# Talk:Matheme

The matheme is a concept introduced in the 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,[1] the term is an equivalent to "mathematical sign". It is not used in conventional mathematics, but is part of Lacan's algebra.

## Schema L

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Schema L

In 1955, Lacan introduced what could be called his first matheme, the relatively simple "schema L", illustrating the imaginary function of the ego.

Schema L identifies four points in the signifying chain:

1. , the unconscious or the "discourse of the Other]", and then .
2. , the subject, which in turn results from the relation between
3. , the ego and
4. , the other.

## Signifier

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The Saussurean algorithm

Perhaps the most familiar matheme is the "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".[2] The matheme links the laws of the unconscious discovered by Freud to the laws 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 signifier is reduced to mere lower-case italic), and that the two are separated by a bar that resists signification and forces the signifier to slide endlessly.[3]

## References

1. Mytheme is a term coined by Claude Lévi-Strauss to denote the basic constituents of mythological systems.
2. Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p. 149
3. Lacan, Jacques. "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." Trans. Alan Sheridan Écrits: A Selection. London: Tavistock, 1977; New York: W.W. Norton & Co., 1977: 146-78].

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They are formulae designed as symbolic representations of his ideas and analyses.

They were intended to introduce some degree of scientific rigour in philosophical and psychological writing, replacing the often hard to understand verbal descriptions with formulae resembling those used in the hard sciences, and as an easy way to hold, remember and rehearse some of the core ideas of both Freud and Lacan.

For example: \$ <> a is the matheme for fantasy for Lacan.

"Matheme", for Lacan, was not simply the imitation of science by philosophy, but the ideal of a perfect means for the integral transmission of knowledge.

Natural language, with its constant "metonymic slide", fails here, where mathematics succeeds.

Though sometimes disparaged as a case of "physics envy" or accused of introducing false rigor into a discpline that is more literary theory than hard science, there is also something of a sense of humor in Lacan's mathemes.

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Lacan begins to use a variety of graphs and 'schemata' at an early stage in his work.

Originally used as teaching aids, these range from teh relatively simply 'schema L' illustrating the imaginary function of the ego in the 1966 pape on psychosis to the complex chart of the workings of desire (1960).

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The graphs and schemata gradually become more complex, and are eventually replaced by an "algebra" of "little letters" or mathemes in which, for instance, "P" is the symbolic fahter, and "M" the symbolic mother.

The function of the formalization that results in the emergence of the amtheme is said by Lacan to be the integral transmission of his teachings on psychoanalysis.
Lacan, Jacques. Le Séminaire. Livre XX. Encore, 1972-73. Ed. Jacques-Alain Miller. Paris: Seuil, 1975.

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The two formulae which are most often referred to as mathemes were created in 1957 to designate points in the graph of desire.

These formulae, which were both created to designate points in the graph of desire, are the matheme for the drive, (\$ <> D), and the matheme for fantasy, (\$ <> a).

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The structural parallel between the two mathemes is clear; they are both composed of two algebraic symbols conjoined by a rhomboid (the symbol <>, which Lacan calls the poinçon) and enclosed by brackets.

The rhomboid symbolizes a relation between the two symbols, which includes the relations of "envelopment-development-conjunction-disjunction."[1]

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Lacan argues that the mathemes are "not transcendent signifiers; they are the indices of an absolute signification."[2]

They are "created to allow a hundred and one different readings, a multiplicity that is admissible as long as the spoken remains caught in their algebra."[3]

- They are constructed to resist any attempt to reduce them to one univocal signification, and to prevent the reader from an intuitive or imaginary understanding of psychoanalytic concepts: the mathemes are not to be understood but to be used.

In this way, they constitute a formal core of psychoanalytic theory which may be transmitted integrally.

"One certainly doesn't know what they mean, but they are transmitted."[4]

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"matheme" (mathème)

The term "matheme" 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 mythological systems).

The mathemes are part of Lacanian algebra.

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Although the term matheme is not introduced by Lacan until the early 1970s, the two formulae which are most often referred to as mathemes date from 1957.

