo-scientificity.
Our introduction here is less ambitious in its scope, yet has the
advantage of allowing us to situate what is crucial: the structural
and operatory modes that a discontinuity of such natural themes
refer to. For this reason our entry is only superficially historical
or epistemological, for if it were, our analysis would remain
at the level of a succession of themes natural to psychoanalysis.
Our introduction is different in so far as it focusses on the manner
in which not only Lacan's topology, but a theory of psychoanalysis
resists such historical and epistemological accounts. It is
this resistence that is necessary to listen to and translate in the
presentation of a theory and practice of analysis.
On the otherhand, we have become
use to those who bravely state that a Borromean falls
apart — or unlocks — when anyone of its three components
is taken away or cut, while never explaining why any of this
should be significant to the aims and goals of the analytic
cure in the first place. For if it were not only with
a bit less haste, surely they could find the time to report
why Lacan never tired of explaining the real problem was to be
found in how the fourth ring of the Sinthome
– Psychic Reality, Oedipus Complex, or Name
of the Father — comes to bear in this problem of unlocking.
My short intervention cannot hope here to resolve this two sided
figure of understanding too much too quickly. Rather
it suffices that we isolate the problem and decipher the reasons
for such complacency, while laying out a few landmarks so
that the reader may begin to orient themselves differently.
One should begin, for instance, with the December 16th 1975 seminar
of Lacan's Sinthome in which he had already
formulated a topological movement that would not only
undo a knot, but also unlock the four ring Borromean lock
by allowing the fourth ring to slip off 3.
In so doing, Lacan isolates a separation from the Sinthome
that was only avoided by the traditional attempts to describe
the aporias of the psychoanalytic cure negatively and not as a positive
moment of dé-nouement. For surely the Gordian problem
is to show that to un-tie a knot – or Sinthome -
is not to non-tie or cut a knot, but more positively to tie
one by adding its per-verse . Without these precautions,
the psychoanalytic in-curable looses its structure
and effectivity, while trivializing into the morbid consciousness
of the non-curable.
What is difficult for some to admit, in the way I have just spoken,
is that a psychoanalytic theory would be able to disengage
itself from the themes that have become so natural and intuitive
to its practice. It would be wrong, however, to allow
oneself to be intimidated by such a separation, as it can
serve here as a guide since it bears witness to a moment of psychoanalytic
history that has become incomprehensible to scholars and psychoanalysts
alike. Far from being an obstacle, it is an indication
of how one can learn from a psychoanalytic theory to read its
history: a moment when the Lacanian introduction of topology,
before being develloped in and of itself, was conceived as a certain
'instrument' that not only resolved certain problems of analytic
theory, but created others. For instance, Lacan's theory of the
mirror stage, still embroiled in the mechanics of representation,
was at the origin destined to rigorously elaborate what Freud had
only discursively isolated as a problem of perversion
4. In neutralizing the aporias
that such a case presentation signals to the analyst, Lacan introduced
the term perversion in structural terms: as a type
of inversion associated to the relation of an object with
its symmetric image 5.
It was precisely at this moment that it became possible for
Lacan to ask: at what point would have Freud needed his fable of
primordial masochism and the infant, if he had had an adequate topology
? Inversely, it also becomes necessary to ask: at what point
does such a structural account itself pose an obstacle to an understanding
that had previously been natural to the practice of psychoanalytic
theory (neurosis, the talking cure, woody allen, etc.) ? Or again,
as if it were a question of recuperation: in what respect does
such a structural account, in all its detours and generality, still
permit the carrying out of the 'initial' practice of psychoanalysis
? Are the words 'ego', 'super-ego', 'id' etc. a literary way for old psychoanalysts
to be able to continue to think their relation to a theory and practice of
psychoanalysis ?
If today it has become common place to narrate the aporias
of psychoanalysis - those historical moments that show
themselves in the construction and deconstruction of its natural
themes of expression - it is only in the isolation of a pure
material of psychoanalysis - its knot
or structure - that such aporias can be shown to
not only generalize its theory, but extend its field
and practice.
Topological Presentation
of the Incurable: The Pere-versely Oriented
It is not in the rupture of Symbolic, Imaginary, and the Real
that defines
perversion, it is that they
are already distinct and that it is necessary to
pose a fourth which is the
Sinthome in occasion [...] that perversion is
nothing other than the version
ver le pere, and that, in sum, the father
is a symptom or Sinthome,
if you want.
