In her essay on the psychoanalytic use of topological structures Nathalie Charraud writes;
‘For Lacan, the structure of the subject of the unconscious as subject of the signifier is, in fact, the Mobius strip; a surface of inscription where front and back are but one continuous side. It is this structure that offers a solution to the problem of double inscription that so vexed Freud”.
The essential properties of the Mobius strip that help us understand the Lacanian structuralist analysis of psychosis are (a) it is infinitely cyclical and so its repetition echoes the return of the repressed and (b) a traversal may be conceived of as a signifying inscription.
Lacan locates the possibility of the foreclosure of primordial signifiers and therefore the emergence of structure to at least the immediate post-natal period; “reality is at the outset marked by symbolic nihilation”, “day and night are signifying codes, not experiences” and “it’s structurally necessary to admit a primitive stage in which the world of signifiers as such appears”. I interpret these central chapters in Lacan’s 1953 seminar on the psychoses as an attempt to demonstrate the existence of binary variables predicated on the presence or absence of core qualities such as pleasure and unpleasure. These may be measured in economic terms via the quota of affect where the yield is drawn in relation to such notions as response (time) to demand, internal/external ‘rhythms’, the closing of the day and so on. But they are actually inscribed in terms of perceptions or wahrnehmungszeichen’ in the mnemic systems of the Freudian reflex apparatus. Lacan, in fact, unhesitantly declares them to be (primordial) signifiers.
Let us say that successive cyclical traversals of the Moebius strip inscribes the early signifying patterns in a fashion that distinguishes quite markedly the normal subject from that of the foreclosed. The propensity to foreclose appears to be a constitutional factor indicated by Lacan’s early remarks that “the great secret of psychoanalysis is that there is no psychogenesis”. His double insertion of the African myth of the fox who ate the primal placenta thereby introducing a primordial dissymmetry and his remarks on the “judgement of existence” in relation to an affective response that is repudiating likewise reinforce this impression. These structural binaries of course mirror the basic dualities that underpin all languages and the relationship between them lies at the heart of Lacan’s dictum that “the unconscious is structured like a language”.
This first layer of ‘symbolisation’ is depicted by Lacan, though not explicitly in these terms, in his addendum to the ‘Seminar on the Purloined Letter’. Lacan generates the basic elements (‘+’ or ‘- ‘) of what will become a self-evolving syntax through the random tossing of a coin. He superimposes two matrices atop this original ‘system’, the second of which, ‘the Greek letter matrix’ is, I suspect, meant to jocularly depict ‘the detestable Danoi’ as they usurped the ancient matriarchal civilizations of the Aegean thereby marking the birth of the ‘Logos’ in a phylogenetic recapitulation of the three times of the Oedipal subject.
We are at the chronological juncture now (circa 18 months; Fort/Da, specular captation, etc) where the arguments for structural factors in pathology have been well-rehearsed. The construction of the imaginary phallus through the particular form taken by the dialectic of desire in the maternal dyad is played out against a Symbolic order that is already announcing itself as a structuring presence. Lacan thus conceives of an imaginary ternate dominated by a dyadic phallus eventually giving way, via the mother’s castration, to a Symbolic ternate with the paternal metaphor acting as a structurally necessary reconfiguring phallus. With regard to schema R, Lacan recommends a cut in the Real defined by the quadrilateral eiMI to produce a Moebius strip. We will immediately perform a double transverse cut on this Mobius producing two rectangular strips; one pertaining to the Imaginary, the other to the Symbolic ternate. It is also important to bear in mind that though Lacan is hesitant in assigning a particular genetic moment to this primordial exclusion it clearly predates Freud’s Oedipus.
We have been concerned with the use of a Moebius strip to further our appreciation of structurally significant events in the formation of the unconscious of the ‘prelinguistic subject of pure need’; that is to say, the infant prior to immersion in the specular captations and illusory Gestalts that will define the moi as frustration in essence, and prior to the decentering Spaltung of the I’ caught in the defiles of the signifier. Leaving aside the ‘cross-currents’, topographical regressions and other numerous factors that tend to conflate the essential disparity of the structural determinants pertaining to each of these moments of the Oedipal movement what we are presented with in essence in the Lacanian study of the psychoses’ are three distinct modes of interrelated foreclosure. Our three Moebius strips can now be sewn side by side producing the four-dimensional ‘impossible’ object known as the asphere or Klein bottle. The ‘hole’ in this topological object whose inside and outside is continuous can be enlarged according to the severity of the primacy of the primary process in the psychic life of the foreclosed subject.
We must however refrain from applying the properties of the Moebius to elucidate mechanisms of the imaginary dialectic such as ‘projection’ and ‘identification’. Here we are following a forgotten rule of prioritisation first sounded by Lacan himself;
“The subject’s constitution in imaginary allusion is the problem on which we need to make progress….. Until now people have been satisfied with this…. People have discovered all the material, all the elements, of the unconscious in it. They seem never to have wondered what was significant from the economic point of view about the fact that by itself this allusion has no power to resolve anything…… “,”
