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Matheme

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| [[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]].
<!-- 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 "[[20th centurymathematics]] " and by analogy with [[Francephoneme]] 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|Frenchmathematical sign]] ". It is not used in conventional [[psychoanalystmathematics]] , but is part of [[Jacques Lacan]]'s [[algebra]]. -->
They are ==Schema L==[[formula]]e, designed as [[symbol]]ic [[representation]]s of his [[idea]]s and [[analysisImage:Schema.L.simplifie.gif|thumb|150px|right|analysesSchema L]].
They were intended to introduce some degree of technical rigour in In 1955, [[philosophicalLacan]] and introduced what could be called his first [[psychologicalmatheme]] writing, replacing the often hard-to-understand verbal descriptions with formulae resembling those used in the relatively simple "'''[[hard scienceschema L]]s'''", and as an easy way to hold, remember, and rehearse some of illustrating the core ideas of both [[Sigmund Freudimaginary|Freudimaginary function]] and of the [[Lacanego]].
'''[[Schema L]]''' [[identification|identifies]] four points in the [[signifying chain]]: # [[Image:CapitalA.gif]], the [[unconscious]] or the "[[Mathemediscourse]] of the [[Other]]]", for and then .# [[LacanImage:Smalls.gif]], was not simply the imitation of [[sciencesubject]] by , which in turn results from the relation between # [[philosophyImage:Schema.L.smalla.gif]], but the ideal of a perfect means for [[ego]] and # [[Image:Schema.L.smalla'.gif]], the integral transmission of [[knowledgecounterpart|other]].
==Signifier==[[Natural]] [[languageImage:SAUSSUREANALGORITHM.gif|thumb|100px|right|Saussurean algorithm|The Saussurean algorithm]], with its constant "metonymic slide", fails here, where [[mathematics]] succeeds.
Contemporary philosopher Perhaps the most familiar [[Alain Badioumatheme]] identifies 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 scientific procedure[[law]]s of [[language]] ([[metaphor]] and [[metonymy]]).
==def==In GreekThis 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.<iref>mathêma{{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].</iref> means "that which is taught."
Following the same path that led [[Freud]] to the discovery of [[slip]]s and [[joke]]s, [[Lacan]] forged connections between the fields of spoken discourse and logical inscription. ==Compendium==
In 1955, he Lacan first introduced what could be called the notion of mathème (matheme) in 1973: in his first [[mathemeseminar]], schema 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 main [[Lacan]]ian Twit', he says that he has mathematized his discourse so that it could be taught: 'the unteachable, I turned into a mathème' ([[mathemeScilicet]]s in order of their appearance are:4, 1973, p. 39).
<i>Schema L</i> (1955), which identifies four points But what exactly is a mathème? What does Lacan have in [[mind]]?Is he [[thinking]] of the signifying chain: first[[formulas]] that [[punctuate]] his [[teachings]], such as the unconsciousformulas for metaphor and metonymy, for [[instance]], or the discourse formulas for [[sexuation]]? Or is he rather thinking of the Other (A), [[topological]] constructions on the torus and then the subject (S)[[cross-cap]] that he had just introduced, not as metaphor, which in turn...but as structure itself?
If one tracks down the word 'mathème' in 'The term Twit', it first appears to be intertwined with the topological [[mathemeconstruction]]presented as contributing to the analytical discourse, to its fabric: '' is No other fabric to endow it with but the language of a neologism coined by pure matheme, in other [[Jacques Lacanwords]] in , the early 1950sonly teachable discourse' (1973, p. Formed by derivation from '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]]' and [[sexual]] relation, which, in point of fact, cannot be transcribed by analogy with any [[phonememathematical]] and Levi-Straussrelation: 's This is why the mathèmes which are transcribed as [[mythemedead]]-ends by the mathematizable, that is, the teachable in the term is an equivalent Real, are likely to be coordinated to this "impossible" from the Real''mathematical sign'(p. 35).
How is the mathème apprehended in the structure of our language? The first mathèmes, the arithmetical [[Lacanfigures]] begins to use , are on the border of language, in its fringe: 'The mathème is a variety product of graphs and the only real which is first recognized in language: the arithmetical [[figure]]'schemata' at any early stage in (1973, p. 37). The arithmetical figure is workon the border between common language and mathematical discourse. The first figures are [[signifiers]], but these quickly become meaningless.
