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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}}

==Neologism==The term "[[matheme|mathème]]" is a neologism which [[Lacan]] derives from the [[word ]] "[[mathematics]]" -- , presumably by analogy with the term ''[[Claude Lévi-Strauss|mytheme]]''.<ref>''Mytheme'' is (a term coined by [[Claude Lévi-Strauss]] to denote the basic constituents of mythological systems[[myth]]ological [[system]]s).<ref>[[Claude Lévi-Strauss|Lévi-Strauss, Claude]]. 1955.</ref> The [[matheme]]s are part of [[algebra|Lacanian algebra]].

==Algebra==<!-- The [[mathemesmatheme]] are 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]]ian 's [[algebra]].-->

==Jacques LacanSchema L==Although the term [[matheme]] is not introduced by [[Lacan]] until the early 1970s, the two formulae which are most often referred to as [[mathemeImage:Schema.L.simplifie.gif|thumb|150px|right|Schema L]]s date from 1957.

==Drive and Fantasy==These [[algebra|formulae]]In 1955, which were both created to designate points in the [[graph of desireLacan]], are the introduced what could be called his first [[matheme]] for , the relatively simple "'''[[driveschema L]], ('''$ <> D''')", and illustrating the [[mathemeimaginary|imaginary function]] for of the [[fantasyego]], ('''$ <> ''a''''').

==Structure=='''[[Schema L]]''' [[identification|identifies]] four points in the [[signifying chain]]: The # [[structuralImage:CapitalA.gif]], the [[unconscious] parallel between ] or the two "[[mathemediscourse]]s is clear; they are both composed of two the [[algebraOther]]ic ]", and then .# [[symbolImage:Smalls.gif]]s conjoined by a rhomboid (, the [[symbolsubject]] '''<>''', which in turn results from the relation between # [[LacanImage:Schema.L.smalla.gif]] calls , the [[ego]] and # [[Image:Schema.L.smalla''poinçon'') and enclosed by brackets.gif]], the [[counterpart|other]].

The rhomboid ==Signifier==[[symbolizeImage:SAUSSUREANALGORITHM.gif|thumb|100px|right|Saussurean algorithm|The Saussurean algorithm]]s a relation between the two [[symbol]]s, which includes the relations of "envelopment-development-conjunction-disjunction."<ref>{{E}} p.280</ref>

==Signification==Perhaps the most familiar [[Lacanmatheme]] argues that is the "[[matheme|algorithm]]" which in 1957 replaces [[Saussure]]'s are "not transcendent signifiers; they are simple diagram / arbor with the indices [[notion]] '''S/s'''. In 1957, [[Lacan]] replaces [[Saussure]]'s diagram of an absolute significationthe [[sign]] with what is now referred to as the "'''[[Saussurean algorithm]]'''"."<ref>{{E}} p. 314149</ref> The [[matheme]] [[links]] the [[law]]s of the [[unconscious]] discovered by [[Freud]] to the [[law]]s of [[language]] ([[metaphor]] and [[metonymy]]).

They are "created 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 allow a hundred mere lower-[[case]] italic), and one different readings, that the two are separated by a multiplicity [[bar]] that is admissible as long as resists [[signification]] and forces the spoken remains caught in their algebra[[signifier]] to [[slip|slide]] endlessly."<ref>{{EL}} p"[[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]. 313</ref>

==Psychoanalytic TheoryCompendium==They are constructed to resist any attempt to reduce them to one univocal [[signification]], and to prevent the reader from an intuitive or [[imaginary]] [[knowledge|understanding]] of [[:category:concepts|psychoanalytic concepts]]: the [[mathemes]] are not to be understood but to be used.

In this wayLacan 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, they constitute a formal core [[Encore]], and p. 108 of the transcript reads: '[[psychoanalytic theoryFormalization]]is our [[goal] which may ], our [[ideal]]. Why? Because formalization as such is a mathème: it can be fully transmitted integrally.'

