Fall Seminar 2017 of PLACE

Constructing Oedipus Finally Achieved: Topology, Logic, Geometry

  The seminar is open to anyone and requires no previous background in Lacanian analysis or mathematics-logic. To register contact the secretary beforehand at: PLACE@topoi.net If you will be attending by Skype, please let us know beforehand. Beginning Date and Time: Saturday, 11:00am-1:30pm, Sept. 30. 2017 Frequency: meets twice per month on the second and last week of every month. See the PLACE calendar at: www.topoi.net Place: 1037 Euclid, Santa Monica, CA Materials: Paper and colored pencils. Reading: Begin 'Preliminaries to Any Possible Treatment of Psychosis', Writings, J. Lacan Instructor: R. Groome   Descriptive: Since 2013 the Constructing Oedipus seminar has sought to problematize the past and present vulgarizations of the Oedipus Complex by situating its aporias. The seminar has, therefore, proceeded in a zig-zag manner through the examination of different schools, theories, and critiques. Generally, we isolated what has been called the St. Christopher’s Dilemma and showed how this dilemma splits the pre-Lacanian  psychoanalytic field into two opposed schools, most often referred to by the epitaphs of Ego psychology and Object Relations. Our goal has been to show how this dilemma, far from being sociological or question of schools, was resolved constructively by Lacan through: 1) an Optics Model, 2) Logic, and 3) Topology. The Oedipus is generalized by Lacan not by showing how it can be modeled in optics, but how problems of optics pose problems of geometry, logic, and topology that are Oedipal (see description below).  Without this constructive and extensive approach, even a born analyst falls back into the conflict of interpretation between schools and theories. We begin this Fall 2017 by turning to the translations between the Optics, Geometry, Logic, and Topology, while showing how this field opens up a return to Freud. A complete timeline of the Oedipus Complex in the work of Freud will be handed out during the first seminars. It shows how the aporias of Freud are finally constructed out in the work of Lacan in terms of their structure. Specifically, we will show how the St. Christopher Dilemma produces a nodal logic that has not only a direct translation in Lacan’s work in topology, but clarifies the reading of his schema L and R. The description below summarizes the trajectory of the constructive work so far.  It is only summary in form here, but will be updated as the seminar progress. A recorded audio will be made available. Narcissism Not Egoism It was first established that the Ego, as defined by Freud, is not narcissistic (the common place mistake) but a ‘default of narcisissm’ that Freud compares to a neurotic narcissism or what he finally calls a psychosis. Consequently, a construction of the Oedipus Complex requires an explication not in atomistic terms, as individuals relating to each other, but as a structure of Narcissism (a relation of relations). In spite of appearances and the inertia of clinical examples, narcissism comes to bear not simply - or primarily - on the problem of identification, but on the object, or in Freud's terms, the object of the libido (desire). Optical Model and Geometry: A First Construction of Narcissism and its Object

With the Optical model Lacan was the first to present a direct construction of narcissism in a way that would no longer rely upon myth. Unfortunately, the post-neo-Lacanians, through infinite commentary and description, have left this optic model at the level of an illustration, i.e., an illustration of psychoanalytic concepts that are presupposed but never critiqued and constructed in their structure. In order to counter the erudite and illustrative use of the Optical model, in 2016-2017 we proceeded to determine the underlying basis of the optical problems in a geometry. We called this the ‘optical cube’ and showed how the symmetries of a mirror could be established in a geometrical system of XYZ coordinates with an added layer of structure situating its object and its reflection. In an initial probe, there was the presentation of the two parts of the mirror, all the mechanical movements in front of the mirror and their reflection behind the mirror, as composed of 24 symmetries on each side, giving a total of 48 symmetries. The question was posed as to whether this group of symmetries sufficed to determine all the movements in 3-d space, if this group would, for instance suffice to determine all the rotations of a ball in space and whether this would be the same problem as determining all the displacements of the dancer in a dance. Where is the dancer in the dance? Or again, where is the painter in the painting ? These type of questions are a prelude to the question as to whether a movement is equivalent to an act and whether the reflection of an object in a mirror is the same thing as the child viewing itself as an object reflected in a mirror. The question was responded to negatively in the seminar by showing how a dancer is never in a 1-1 correspondence with his/her position in space just as a child is never in a 1-1 correspondence with the image of the object reflected behind the mirror: in both cases, there is an indiscernible and hesitation of the gest with regard to act, image, and object. A definition of Optics was posed as presenting a dynamic geometry, where the ‘act of reflection’ presents a contingency of the geometrical system. It was left open as to how to determine all the interrelations of the 48 different symmetries of the optical cube. What was posed is that Lacan’s optical model, if at all founded, would be based on on these fundamental symmetry operations of geometry. It was proposed to show how this geometry can be formulated as a group and where this group presentation begins to break down. It was also shown that just as the dancer of a dance – the place of the object and act – is not in a 1-1 correspondence with its position defined by the XYZ spatial axis, the problem of sex identified in the Oedipus Complex – is it masculine or feminine? – is not in a 1-1 correspondence with the position defined by the nomenclature of the kinship system of Mother/Father/Child. Defined in its most extensive manner, the Oedipus Complex is a question of how to introduce an act into a system. Similarly, an Optical Complex is a question of how to introduce an act into geometry so that the problem of reflection is given a dynamic symmetry where the image is not the same as the object. Once this was determined, it was shown how this act implies a nomination and how the Oedipus Complex, once defined extensively, becomes a question of how to introduce a name into a system.

