Why Topology and Psychoanalysis?“Topology is the discipline that comes to bear on the traits at the origins of civilization” Maurice Fréchet
The difficulty that post-Freudo-Lacanian psychoanalysis faces today is that it asks important questions without having an effective means to respond. By effective we mean the means by which to account for the necessity of a psychoanalytic discourse beyond the appeal to speech and the inertia of descriptive commentary. Why is this effectivity important? Clinically, anyone who addresses a symptom poses it. Ethically, there is no real cause to work in analysis if it can not be assumed. Of course, it is always possible to begin an analysis just because someone mentions a theory and practice or a cure. But this ‘possible’ analysis will always remain at the level of a rumour or transfer, if it does not engage the problem of its use or necessity.
Though not alone, Lacan was the first to render account of an effective analysis by extending it to the research of linguistics, logic, and mathematics. What these domains of rationality have in common is a focalization on the material and formal procedures of inscription beyond the contents of description. In avoiding such domains, psychoanalysis has historically been assimilated to the irrational and mythology; or worse yet, sought to prop itself up on the contents of scientific disciplines – neuroscience, biology, genetics, etc. – having little or no correlation to an intrinsic necessity. In spite of the extrinsic of myth and science, it is important to show how such an intrinsic necessity may be achieved in the construction of a topology.
The Place of the Subject and the Object of Desire
Freud and his first generation inheritors focalized on the voice while the gaze was only considered passively and indirectly – as remembering a dream, recounting a scene or fantasy. In each case, the gaze was never directly constructed in practice, but left as a problem of imagination, then constructed in models of the neuron and optics.
By the time of Lacan the gaze is constructed directly in practice and theory with a special concern for its interpretation in a topology. A practice of topology in this respect consists in separating the voice from the gaze and drawing the implications this has for a reading and writing of the subject. The term ‘subject’ has been introduced in Lacanian psychoanalysis to account both for the birth of modern science and what Freud first postulated as the id: an agency of a drive or desire incongruous to the ego and its self-representations. If psychoanalysis has arrived to disengage such a subject from the ego through its effects of impediment, break, and slips of speech, it often does so without ever being able to give the subject a place beyond a field of passion and human error. Left at this theatrical level, the subject only finds a place in a passionate development; that is to say, in the masquerade of psychotherapy or in reference to the arts – film, literature,etc. – and social critique. It is not surprising, therefore, that the most current and readable applications of psychoanalysis to the social scene – film, literature, politics, etc. – also produce some of the most retrograde and stereotypical conceptions of actual psychoanalytic practice.
The source of this avoidance consists in confusing desire with passion. Since Lacan the practice of psychoanalysis consists in making room for a place of the subject whose reading and writing would not be systematically effaced with a reference to the place of passions – whether it be reference to the dramas of the therapeutic ‘talking cure’ or applied psychoanalysis. The familiar Woody Allen version of psychoanalytic therapy as a place for passionate speech is pre-Lacanian to the degree that the relation to the gaze remains un-constructed and, therefore, reduced to theatrical imagination or a psychological conception of visual experience. What is wanted is a place for a psychoanalytic discourse: a topos that would not reduce the singularity of the gaze or clinic to a psychology of the faculties or an aesthetics. Without this topology of the subject the object of desire is avoided and assimilated to a place of passion through a set of historical fossils –psychiatry, psychology, and psychotherapy – and ritual.
Despite the recognition of the debt Lacanian analysis owes to topology, many today have not arrived to incorporate topology into their practice. Indeed, in combining topology with psychoanalysis one encounters two theses with regard to the formation of its place:
A) The abstract hypothesis that views topology as a formal discipline that is only concerned with conceptualization and concerns of theory;
B) The concrete hypothesis that views topology as a doctrine of structure concerned not simply with theory, but with the foundation and practice of its clinic.
The former, (A), views topology as a complement to psychoanalysis that is inessential for its presentation to the public or the clinic.
The latter, (B), takes topology as a supplement to psychoanalysis that is, however, necessary both to its presentation and its clinic.
The former, (A), as may be expected does little with the topology except through metaphor and historical commentary, i.e., the ‘late’ Lacan, etc. Remaining at this level, the results have been largely disappointing as ‘Lacanian topology’ digresses into an academic and esoteric reference to Borromean Rings and Mobius bands.
Though it is less well-known and its participants fewer in number, (B) founds a purely analytic clinic through an experimental framework and topological presentation that cut across the disciplinary boundaries. There is no need to call such a structural approach ‘interdisciplinary’ since it is not a question of transferring contents from one discipline to another, but of determining the formal and material means of a discourse. There is no need to fetishize a knot or mobius band since what is at stake is the logic that such intuitive constructions provide.
Since there is a lot of work in the field to come, our first aim is to furnish the necessary references to those seeking to develop a more precise practice of this topology. These references do not simply consist in following the indications left by Lacan, but in constructing the object that he discovered – the little object a – beyond a literary, philosophical, or political reference.
Why Study Topology?
