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26 may. 2008

Symptom in the Machine: Lacan, Joyce, Sollers

By Louis Armand

Writing has no sooner begun than it inseminates itself with another reading. The Wake, fin negans, begets only beginnings but invalidates all origins, in a system which can be described as a word-machine, or a complex machination of meanings, probing and programming the seedy sides of meaning.1


Once again, we’re dealing with a mirror.
What is the image in the mirror? The rays which return on to the mirror make us locate in an imaginary space the object which moreover is somewhere in reality. The real object isn’t the object that you see in the mirror. So here there’s a phenomenon of consciousness as such. […] That is already enough to raise the question–What is left in the mirror?2

It is in a later seminar, in 1954, that Jacques Lacan, reflecting on the technics of the mirror dialectic, assigns a "materialist definition" to the phenomenon of consciousness by means of a metaphor of a particular type of photography. This will have entailed a revisiting, however elliptically, of a Cartesian cybernetics, an ego ex machina, playing against Walter Benjamin’s 1937 essay "Das Kunstwerk im Zeitalter seiner technischen Reproduzierbarkeit" (it is precisely the camera, as a mechanism of the gaze, by means of which Lacan envisages a certain "aura" as affecting itself, as we shall see).

In a hypothetical, post-humanist world from which man has disappeared, there remains only this mechanical form of reflexivity: a camera alone in nature. The "presence" of this camera is made to "mirror," in a sense, the non-presence of man. At the same time, an actual mirror, although we are not told this (we expect it), is itself "in" the camera, while the camera itself is trained on the surface of a lake, in which there appears an inverted image of a mountain. And despite, as Lacan says, "all living beings having disappeared, the camera can nonetheless record the image of the mountain in the lake," which is thus also (paradoxically) a record of its non-presence there. But Lacan goes further and ponders a certain incendiary intervention:

We can take things further. If the machine were more complicated, a photo-cell focused on the image in the lake could cause an explosion to take place somehow–it is always necessary, for something to seem efficacious, for an explosion to take place somewhere–and another machine could recall the echo or collect the energy of this explosion.3

But there is a slightly different way of looking at this: supposing that in place of this oppositional arrangement of the organic and inorganic (physis/technē), with its Rousseauesque overtones, there were merely the camera positioned in front of a mirror. Assume, then, that something or other sets in train the course of events described by Lacan above: photo-cell, explosion, echo, an "other" machine. What is left in the mirror? in the illusory depth beyond the gliassant surface of the lac? Perhaps, after all, it will be nothing but an illuminated blind, a trail of light, in which the image of the explosion in fact ruins the visible. And whether or not this is recorded by some third party, it will have been nothing other than the "consciousness" of an impossible event, in which the ego has still not managed to resurrect itself.

Of what is left in this double mirror–kept or retained there, the trace of a circuit of symbolic capture. (The illusionism of a mirror which both reflects and transmits.) A mechanism or aperture effect: written on the sensitised film (memory screen), which is immediately exposed, "erased" the moment the film loses its transparency, becomes opaque in the light. Explosion, after effect of the image burnt into the mechanised retina. (The incendiary counterpart of that other mystic writing pad?) But as Lacan says, "the symbolic world is the world of the machine." Hence it is a matter of having confused the symbolic relation as being some thing–some thing which thinks–beyond the surface appearance, or disappearance, of reflexivity. This "mechanism" is not identical to the auto-mobile, god-like phantom of metaphysics described by Pythagoras (anima est numero se ipsum movens, "the spirit is the number that moves itself") and Aristotle (who in De Anima argues that the soul, as seat of consciousness, is the principle of all movement, or prime mover). Consciousness, rather, "is linked to something entirely contingent, just as contingent as the surface of a lake in an uninhabited world." Moreover, for "consciousness to occur each time" there needs to be a surface on which it "can produce what is called an image." But this production does not describe an affirmation of the "subject" in itself or of a "psychology" in nature: it is a symbolic play of production, and insofar as he is committed to a play of symbols, "man is a decentred subject."4