<blockquote>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"One certainly doesnfrom 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't . 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 what they mean]] 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 they also the Borromean [[knot]], the torus, the Möbius [[strip]], and the geometrical [[projection]]. These objects are transmittedno 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:  <refblockquote>{{S20}} 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. 10011)</refblockquote> The stakes of the mathème are many. After the fundamental stake, which has to do with the aim of the cure, there is teaching, as my first allusions to the mathème and its definitions make clear; then there is a [[political]] stake and a [[clinical]] one.  If the only valuable teaching is the one that can be transcribed into a mathème, then the teacher's [[role]] is reduced to the ultimate: to transmit an elaboration without having anything to do with it. The consequence is the same with all writing: Scilicet, the journal where 'The Twit' ('L'Étourdit') was first published is — except for Lacan's [[texts]] — a collection of unsigned articles after Bourbaki's style of presentation, Bourbaki being one of the collective and anonymous mathematical writers of the [[time]]. As J. C. Milner points out in his book on Lacan, the [[master]]'s figure [[disappears]] with the mathèmes: 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]].  Later, J. A. Miller took up the clinical stake. He focused on interpretation. There is a trace of this concern in Revue de la cause Freudienne, No. 34. The classical interpretation that focused on [[meaning]] is no longer convincing; we are witnessing what S. Cottet would describe as 'the decline of interpretation'. This led J. A. Miller to devise a conception of interpretation aiming at the level of the Real where 'it is loving it' (ça jouit) rather than at the level where 'it speaks' (ça parle). If the analytical interpretation is that through which the Real is asserting itself, then interpretation is a matter of formalization — supposing that the mathematical formalization is the only one that can reach the Real. This is what Lacan explores (1996, p. 18).  The Borromean knot provides an illustration of what Lacan was striving to achieve with a 'mathematical clinic'. This knot consists of [[three]] 'loops of string': two of these loops are loose while the [[third]] is tied. Thus, when one loop becomes undone, all three become undone. This first enabled Lacan to illustrate the [[solidarity]] of the three [[registers]], that is, [[the Imaginary]], the Real, and [[the Symbolic]], in the knot which defines the [[human]] subject. But in the year of his seminar on [[Joyce]], which is when the question of the structure of the writer arises, Lacan devises a knot with three untied loops that would collapse unless a fourth loop ties [[them]] all together. Lacan identifies this fourth loop with the symptom - spelled [[sinthome]] in Joyce's case. Thus, Joyce's [[psychosis]] never manifested, because his writing acted as a [[substitute]] that held together the three registers, despite Joyce's obvious [[lack]] of the [[paternal function]]. One could therefore generalize the question of the real of the symptom as being equivalent to the [[Father]], as father version (or to [[invert]] elements in the pun, père-version), that holds the knot together. It might now be possible to differentiate between types and to [[outline]] a clinic.  </blockquote!--See also: Borromean knot, formulas, imaginary, real, symbolic, topology other [[terms]]: fantasy, interpretation, symptom, torus   References Lacan, J. (1973) 'L'Étourdit' (The Twit). Scilicet, 4. Lacan, J. (1975) [1972-73] De Séminaire XX Encore. Paris, Seuil. Lacan, J. (1976) De Sinthome, Séminaire XXIII (1975-76), [[ornicar?]] 6, 7, 8, 9, 10, 11 [Provisional transcription]. Lacan, J. (1986) [1945-46] Esquisse. ornicar? 36. Miller, J. A. (1996) 'Retour de Granade: [[Savoir]] et satisfaction'. Revue de la cause Freudienne, 33: 7-15. Miller, J. A. (1996) 'De monologue de l'appard'. Revue de la cause Freudienne, 34: 7-18. Milner, J. C. (1995) D'oeuvre Claire. Paris: Seuil. Nathalie Charraud (trans. Dominique Hecq)-->

{{AlsoSee}}

* [[FantasyFormula]]s