Auteur: Alexandre Leupin

Alexandre Leupin est professeur distingué au département d'études françaises à Louisiana State University.

A partir de Lacan : Analyse topologique du signe linguistique et Formalisation mathématique des coupures épistémologiques

 

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2 Responses to “A partir de Lacan : Analyse topologique du signe linguistique et Formalisation mathématique des coupures épistémologiques”

  1. KOUAME dit :

    Je suis M. KOUAME KAN. Je prépare une thèse de doctorat en linguistique. Mon sujet de thèse est le suivant: essai sur les propriétés syntaxiques et sémantiques des verbes de mouvement en baoulé. Ma recherche s’inscrit dans la ligne des travaux d’Antoine CULIOLI.
    Je suis à la recherche de documents se rapportant aux notions de: verbe de mouvement, forme schématiques et opération d’identification. J e serai heureux de recevoir des articles, des livres, des exemplaires de thèses pouvant m’aider à réussir mes travaux.
    Merci

  2. alex dit :

    Une réponse de Robert Groome, qui prépare un livre intitulé Re-Reading Tait’s On Knots: A Construction in The Theory of Freud and Lacan
    June 17, 2010

    Dear Alexandre Leupin and Steve Wallace,

    I will only indicate here that my critique of your article Universal Language, begins with chapter (2) The Model used on page four and may in fact be a further extension of what seems to be your auto-critique in (4) A New Model. In either case, I will not introduce any of the Lacanian nomenclature except as one basic premise: in the context of analysis, what we are looking for is a question of a topology of time and not space. No doubt, the Reimann model of the mobius band that Nasio introduced in Lacan’s seminar Le Topologie et le Temps situates the problem, but also trivializes it as I would also like to call attention to Vappereau’s veiled critique of this model in the same seminar. I will only state the problem and one solution here in ordinary language and will leave a more detailed and formal presentation open if you deem these reflections relevant to your endeavors.
    Firstly, taking the premise of a topology of time as a given, we can neither spatialize it into the fourth dimension, nor simply embed the mobius band into the 3rd dimension without already trivializing the temporal problem into a spatial one. You indicate this somewhat yourselves by noticing that your model cannot merely « change linearly with time », but you continue to view the ‘model’ as embedding into space. When you get to the time argument in 4.1 Cuts and Births , I then get the impression that we are really getting to the crucial problem of time part, but it is still set up in a ‘before’ and ‘after’ aspect which I believe is conditioned by the notion that the model is embedded into space, while time is simply a succession in space, that is interrupted as a before and after.
    The question I pose is what type of topology can determine the aspect of the verb: not simply the tense of before and after, but what Freud asks in « Wo es War, soll Ich Werden » (Where it was, I shall become) that becomes with Lacan the anticipation of the real and its achievement: where it has always been (the real) I will have become (the subject). I will not respond directly to this problem here, but will situate it with a purely topological problem.
    One last descriptive comment: there needs to be a way to construct the mobius not as a model, but as a structure – you may have also signaled this implicitly when you begin to speak of a series or « copies » of models. I would propose to simply speak of a structure and to distinguish this as radically different than a model. This problem of model-structure is intimately related to the problem of situating the embedding space that one puts the mobius band in. If this refinement is possible, then I think we may begin to speak of a topology of a subject and structure in the manner of Lacan – and not an object and model.
    In any case, beyond these introductory comments, hopefully I can situate the problem in more simple topological terms that really do not require much formalization for the moment.

    I would propose that the way you have defined the mobius band is to precisely make a model of it: not simply that the mobius band is being used as a model for analysis, but by putting the band into the Cartesian coordinates R3 there is the creation of a model of the mobius band. No doubt, this is a valid procedure just as it is valid to call a point an ordered pair on the plane R2. But what is important to recognize is that this is an extrinsic model of the mobius band, just as an ordered pair is an extrinsic model of a point.
    Let me begin otherwise by indicating what an intrinsic structure would be and number the argument:
    1) There is an intrinsic formulation of a mobius structure that must begin not by embedding the mobius band into any context or higher dimensional space, but in two ways:
    1a – embedding things into the mobius band– cuts or holes – ; here the mobius can serve as the non-orientable ’embedding space’ provided it is set up properly (one could think here of a ‘fibering’ the band, but it is not necessary to bring in the mathematical framework at this point);
    1b – using the mobius band itself as an operator – or functor – between spaces, i.e., actually taking the functor itself as mobius, it is no longer an object (noun) to be modeled but more akin to an act (verb) of a structure.
    In this first pass, I will not detail 1a or 1b or show how the problems of time that you mention in your article can be resolved in this way, but simply point out what happens if we do not adopt something like the intrinsic strategy I am proposing in (1) … and adopt the extrinsic strategy which I believe is your position in the article.
    If one aims to identify the mobius band by embedding it as an object into a three dimensional space, one may then call the band unilateral with regard to the unit ‘normal’ pointing from the surface to extrinsic embedding space. Yet, if one proceeds in this way, one has in fact defined the band in terms of a double cover – or Riemann surface – which is a model of the mobius band. It is important to observe that by this definition the mobius band is still being defined in terms of an orientable surface – the double cover is an oriented surface – while the problem of the face and the intrinsic non-orientable quality of the band has slipped out: for in such a presentation the use of ‘laterality’ to indicate a face is in fact an abuse of language as one is always on an intrinsic orientable surface (a ‘cover’ not a face) so that a unilateral band is simply defined as a double cover, i,e, an orientable surface that covers the mobius band twice. As a further consequence, in such a presentation there is no intrinsically non-orientable band (one is always in an orientable surface). Thus, in your model you always are working on the unilateral mobius band with the normal pointed outward and never on the intrinsic nonorientable mobius band with the normal in the surface.
    The oppositions are: intrinsic: non-orientable:: extrinsic: unilateral
    And the tendency is to reduce the non-orientable and extrinsic to orientable intrinsic, leaving both a true definition of the extrinsic face and non-orientation at bay. For example, when identifiying a knot in the theory of knots by using Seiffert surfaces the mathematician reduces the nonorientable characteristic quality of the knot to the calculation of an orientable cover. This is a perfect good model, but it has similar problems, both mathematically and psychoanalytically, as to your presentation of the mobius band.
    Again, the problem with the Riemannian model of the mobius band is two-fold: strictly speaking, the ‘face’ or ‘unilaterality’ of the band is never identified precisely, but defined away in terms of an intrinsic theory of orientable covers; second, the intrinsic non-orientable aspect of the band is reduced to the reversal of the normal vector into space on an orientable cover – and not the reversal of the normal in the intrinsic uncovered band itself. No doubt, these two normals can hook up, just as the covered and uncovered band do, but it is how one makes them hook up that is important and needs to be explained. I believe in so doing, we begin to open up the problems alluded to in (1) above, where the intrinsic mobius band is brought out as both a structural and temporal problem.
    To conclude, I sincerely believe that the mobius band is a most difficult ‘thing’ to formalize and commend your efforts in doing so to the extent that you have. It has afforded me the occasion to reformulate some problems I have had for sometime now in analysis and topology. If my comments seem followable or not, I will wait on your response to confirm or disaffirm this.

    Cordially,
    Robert Groome
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