In 1955L'Oeuvre Claire (1995), he introduced 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 could be called his first J. A. [[mathemeMiller]]means when, talking [[about]] the mathème in the Revue de la [[schema LCause]]Freudienne No. 33, illustrating he says that the aim of the analytical [[experience]] is to `[[know]] one's own mathème' (1996). What is important then, is less to [[imaginaryformalize]] function of the knowledge achieved during the [[cure]], than to [[egoidentify]]with one's own mathème.
Originally used 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 teaching aidsthe [[triangle]] or the sphere, these range from teh relatively simple 'schema l' illustrating but also the Borromean [[knot]], the torus, the Möbius [[strip]], and the geometrical [[imaginaryprojection]] function . These objects are no longer at the edge of language, but rather at the point where the real, [[egothe imaginary]] in , and [[the 1955 paper on symbolic]] intersect. Rather than [[psychosisbeing]] atoms of knowledge, each one of these objects is a concentrate of knowledge: that which governs the subject's relation to the complex chart of Real. This means that, as J. A. Miller makes clear in the abovementioned article, the knowledge which is formalized in the workings of mathème (and intertwined with [[desiresatisfaction]].), represents a stake for the ending of the cure:
In <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 [[Greekconditions]], ''mathêma'' means "that which is taughtindeed, determines, whatever keeps Mr So and So going all through his [[existence]]. (p." The main Lacanian mathemes in order of their appearance are:11)</blockquote>
# [[Schema L]] (1955), which identifies four points in The stakes of the signifying chain: first, mathème are many. After the [[unconscious]]fundamental stake, or which has to do with the [[discourse]] aim of the [[Other]] (A)cure, there is teaching, as my first allusions to the mathème and its definitions make clear; then the there is a [[subjectpolitical]] (S), which in turn results from the relation between the [[ego]] (stake and a) to the [[otherclinical]] (a) to the other (d)one.
# The If the only valuable teaching is the one that can be transcribed into a mathème, then the teacher's [[formularole]] of 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 [[signifier]] journal where 'The Twit' (1957'L'Étourdit'), S/was first published is — except for Lacan's, links the [[lawtexts]]— a collection of unsigned articles after Bourbaki's style of presentation, Bourbaki being one of the collective and anonymous mathematical writers of the [[unconscioustime]] discovered by [[Freud]] to . As J. C. Milner points out in his book on Lacan, the [[lawmaster]]'s of figure [[languagedisappears]] ([[metaphor]] and [[metonymy]])with the mathèmes: we are left with professors.
Perhaps 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 most familiar is light of what Lacan called the 'algorithm' topology of signifiers, which taps in 1957 replaces the general topology of kinship between signifiers, a topology which, according to Lacan, is budding, if not [[Saussureborn]], in Freud's simple diagram '[[Project]]' (Esquisse, see [[Ornicar]]? 36). Inasmuch as it can be separated from the [[clinic]] of signifiers, the clinic of the [[signobject]] / arbor with is spotted in, by, and through, the notation S/stopology of surfaces, just as Lacan shows in 'The Twit' and in some of his later [[seminars]].
This Later, J. A. Miller took up the clinical stake. He focused on interpretation. There is to be understood as demonstrating a trace of this concern in Revue de la cause Freudienne, No. 34. The classical interpretation that the focused on [[signifiermeaning]] is above 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 [[signified]]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, and then interpretation is a matter of formalization — supposing that the two are separated by a [[bar]] mathematical formalization is the only one that resists [[signification]] and forces can reach the [[signifier]] to slide endlesslyReal. 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 [[big graphlack]]" 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 (1957or to [[invert]] elements in the pun, père-version) represented two different stages of , that holds the knot together. It might now be possible to differentiate between types and to [[signifying chainoutline]]a clinic.
<!--See also: Borromean knot, formulas, imaginary, real, symbolic, topology other [[Lacan]] situated [[jouissanceterms]]: fantasy, [[castration]]interpretation, the [[signifier]]symptom, and the [[voice]] at the various points of intersection on this graph.torus
# The [[four discourses]] (1969) were used to link the discourses of the [[master]], the [[university]], the [[hysteric]], and the [[analyst]].
