fragment: matheme, nonknowledge

What is the definition of nonknowledge operational here? How are we to conceive of mathematical knowledge as being non-conceptual, non-discursive, nonknowledge? The most salient definition is not found in Bataille (who originated the concept) but rather the psychoanalytic concept of the Lacanian matheme.[1] The word matheme designates a pedagogically useful (from the Greek μάθημα: “lesson”)[2] algorithm or formula which is often “algebraic,” such as the Saussurean equation “S/s” (the signifier over the signified). However, it is also meant to describe a “mathematized” code or procedure that is undertaken according to the operations designated by intelligible signs. Lacan considered the matheme qua “lesson” to be a useful device for transmitting psychoanalytic (non)knowledge; however, we should assert that the name “matheme” is not purely an invention relevant to the psychoanalytic field but is rather a description of what is represented by a mathematical algorithm, formula, or operation in all mathematically formalized fields. This second nonpedagogical usage indicates that it is not merely a schema for representing psychoanalytic concepts but a way of designating those objects which are subordinated to mathematical laws and operations (this would be the minimal difference between Lacan and Badiou’s conception of the matheme).[3] In other words, a matheme represents knowledge insofar as it is purely procedural, operational, and symbolic; this definition of what the matheme represents we can take to be coextensive to nonknowledge. Or, rephrased, a matheme represents knowledge insofar as knowledge exists without a subject, i.e., it can be repeated by any subject and function autonomously (e.g., if a matheme uses quantitative variables it could be calculated by a computer).

[1] Wikipedia: “They are formulae, designed as symbolic representations of his ideas and analyses. They were intended to introduce some degree of technical 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: ‘$<>a’ is the matheme for fantasy in the Lacanian sense, in which ‘$’ refers to the subject as split into conscious and unconscious (hence the matheme is a barred S), ‘a’ stands for the object-cause of desire, and ‘<>’ stands for the relationship between the two.”

[2] Ibid.

[3] R.T. Groom summarizes this fairly well while illustrating some inherent problems with the matheme: “The ‘matheme’ […] has subsequently been interpreted along two different modes, one we will call philosophical and stenographical-poetic (I), and the other we will call psychoanalytic and abbreviative-mathematic (II). […] Both (I) and (II) have this minimum in common: the matheme will be to mathematics as the phoneme is to phonematics—just as the former is a unit of knowledge (savoir), the latter is a unit of phony. The crucial question remains, however, how to determine whether a matheme is not merely a scribble or jumble of letters. And if it is not, how do we account for its correlation to a minimal unit (-eme) of knowledge (savoir). If this correlation is left at the intuitive level, one can very well seek to respond to such a query by proposing to establish the effectivity (Wirlichkeit) of the matheme at the level of transmissibility. In which case the scope of the term effectivity reduces to a mode of stenography: much as a secretary uses certain glyphs to economize longhand or spoken discourse. […] Whatever one may think of such a claim, at least the position of interpretation (I) is clear: a) the matheme assures the integral transmissibility of a knowledge (savoir); b) the matheme conforms to the paradigm of mathematics; c) the matheme is the basis on which to assure teachings of a School, not as master-disciple of the academy, but as a purely positional transmission of the doctrine of modern mathematics” (“From L'être et l'événement to Lettre et significant, p. 1).

• La palabra <Mathem> es una palabra anglosajona del inglés antiguo que quiere decir literalmente “regalo”, “ornamento” o, más propiamente, “tesoro”. Generalmente se la utilizaba para definir a todo aquel presente dado por un pariente. No obstante “pariente” en un sentido tradicionalista escandinavo abarca cualquier persona estimada sea o no de la misma sangre. Si bien durante los periodos de la Edda se obtenían multitud de regalos con motivo de las hazañas y las conquistas sólo uno o dos llegaban a la calidad de <mathem> entendido como <tesoro> en un sentido de legado místico. Ejemplo de esto podemos encontrarlo en el la épica de Beowulf donde en  los momentos antes de su muerte le confiere su espada (en otras versiones un collar) a su sobrino  Wiglaf, clamándole como nuevo rey en su lugar. El objeto en cuestión termina convirtiéndose en un <Mathem>; el mathem de Wiglaf.