In this contingent, eruptive play, of language, a surface (of the lac of an uninhabited world) describes a place of the encounter and struggle of the ego and its others: the incendiary topos of a violent "anthropology" versus an "implacable dialectic of transcendent consciousness" (Deus ex machina as machina ex Deo). Continuous with Lacan’s critique of the cogito, then, is a critique of Descartes’s mechanistic interpretation (Discours de la Méthode) of biological phenomena as automata, which links back to the mimetic technologies of Plato and Aristotle. As Georges Canguilhem has argued:

The construction of a mechanical model presupposes a living original […]. The platonic Demiurge copies the ideas, and the Idea is the model of which the natural object is a copy. The Cartesian God, the Artifex maximus, works to produce something equivalent to the living body itself. The model for the living machine is that body itself. Divine art imitates the Idea–but the Idea is the living body.5

Canguilhem’s discussion of Descartes points to one way in which technology has been made to relate to a "non-technological" world, according to the old philosophical dualism physis/technē, which works to sustain the fallacy that technē is somehow "opposed" to physis.

By ascribing a materialist organisation to consciousness, however, Lacan departs from the analogical thinking which previously sought to establish a direct relation between machines and organisms, thus circumventing the dualistic fallacy and the anthropomorphism which sustained it. The machine does not take the place of consciousness (or of conscience), nor does it absolve the subject of the burden of the "Real." Rather it situates the subject as a figure of recursion (a mechanism, in fact, of recursive substitution), simultaneously inscribed within and exceding the symbolic organisation of the machine, since 1. "the ego can in no way be anything other than an imaginary function, even if at a certain level it determines the structuration of the subject"; 2. "for the human subject to appear, it would be necessary for the machine, in the information it gives, to take account of itself, as one unity among others."6 And yet this is precisely what the machine cannot do. On the other hand, as Lacan points out, the ego isn’t just a function, since from the moment when the symbolic system is instituted it can itself be used as a symbol. This would seem to return the ego to the domain of the machine, and insofar as the subject comes to identify with the ego it assigns to itself an implicitly mechanical placement in the circuit of symbolic exchange.

What this might seem to suggest, at least in part, is that the machine in some way "returns" something to the subject. At the moment when Lacan asserts that there is not the "shadow of an ego" in the machine, he gives to the subject a recursive figuration as the I who is nevertheless "up to something in it." That is, in the machine–or we might say, as the spectral counterpart to what is left in the mirror (as its "symptom," for which the machine, as a "topological" figure, describes what Lacan will later term the sinthome): "The machine is the structure detached from the activity of the subject. The symbolic world is the world of the machine."

Elsewhere Lacan relates the aperture effect of this symbolic machine (mirror apparatus) to the base materialism of a certain selbstgeschaffene game, within the schematic of the Freudian complex. Watching his grandson playing in his pram one day, Freud observed him throwing a toy out of the pram and exclaiming in sounds that Freud interpreted as signifying the German word fort! (away), then hauling it back in by means of a leash to the cry of da! (here).7 The mechanical repetition of this game not only describes an ellipsis in the subject relation (which it prototypically structures), but also as a type of metonymic forethrow, in which the subject’s relation to self (its Being-there) is already structured as a rebus or symptom (a signifying chain inaugurated by its "primordial symbolisation").8 The fort/da mechanism likewise opens up a space which is not contained within the narrative sequence but which describes a space of repetition itself, what Lacan terms the "‘perverse’ fixation at the very suspension-point of the signifying chain."9 This space, however overly determined, allows for possible contingencies to arise (for instance, the "chance" of the object not being returned). Without this possibility the game itself could have no force, other than that of an attempt to dispense with any responsibility for the "it" to which the subject is tied. Such an outcome, which would mark the game’s termination, necessarily stands outside the "system" described (in the form of a detour or détournement) by the fort/da game. Moreover, the material function of the game, while foregrounding a certain objecthood, nevertheless conceals its object: the "object" which the subject "causes" to appear and disappear, is also a rebus, whose decipherment points to the subject’s own disappearance from the game, as an "object in itself." In a sense, this possibility marks the dissymmetry between the closed system (of a dialectics, of identification, desire, etc.) and its discursive apparatus (within which the system is inscribed but which cannot be totalised or brought within that system, let alone be comprehended by it). Hence the "possibility" of a terminus (the accession to the object via a dialectic of return) functions as the locus of the fort/da ritual as well as of its incendiary Phoenix-like myth–as the terminus of possibility itself.