To date the results in psychoanalytic theory and practice have been underwhelming. Despite the claims of progress, contemporary psychoanalysis, be it post-freudian or post-lacanian, seems to be no better or worse than what came before. When it has become possible to say and publish anything in the culturally accepted jargon of analysis, one must ask at what point future analysts will look back upon the current scene as nothing more than literary fantasy and ‘folk psychology’. Without denying the folklore, it would be a progress to introduce a purely analytic clinic that proceeds on the basis of its proper discourse without being appropriated by the missions of, on one hand, psychology, psychotherapy, and psychiatry, on the other, philo-lit-crit theory. The interest of our topological work is to make room for this more precise development.
To get a handle on what is at stake, look at a similar situation: ask an architect what his or her profession would be like if you took away the geometry and logic of a construction. Within no time at all such an occupation would be reduced to the skill set of a building code inspector. Though geometry may appear without a direct utility or appear as a mere conceptual basis of the theory, with a second look it is also what allows the architect to disengage a practice from the power relations of the building code inspector. Without this basis, the architecture of modern psychoanalysis consistently falls back into the mission of a psycho-inspector: someone – a nurse, social worker, psychologist, literary professor, psychiatrist, life coach, spiritual guide, etc. – who may arrive to monitor and describe someone in the language of psychoanalysis without ever being able to assume the consequences of an analytic theory and practice as such. Call this with Lacan the ideology of analysis:
“What the ideology of contemporary psychoanalysis suffers from today is the lack of an adequate topology”
J. Lacan, Seminar XVI, D’un autre à l’Autre
This is not to suggest that psychoanalysis is based on topology in the same way that architecture is based on geometry, but that any practice or theory that does not effectively construct the site and logic of its discourse is a participation in ignorance. In short, it is the propagation of a technical ‘know-how’ having little to do with the place of the analyst. Today, much of the stagnation of psychoanalysis occurs precisely at this place of ignorance: the well-intentioned asking important questions that, in the lack of an effective and constructive response, are co-opted into the ideological mission of a psycho-inspector qua technician. Of course, it is always possible to deny the place of analysis itself and take up a philosophical position with regard to its theory-practice. But we find it not only ineffective but worrisome that psychoanalysis not only in the U.S. but elsewhere – Europe and South America – often finds itself split into this divide. As a counter-measure, what is wanted is a practice of a theory that is open to anyone, yet does not fall back into the false innocence of the technician or the anarchy of the philosopher; what is required is a place to determine the ethics and effectivity of a theory and practice in a way that does not devolve into a professional institute or a utopia.
1) Freud – The psychoanalysis of Freud wanted to be a science. Outside of this desire it does not have much of a status and can only be confused with practices – hypnosis, spiritualism, hot-tub relief, etc. – that one regroups under the name of the arts or therapy. No doubt, the term ‘science’ brings with it no evidence of its own, while several epistemological investigations of Freudian psychoanalysis have been not surprisingly negative. Nonetheless, we must go beyond this history. The question of how science is pertinent for psychoanalysis must be still be asked today. Moreover, for reasons that remain to be shown, to explain the detours of psychoanalysis as a practice and theory, it is necessary to go beyond the assumptions of an epistemology: science is not an ideal of its theory, but only a necessary condition of its existence. It is important to recognize with Freud the desire for One Science, not a two science epistemology which opposes a hard science (physics) to those other ‘soft’ or humanities based sciences. Psychoanalysis has the same subject as science – the subject of modern science at least since Descartes – but unlike modern science, it persists in the construction of an object. What is important to recognize is that modern science no longer explains or constructs ‘heat’ or ‘weight’, but passes beyond any particular object to determine a field of relations and their laws (mass not ‘weight’, for example). Psychoanalysis, on the other hand, persists in the construction of an object that not only poses an obstacle to an epistemology of science but is irreducible to its inclusion within a methodology of the soft sciences or humanities. Opposing a science of construction to an art of interpretation, Freud writes:
Twenty-five years of intensive work have had as a consequence of assigning to psychoanalytic technique goals immediately different from those of the beginning. At the beginning, all the ambition of the medical analyst was to conjecture what was hiding in the unconscious of the sick person, and to reunite these elements in a whole and communicate them when it was proper. Psychoanalysis was above all an art of interpretation. But the psychotherapeutic task was not however resolved by this. A new approach has come to light that consists in obtaining from the ill person a confirmation of a construction [...]”
(S. Freud, Beyond the Pleasure Principle, 1920)
“Psychoanalysis is not an art of interpretation, it is a construction. Interpretation comes to bear on a material element ( missed acts, lapsus, etc.). Construction, on the contrary, comes to bear on the entire course of an existence, most notably on the initial and determining phases.”
(S. Freud, Constructions in Analysis, 1932
3) Topology: we make reference to the tradition of mathematics-logic to follow the problems and solutions offered by its method of writing. Summarily, topology can be grouped into five branches, then generalized into a theory of Topoi and Sketches:
General Topology Topos Theory Sketches (Esquisse)
(Alexandrov) (Grothendieck) (Ehressman)
Algebraic Topology Topological Algebra
Point Set Topology Combinatorial Topology
(to be continued)