Four terms—S1References Lacan, the [[master signifier]]; S2J. (1973) 'L'Étourdit' (The Twit). Scilicet, [[knowledge]]; /S4. Lacan, the J. (1975) [[subject1972-73]]; and aDe Séminaire XX Encore. Paris, [[surplus enjoyment]]—turn in a circular motion to take up four successive positions defined by the [[discourse]] of the [[master]]: the [[agent]]Seuil. Lacan, the [[other]], the production of the discourseJ. (1976) De Sinthome, and [[truth]]. # The [[formulas of sexuation]] Séminaire XXIII (19721975-76) present , [[sexual differenceornicar?]] as a logical inscription.  Using the signs ∃x6, 7, 8, Φx9, and ∀x outside of the field of [[mathematics]] where they originated10, 11 [[Lacan]Provisional transcription] inscribed a [[masculine]] [[psychical]] [[structure]] on one side and a [[feminine]] [[psychical]] [[structure]] on the other. The graphs and schemata gradually become more complexLacan, and are eventually replaced by an '[[algebra]]' of 'little letters' or [[matheme]]sJ. The function of the (1986) [[formalization]] that results in the emergence of the [[matheme]] is said by [[Lacan]] to be the integral tranmission of his teachings on [[psychoanalysis]1945-46]Esquisse. The [[Lacanian]] [[matheme]] is characterized by being both open and asymmetricalornicar? 36.  It does not tend towards closing discourseMiller, and in spite of its character as a [[statement]], it is primarily an [[enunciation]]J. A.  And there lies the paradoxical aspect of the enterprise—to found a (1996) 'Retour de Granade: [[science]] of the [[subjectSavoir]]et satisfaction'.  Even though [[Lacan]] finally concluded that there can be no transmission of [[psychoanalysis]]Revue de la cause Freudienne, he always situated [[psychoanalysis]] within [[knowledge]]33: access to the [[unconscious]] is legible and transmissible7-15.  [[Matheme]]s advance and illustrate the theses that in relation to [[speech]] and writingMiller, another [[structure]] besides that of grammar or syntax organizes [[speech]], namely the [[structure]] of the [[signifier]]J. A.  The [[Lacan]]ian [[matheme]] proceeds neither by faith nor by pure [[mathematics]](1996) 'De monologue de l'appard'.  [[Lacan]] situates [[religion]] on the side of making [[real]]Revue de la cause Freudienne, or "realizing," the [[symbolic]] of the [[imaginary]]34: 7-18. Milner, or RSIJ. On the other hand, [[Lacan]] defined [[mathematics]] as imagining the [[real]] of the [[symbolic]], or IRSC.  If such were the case with the [[matheme]], then it could become a model of the [[real]](1995) D'oeuvre Claire.  In fact, it is no such thingParis: Seuil.  [[Lacan]] never used [[mathematics]] as a demonstration, but as an exercise necessary for a better reading of the [[unconscious]]Nathalie Charraud (trans. Dominique Hecq) Thus the [[matheme]]s should be read with a shift that allows for them to be situated as a [[symbolizing]] of the [[imaginary]] of the [[real]], or SIR .-->
==See Also==
{{See}}* [[Algebra]]* [[Borromean knot]]* [[Drive]]* [[Four discoursesFantasy]]||* [[Formula]]s* [[Graph of Desiredesire]]* [[Imaginary]]* [[L and R schemasInterpretation]]||* [[Forumalas of SexuationKnowledge]]* [[Mathematics]]* [[Real]]* [[Schema]]||* [[Signification]]* [[Structure]]* [[Subject]]* [[Symbol]]||* [[Symbolic]]* [[Symptom]]* [[SignifierTopology]]/* [[signifiedTorus]]{{Also}}
==References==
<div style="font-size:11px" class="references-small">
<references/>
* [[Lacan, Jacques]]. (20021973)Écrits: A selection 'L'Etourdit' (Bruce FinkThe Twit). Scilicet, Trans4.* [[Lacan, Jacques]]. (1975)[1972-73] Le Seminaire xx Encore. New York: WParis, Seuil. W* [[Lacan, Jacques]]. Norton(1976) Le Sinthome, Seminaire XXIII (1975-76), Ornicar? 6, 7, 8, 9, 10, 11 [Provisional transcription].* ——[[Lacan, Jacques]]. (1986) [1945-46] Esquisse. Ornicar? 36. Le Séminaire* [[Miller, Jacques-Livre XXIAlain]]. (1996) 'Retour de Granade: Savoir et satisfaction'. Revue de la cause Freudienne, Les non33: 7-dupes errent 15. * [[Those Who ArenMiller, Jacques-Alain]]. (1996) 'Le monologue de l'appard't Duped Err/The Names of the Father. Revue de la cause Freudienne, 34: 7-18. * [[Milner, Jean-Claude]] . (1973-19741995)L'Oeuvre Claire. Unpublished seminarParis: Seuil.</div> {{OK}}
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