The mechanism of the fort/da relation might consequently be thought of as describing what chaos theorists term a "strange attractor" (in its manner of operating as a structural axis or hinge between the mechanics of chance and sublimation of desire). The illusion of the either/or repetitiveness of the game is belied in the nature of the absence which prefigures it and determines its dynamic as a play towards loss, to an always prior loss, of which it is the graphic expression. In other words, the fort/da "repetition" is in fact a repetition only in the sense that it presents a figure of an entropic forethrow towards the "there" of da which is never "here," and to which the psychoanalytic subject is tied by a kind of metonymic leash. What is more, the movement of this forethrow is such that the subject is "subverted"–a "turning under" which defines a tropic spiral in the dialectic of desire, a vectoral clinamen which Lacan locates in the paradoxical structure of the Freudian drives:


This paradox (between aim and goal) rests in what Lacan terms a "fundamental reversion," which at the level of each of the drives "is the movement outwards and back in which it is structured."10 Moreover, this paradox is irreducible and is in fact the structural motivation of the drive, just as the unassimilable repetition of the "there" stands as the point of motivation in the compulsive fort/da ritual. The reduction of the subject to a moment of repetition, or locus in the cyclical reversion of the drives, defines a fundamental redundancy in which the subject is lost through a series of substitutions whose site it is (as a type of hole or void which must be filled). At the same time, it is the nature of the unassimilable object which prevents the structural subject from vanishing entirely, and instead sustains it (as a figure of lack) within an apparently limitless play of signifying substitution which, while defining a movement of entropy, can nevertheless be regarded as generative.

For Freud, this fort/da game is interpreted on one level as depicting the child’s symbolic mastery over the mother’s absence, and is accordingly taken to provide the basis of all future narratives of loss and recovery. It is for this reason that Lacan describes the "circularity" of the trajectory of the subject’s desire–a circularity which remains unclosed and elliptical or decentred–as "la parabole de la lettre."

We could also say that this serial repetition (of repetition itself) gives rise to a form of "telepathy" whereby the subject is put into communication with the Other (or rather, by which the child is communicated as subject of its signifying attachment to an imaginary (m)other). Importantly, Freud describes this movement by the verb fortgehen, "to go away," which necessarily leaves open the possibility of return and remains ambiguous in this sense (as in fort, to continue)–as opposed, for instance, to weggehen, to go away or leave, which suggests a definite absence. This possibility of return (of "revealing"), which poses itself as an imminence (the impossibility of which, beyond substitution, poses a threat which is concealed precisely through repetition), describes a destining that, in "Die Frage nach der Technik" (1954), Heidegger identifies with a certain technological movement. This is elaborated in a passage dealing with two words from Goethe which echo, in an intriguing way, the text of Freud:

The way in which technology unfolds lets itself be seen only on the basis of that permanent enduring in which enframing [Gestell] propriates as a destining of revealing. Goethe once uses the mysterious word fortgewähren [to grant continuously] in place of fortwähren [to endure continuously]. He hears währen [to endure] and gewähren [to grant] here in one unarticulated accord. And if we now ponder […] what it is that properly endures and perhaps alone endures, we may venture to say: Only what is granted endures. What endures primally out of the earliest beginning is what grants.11

