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Matheme
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{{Top}}| align="[[left]]" style="margin-right:10px;line-height:2.0em;text-align:left;align:left;background-color:#fcfcfc;border:1px solid #aaa" | [[French]]: ''[[mathème{{Bottom}}
The term [[matheme|mathème]] is a concept introduced in neologism which [[Lacan]] derives from the [[{{LB}}word]] "[[mathematics]], presumably by analogy with the term ''[[mytheme]]'' (a term coined by [[Claude Lévi-Strauss]] to denote the basic constituents of [[myth]]ological [[system]]s).<ref>[[Claude Lévi-Strauss|workLévi-Strauss, Claude]]. 1955.</ref> The [[matheme]] s are part of [[Jacques Lacanalgebra|Lacanian algebra]].
<!-- The [[matheme]] is a [[concept]] introduced in the [[{{LB}}|work]] of [[Jacques Lacan]]. The "[[matheme]]" is a neologism coined by [[Jacques Lacan]] in the early 1970s. Formed by derivation from "[[mathematics]]" and by analogy with [[phoneme]] and [[Lévi-Strauss]]'s [[mytheme]],<ref>''Mytheme'' is a term coined by [[Claude Lévi-Strauss]] to denote the basic constituents of mythological systems.</ref> the term is an equivalent to "[[algebra|mathematical sign]]". It is not used in conventional [[mathematics]], but is part of [[Lacan]]'s [[algebra]]. -->
==Schema L==
[[Image:Schema.L.simplifie.gif|thumb|150px|right|Schema L]]
But what exactly is a mathème? What does Lacan have in [[mind]]?
Is he [[thinking]] of the [[formulas]] that [[punctuate]] his [[teachings]], such as the formulas for metaphor and metonymy, for [[instance]], or the formulas for [[sexuation]]? Or is he rather thinking of the [[topological]] constructions on the torus and the [[cross-cap]] that he had just introduced, not as metaphor, but as structure itself?
If one tracks down the word 'mathème' in 'The Twit', it first appears to be intertwined with the topological [[construction]] presented as contributing to the analytical discourse, to its fabric: 'No other fabric to endow it with but the language of a pure matheme, in other [[words]], the only teachable discourse' (1973, p. 28). The definition, which [[identifies]] the mathème with the teachable, supersedes the mathematizable itself, since [[the Real]] can only be apprehended through mathematics, except the real of the [[impossible]] [[sexual]] relation, which, in point of fact, cannot be transcribed by any [[mathematical]] relation: 'This is why the mathèmes which are transcribed as [[dead]]-ends by the mathematizable, that is, the teachable in the Real, are likely to be coordinated to this "impossible" from the Real' (p. 35).
How is the mathème apprehended in the structure of our language? The first mathèmes, the arithmetical [[figures]], are on the border of language, in its fringe: 'The mathème is a product of the only real which is first recognized in language: the arithmetical [[figure]]' (1973, p. 37). The arithmetical figure is on the border between common language and mathematical discourse. The first figures are [[signifiers]], but these quickly become meaningless.
In L'Oeuvre Claire (1995), J. C. Milner attempts to define the mathème on the basis of the definitions of phoneme (the [[linguist]]'s phonetic unit) and mytheme (part of a myth). Milner proposes that the mathème is an `atom of knowledge'. But, apart from mathematical [[objects]], there is no such [[thing]] as an atom of knowledge in mathematics. This is in fact what J. A. [[Miller]] means when, talking [[about]] the mathème in the Revue de la [[Cause]] Freudienne No. 33, he says that the aim of the analytical [[experience]] is to `[[know]] one's own mathème' (1996). What is important then, is less to [[formalize]] the knowledge achieved during the [[cure]], than to [[identify]] with one's own mathème.
If the only valuable teaching is the one that can be transcribed into a mathème, then the teacher'''s [[Schema Lrole]]''' [[identification|identifies]] four points in is reduced to the [[signifying chain]]ultimate: # [[Imageto transmit an elaboration without having anything to do with it. The consequence is the same with all writing:Biga.gif]]Scilicet, the journal where 'The Twit' ('L'Étourdit') was first published is — except for Lacan's [[unconscioustexts]] or — a collection of unsigned articles after Bourbaki's style of presentation, Bourbaki being one of the "[[discourse]] collective and anonymous mathematical writers of the [[Othertime]]]", and then .# [[Image:SmallsAs J. C.gif]]Milner points out in his book on Lacan, the [[subjectmaster]], which in turn results from the relation between # 's figure [[Image:Smalla.gifdisappears]], with the [[ego]] and # [[Imagemathèmes:Smalla'.gif]], the [[counterpart|other]]we are left with professors.
If one takes Lacan's topology and mathèmes seriously, the clinical [[scene]] changes too. That which makes the symbolic ensnare and bump into the impossible of the real becomes clearer in the light of what Lacan called the topology of signifiers, which taps in the general topology of kinship between signifiers, a topology which, according to Lacan, is budding, if not [[born]], in Freud's '[[Project]]' (Esquisse, see [[Ornicar]]? 36). Inasmuch as it can be separated from the [[clinic]] of signifiers, the clinic of the [[object]] is spotted in, by, and through, the topology of surfaces, just as Lacan shows in 'The Twit' and in some of his later [[seminars]].
{{See}}
* [[Algebra]]
* [[Borromean knot]]
* [[Drive]]
* [[Fantasy]]
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* [[FantasyFormula]]s
* [[Graph of desire]]
* [[Imaginary]]
* [[Interpretation]]
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* [[Knowledge]]
* [[Mathematics]]
* [[Real]]
* [[Schema]]
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* [[Signification]]
* [[Structure]]
* [[Subject]]
* [[Symbol]]
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* [[Symbolic]]
* [[Symptom]]
* [[Topology]]
* [[Torus]]
{{Also}}
<references/>
* [[Lacan, Jacques]]. (1973) 'L'Etourdit' (The Twit). Scilicet, 4.
* [[Lacan, Jacques]]. (1975) [1972-73] Le Seminaire xx Encore. Paris, Seuil.
* [[Lacan, Jacques]]. (1976) Le Sinthome, Seminaire XXIII (1975-76), Ornicar? 6, 7, 8, 9, 10, 11 [Provisional transcription].
* [[Lacan, Jacques]]. (1986) [1945-46] Esquisse. Ornicar? 36.
* [[Miller, Jacques-Alain]]. (1996) 'Retour de Granade: Savoir et satisfaction'. Revue de la cause Freudienne, 33: 7-15.
* [[Miller, Jacques-Alain]]. (1996) 'Le monologue de l'appard'. Revue de la cause Freudienne, 34: 7-18.
* [[Milner, Jean-Claude]]. (1995) L'Oeuvre Claire. Paris: Seuil.
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