These formulae, which were both created to designate points in the graph of desire, are the matheme for the drive, (\$ * D), and the matheme for fantasy, (\$ * a).

The structural parallel between the two mathemes is clear; they are both composed of two algebraic symbols conjoined by a rhomboid (the symbol *, which Lacan calls the poinçon) and enclosed by brackets.

The rhomboid symbolizes a relation between the two symbols, which includes the relations of "envelopment-development-conjunction-disjunction."[5]

##### More

Lacan argues that the mathemes are "not transcendent signifiers; they are the indices of an absolute signification."[6]

They are "created to allow a hundred and one different readings, a multiplicity that is admissible as long as the spoken remains caught in their algebra."[7]

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

In this way, they constitute a formal core of psychoanalytic theory which may be transmitted integrally.

"One certainly doesn't know what they mean, but they are transmitted."[8]

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The matheme is a concept introduced by French psychoanalyst Jacques Lacan.

Mathemes are formulae, designed as symbolic representations of his psychoanalytic conceptss.

The term 'matheme is a neologism coined by Jacques Lacan in the early 1950s.

Formed by derivation from 'mathematics' and by analogy with phoneme and Levi-Strauss's mytheme, the term is an equivalent to mathematical sign'.

Lacan begins to use a variety of graphs and 'schemata' at any early stage in is work.

They were intended to introduce some degree of technical rigour in philosophical and psychological writing, as an easy way to hold, remember, and rehearse some of the core psychoanalytic conceptss.

"Matheme", for Lacan, was not simply the imitation of science by philosophy, but the ideal of a perfect means for the integral transmission of knowledge.

## Mathemes

The main Lacanian mathemes in order of their appearance are:

Originally used as teaching aids, these range from teh relatively simple 'schema l' illustrating the imaginary function of the ego in the 1955 paper on psychosis to the complex chart of the workings of desire.

In Greek, mathêma means "that which is taught."

1. The "big graph" (1957) represented two different stages of the signifying chain.

Lacan situated jouissance, castration, the signifier, and the voice at the various points of intersection on this graph.

1. The four discourses (1969) were used to link the discourses of the master, the university, the hysteric, and the analyst.

Four terms—S1, the master signifier; S2, knowledge; /S, the subject; and a, surplus enjoyment—turn in a circular motion to take up four successive positions defined by the discourse of the master: the agent, the other, the production of the discourse, and truth.

1. The formulas of sexuation (1972) present sexual difference as a logical inscription.

Using the signs ?x, Fx, and ?x outside of the field of mathematics where they originated, Lacan inscribed a masculine psychical structure on one side and a feminine psychical structure on the other.

The graphs and schemata gradually become more complex, and are eventually replaced by an 'algebra' of 'little letters' or mathemes.

The function of the formalization that results in the emergence of the matheme is said by Lacan to be the integral tranmission of his teachings on psychoanalysis.

The Lacanian matheme is characterized by being both open and asymmetrical.

It does not tend towards closing discourse, and in spite of its character as a statement, it is primarily an enunciation.

And there lies the paradoxical aspect of the enterprise—to found a science of the subject.

Even though Lacan finally concluded that there can be no transmission of psychoanalysis, he always situated psychoanalysis within knowledge: access to the unconscious is legible and transmissible.

Mathemes advance and illustrate the theses that in relation to speech and writing, another structure besides that of grammar or syntax organizes speech, namely the structure of the signifier.

The Lacanian matheme proceeds neither by faith nor by pure mathematics.

Lacan situates religion on the side of making real, or "realizing," the symbolic of the imaginary, or RSI.

On the other hand, Lacan defined mathematics as imagining the real of the symbolic, or IRS.

If such were the case with the matheme, then it could become a model of the real.

In fact, it is no such thing.

Lacan never used mathematics as a demonstration, but as an exercise necessary for a better reading of the unconscious.

Thus the mathemes should be read with a shift that allows for them to be situated as a symbolizing of the imaginary of the real, or SIR .