It is, as always, a question of granting agency in that which speaks: ego, cogito–and its transposition in the passive voice, as that which is placed, situated in the ergo, which is also the ergon of an auto-poietic discursus–and which describes "l’ergo retourné d’un nouveau cogito."12


In cybernetics the term autopoietic refers to machines organised as a network of processes of production, transformation and destruction. This network gives rise to components which, through their interactions and transformations, regenerate and in turn realise the network or processes that produced them. At the same time these components constitute the network as a concrete unity in the space in which they exist by specifying the "topological domain of its realisation."13 In other words, the components of autopoietic machines generate recursively, by means of their interaction, the same network of processes by which they themselves are produced.

To a significant extent, the idea of the autopoietic machine operates between what Viktor Tausk conceived as an "influencing machine" and what Antonin Artaud described as a "the body without organs": a body which "is produced as a whole, but in its own particular place within the process of production, alongside the parts that it neither unifies nor totalizes."14 This sense of a body-machine, produced "alongside" its parts, echoes Tausk’s notion of the influencing apparatus as a type of perverse specular counterpart–the terminal manifestation in a symptomatology whose etiology is one of alienation and regressive loss of ego boundaries. Like Artaud’s body without organs, the influencing machine operates as a body prosthesis, whose substitution for the material body initiates a chain of other substitutions, of which it becomes the symptomatic expression, while at the same time nevertheless representing a mechanism of objectification.15 Hence for Tausk, this machine is above all a symptom, whose relation to the alienating process of its objectification can be described as autopoietic, since it is also a projection and sublimated identification (through which lines of "influence" are preserved and in fact reinforced). Similarly, when the body without organs "turns back upon" its other parts, it brings about–what Gilles Deleuze and Félix Guattari subsequently described as:

transverse communications, transfinite summarizations, polyvocal and transcursive inscriptions on its own surface, on which the functional breaks of partial objects are continually intersected by breaks in the signifying chains, and by breaks effected by a subject that uses them as reference points in order to locate itself.16

In a key passage towards the end of Book I of Finnegans Wake, James Joyce describes a like process of autoproduction and topical recursion (symptomatisation), in which the plagiarist-author figure of Shem-the-Penman is depicted as producing:

nichthemerically from his unheavenly body a no uncertain quantity of obscene matter not protected by copriright in the United States of Ourania or bedeed and bedood and bedang and bedung to him, with his double dye, brought to blood heat, gallic acid on iron ore, through the bowels of his misery, flashly, nastily, appropriately, this Esuan Menschavik and the first till last alchemist wrote over every square inch of the only foolscap available, his own body, till by its corrosive sublimation one continuous present tense integumented slowly unfolded in all marryvoising moodmoulded cyclewheeling history. [FW 185.29, 186.02]

Writing with his excrement across the entire surface of his own body, Shem ("name" in Hebrew) symbolically obscures the distinctions between tropos and topos (or perhaps copros) in a single act of "reflexivity" or autopoiesis (the retroverted nom-du-Père whose metonym–nom-du-fils–is a "coprophagic" counterpart, à la Artaud). Or rather, this narcissistic/anal reversion crosses between a topological space within language ("letter from litter") and a tropological space within the topos of this relation, whereby we might think of Finnegans Wake (whose metonym this excremental writing is) as emerging from a symptomatology of autopoietic involution, or what Joyce calls "morphological circumformation" (FW 599.09-17).

Such a mechanism of "circumformation" recalls what Jacques Derrida, in his essay "Deux mots pour Joyce," terms "a hypermnesiac machine."17 Following Joyce’s writing practice in Finnegans Wake, Derrida is interested in how the idea (eidos) put to work hypermnemically, as an alternative to the intuition or direct experience of phenomenology, is not the signified concept but the elision of meaning brought about in language by the symptomatic re-alignment of narratives, tropes, themes, genres, but also individual words, letters or phonemes.

