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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 neologism which [[Lacan]] derives from the [[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|Lévi-Strauss, Claude]]. 1955.</ref> The [[matheme]]s are part of [[algebra|Lacanian algebra]].
In 1955, [[Lacan]] introduced what could be called his first [[matheme]], the relatively simple "'''[[schema L]]'''", illustrating the [[imaginary|imaginary function]] of the [[ego]].
==Signifier==
[[Image:SAUSSUREANALGORITHM.gif|thumb|100px|right|Saussurean algorithm|The Saussurean algorithm]]
Perhaps the most familiar [[matheme]] is the "[[matheme|algorithm]]" which in 1957 replaces [[Saussure]]'s simple diagram / arbor with the [[notion]] '''S/s'''. In 1957, [[Lacan]] replaces [[Saussure]]'s diagram of the [[sign]] with what is now referred to as the "'''[[Saussurean algorithm]]'''".<ref>{{E}} p. 149</ref> The [[matheme]] [[links]] the [[law]]s of the [[unconscious]] discovered by [[Freud]] to the [[law]]s of [[language]] ([[metaphor]] and [[metonymy]]).
This is to be [[understood]] as demonstrating that the [[signifier]] is above the [[signified]] , showing the primacy of the [[signifier]] (which is capitalized, whereas the [[signified]] is reduced to mere lower-[[case]] italic), and that the two are separated by a [[bar]] that resists [[signification]] and forces the [[signifier]] to [[slip|slide]] endlessly.<ref>{{L}} "[[The Agency of the Letter in the Unconscious or Reason Since Freud|L'instance de la lettre dans l'inconscient ou la raison depuis Freud]]." ''[[Écrits]]''. [[Paris]]: Seuil, 1966: 493-528 ["[[The Agency of the Letter in the Unconscious or Reason Since Freud|The agency of the letter in the unconscious or reason since Freud]]." Trans. [[Alan Sheridan]] ''[[Écrits: A Selection]]''. [[London]]: Tavistock, 1977; New York: W.W. Norton & Co., 1977: 146-78].</ref>
==Compendium==
Lacan first introduced the notion of mathème (matheme) in 1973: in his [[seminar]], of course, but more particularly in 'The Twit' ('L'Étourdit'), his last major piece of [[writing]]. That was the year of Seminar, Book XX, [[Encore]], and p. 108 of the transcript reads: '[[Formalization]] is our [[goal]], our [[ideal]]. Why? Because formalization as such is a mathème: it can be fully transmitted.'
In 'The Twit', he says that he has mathematized his discourse so that it could be taught: 'the unteachable, I turned into a mathème' ([[Scilicet]] 4, 1973, p. 39).
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.
Miller gives the witty example of the triangles and the spheres, but it is obvious that in this [[particular]] context the mathèmes are mathematical objects, such as the [[triangle]] or the sphere, but also the Borromean [[knot]], the torus, the Möbius [[strip]], and the geometrical [[projection]]. These objects are no longer at the edge of language, but rather at the point where the real, [[the imaginary]], and [[the symbolic]] intersect. Rather than [[being]] atoms of knowledge, each one of these objects is a concentrate of knowledge: that which governs the subject's relation to the Real. This means that, as J. A. Miller makes clear in the abovementioned article, the knowledge which is formalized in the mathème (and intertwined with [[satisfaction]]), represents a stake for the ending of the cure:
<blockquote>This is what Lacan has reformulated when he suggested that the experience be carried on to the point when the subject accedes to his own mathème, and more particularly the mathème of the primary fantasy, since this fantasy [[conditions]], indeed, determines, whatever keeps Mr So and So going all through his [[existence]]. (p. 11)</blockquote>
{{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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