What was left open, is how this strategy of reading the Oedipus in a geometry is nothing other than what Lacan defined as the task of contemporary psychoanalysis: to introduce the Name of the Father into the discourse of Science (Writings, Science and Truth) The Fall 2017 Seminar will go back over these arguments, then extend them to include a topological formulation of the Oedipus and its principle operation of the Name of the Father in the theory of knots as it begins to be reformulated in terms of the Sinthome. Knot Theory via Non-Knots In the 2017 Summer Immersion, it was shown how the extrinsic Mobius band has a sense of left and right that can be determined by isotopy and the non-knot: the linking number as a positive one link or negative one link. This was called the Kauffman representation of mirror symmetric Mobius bands by mirror symmetric linking numbers (see: http://homepages.math.uic.edu/~kauffman/   ). Here ‘left’ and ‘right’ are, strictly speaking, just different objects in space whose difference corresponds to the reversal of one direction – front and back - of the underlying Cartesian coordinates. It is only an abuse of language in this presentation to speak of the difference of object and image in the sense of the optics of a mirror: there is only an object-object correspondence. It was shown in the 2017 Summer Immersion that there is another orientation required if we begin with the intrinsic Mobius band: that, in fact, there is only one intrinsic Mobius band which is neither left nor right-handed, but can become either once the band is cut once around it central axis. A similar phenomenon is discovered with a mirror: a two dimensional image is not reversed in a flat two dimensional mirror, it is neither left nor right-handed, it is only by adding the third dimension that the object in front of the mirror is reversed with regard to the image of the object behind the mirror. Thus, there are four propositions between the topology of the Mobius band and the geometry of the optics of a mirror that can be put into correspondence: 1)   The intrinsic Mobius band does not have a sense, i.e., does not have two different left and right hand presentations. 2)  A two dimensional image does not change its sense in a two dimensional mirror, i.e., does not have two different left and right hand presentations. 3)   The intrinsic Mobius band can be given a sense – made bilateral - by cutting it through its core axis. 4)   A two dimensional image reflected in a mirror can be given a sense – determined as left or right – by adding a third dimension to the underlying coordinate system. When this is done, it is possible to speak of the image in the mirror not being the same as the object in front of the mirror. In fact, the mirror image has reversed one direction of the XYZ axis. The 2017 Fall Seminar will give the details of 1-4, while showing the implications for this correlation by constructing a theory of knots that takes into considerations properties of reflection where the object is not the same as the image. Lacan calls this a Topology of the Subject since the act emerges in the system as a cut that can be substantiated in what he first called a Sinthome. We construct this correspondence specifically through different examples, then show how it entails a projective theory of knots bringing together a theory of non-knots and the knot. When all is said and done, our goal is to give a constructive definition of the Sinthome by showing how it is operative in a topology and the clinic that no longer has need of the repetitive commentaries on Lacan, Joyce, Schreber, etc. Robert Groome Fall 2017 Santa Monica, CA