J.Lacan,
Le Sinthome, 1975-76
The remarks of our last
section, as brief as they may have been, begin to justify the diagrams
below as they present a psychoanalytic place not as a description
of what occurs on the analytic couch, but as an inscription of
what occurs in the structure of an analytic practice. In such
a movement we are no longer asking the trivial topological question
of whether an analysand should sit or lie down on a couch,
or where the analyst should be in the session, rather we are interrogating
the act and topos of psychoanalysis itself, without trivializing
this encounter to the professional status of the doctor/patient
relation. Here then, reformulating our questions at the place
of the Subject and the Other, we must ask: What is the interaction
of two Borromeans: analyst and analysand, are they one or two ?
fig. 2
The Analytic Situation
In fig. 2 the structure
of the subject is presented with two Borromeans (Bos)
that have been brought together and embedded in the plane.
The rings of the Bo are colored red, green, and blue with the
lock on the left having a fourth black ring ∑ interwoven
amoung the three. We have joined the Bos by putting them in
correspondence by bands - double strands - joining rings of the
same color. This putting into correspondence by bands assures
that the rings remain closed curves after joining (a closed curve
joined to a closed curve by a band remains a closed curve). Such
a correspondence between two Bos was first proposed in the literature
by Sourry and Lacan as a way to 'un-do' a lock, not by cutting, but
by adding another perversely oriented lock. This act of dénouement
being nothing other than, psychoanalytically speaking, what
occurs in the interpretation of the Sinthome.
fig. 3
Dénouement
of the Sinthome
Here, then, in fig.3 we
have shown only the end result of the process of interpretation:
a veritable dénouement where the various arcs of
the rings of the Bos in the plane are deformed so that the Sinthome
falls away (the dimensions of the problem permitting no cutting,
re-drawing, tearing, etc. of the figure).
To conclude, I hope the
reader will find the time and enjoyment to construct
this clinical problem for themselves by actually transforming
figure [2] into figure [3], thereby filling in the missing
diagrams. For it is by addressing this separation from the
Sinthome that contemporary Lacanian theory passes from
a practice in intension to a practice in extension:that
is to say, operates an involution from the place of a psychoanalytic
practice to a practice of a psychoanalytic place.
Robert Groome
Santa Monica,
Winter 2006
Footnotes
1/ Appearing initially in
la Psychanalyse, then republished in his Ecrits,
"Of A Preliminary Question..." p.531-583, Lacan only
adds the topological presentation of the Mobius band and the
corresponding footnote in 1966. This much said, the importance
of "Of a Preliminary..." becomes apparent, not only
in so far as this article is the only Ecrits (Writings)
with a workable topological presentation, but when the article
is juxtaposed with his earlier articles and still illustrative
use of graphs in such articles as the Subversion of the
Subject and the Dialectic of Desire, p.793-827 Ecrits, (1960).
2/ The over and under weaving
is indicated in the following way: over = solid line,
under = broken line.
3/ The Borromean is neither properly speaking a
knot nor a chain, but a lock. Or at least, the necessity
for this triadic classification of spatial connection was first
put forward in P.G. Tait's On Knots (1876)
Later, with the work of Milnor - Link Groups (1954)
- this triadic classification would trivialize into a
binary relation between knots and homotopy chains.
4/ The psychoanalytic scholar will perhaps be perplexed over
the use of the term 'perversion' in reference to Lacan's preliminary article,
"The Mirror Stage as the Formative Function of the I" (1949), which
is purportedly about paranoia and the "paranoiac alientation that
dates back to time at which the specular I turns into the social I".
Yet, later, by sharpening his concept of paranoia beyond the representational
metaphors, Lacan would drop the illustrative use of mirrors to introduce
a more precise topological definition of perversion.
5/ There are two delicate questions here that
have been presented in the seminars and will be presented in future articles:
firstly, the case where the image is an inversion of its object,
must be distinguished from the case where it is a perversion.
The use of this language goes back at least as far as Listing's Vorstudien
zur Topologie (1847) and is today standard in the traditional textbooks
of optics. Secondly, the question of at what point the relation
of the image to the object must be problematized as a certain nonrelation
- as not a 1-1 correspondance - is most often brought out by distinguishing
two different theories in which the figure is posed: the image as a mathematical
entity and the image as a psychological entity (the figure 'seen'). The
former being a 1-1 correspondance, the latter not, thus, introducing considerations
of what became known after Locke as 'secondary qualities': color, error,
luminosity, orientation, etc. This difference goes back at least as far
as Kepler's distinction between 'pictures' and 'images of things'; the
former being what allows the formation of a science of optics, the latter
being what would open up to, at first, a theory of psycho-physiological
vision: from Bouguer's Essai d'optique sur la graduation de la
lumiere (1729) to Weber's (1831) and Fechner's study of differential
perception and the formulation of a constant: the logarithm of the psycho-physical
relation. If modern research has critiqued their results by showing that
this constant is only the case in what concerns a statistical average of
a zone of excitation conforming to the law of Gauss, there is still
an open question on the structural problem of continuity presupposed, but
not explicity brought out in the natural themes of psycho-physiology. See
Poncaire's topological critique of the Weber/Fechner conjectures.
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