Elsewhere Derrida suggests that this elision would give rise to a type of hypertextual apparatus which would operate "in two absolutely different places at once, even if these were only separated by a veil,"18 an idea he further elaborates upon in "Deux mots pour Joyce":

Paradoxical logic of this relationship between two texts, two programmes or two literary "softwares": whatever the difference between them, even if [...] it is immense and incommensurable, the "second" text, the one which, fatally, refers to the other, quotes it, exploits it, parasites it and deciphers it, is no doubt the minute parcel detached from the other, the metonymic dwarf, the jester of the great anterior text [...] and yet it is also another set, quite other, bigger, and more powerful than the all-powerful which it drags off and reinscribes elsewhere in order to defy its ascendancy. Each writing is at once the detached fragment of a software more powerful than the other, a part larger than the whole of which it is a part.19

This topological structure of the relationship, between two textual programmes, describes a species of mise en abyme, wherein a "totality" "is represented on the model of one of its parts which thus becomes greater than the whole of which it forms a part, which it makes into a part"; a metonymic "chain of substitutions," of the supplément [Nachtrag], or operation of "decentring," which suggests analogies to what the mathematician Henri Poincaré termed the "Vicious Circle Principle" and which Bertram Russell in 1908 defined as an exclusion of metonymic totality.20 For Russell, "whatever involves all of a collection must not [itself] be one of the collection."21

In the "Mamafesta" section of Finnegans Wake (I.5), this set theoretical principle of metonymic exclusion is posed against the function of A.L.P.’s letter ("Anna’s gramme")–a "metonymic dwarf" of Joyce’s "nightbook" as a whole, in which the letters A.L.P. (nominally "Anna Livia Plurabelle") simultaneously describe the recurrent "vicious circle" of a Freudian repetition compulsion in which the form Alp is also, for example, the German word for nightmare. As this "epistolear" becomes more and more a part of the textual apparatus that surrounds it, and less distinguishable from its own analysis or exegesis, it begins to take on a mythological aura as the site of endless co-ordinates for an impossible rendez-vous with itself. Like the letters A.L.P. and H.C.E., this "nightletter" serves as a kind of topological, or tropological site of what Jean-Michel Rabaté terms a lapsus–a point of "continuity" which at the same time marks out a chain of "dis-continuities," or the symptomatic "disarticulation" of a sequence of encoding and decoding.

As with Derrida, Rabaté envisages a machine in which production is driven by an internal division (memory or desire) which opens a place of potentially limitless substitutions–a movement which finds itself programmed in advance by the irreducibility of the machine’s own internal paradox. This paradox is pervasive, but it might be said to be most fully accommodated in the purpose of the machine to supersede itself–a form of "built-in obsolescence," which is also a form of projective self-substitution and auto-production. As Rabaté suggests, this paradox functions as a "lapsus" and points to the way in which a programmatic discourse would "attempt to fill the blank space of desire left hollow by–or in–the machine." 22

This "desiring machine," miming the totalising movement of an exegesis, or exe-genesis, approaches a topological relation to itself similar to that of the Turing machine, or of Cantor’s continuum problem (the problem of determining whether there is a set with cardinality greater than that of the natural numbers but less than that of the continuum). In 1901, Russell reformulated this problem as arising from a consideration of the set of all sets which are not members of themselves, since this set must be a member of itself if and only if it is not a member of itself. Cesare Burali-Forti, an assistant to the mathematician Guiseppi Peano, discovered a similar antinomy in 1897 when he observed that since the set of ordinals is well ordered, it therefore must have an ordinal itself. However, this ordinal must be both an element of the set of ordinals and yet greater than any ordinal in the set. By definition, the paradoxical sets of Forti and Russell deny self-similarity since they must of necessity contain the term that both defines and exceeds them, ad infinitum, as a type of interminable destiny. In the absence of any limiting or stabilising "identity," the set paradox tends towards unlimited proliferation–a type of desiring machine caught, like the Lacanian subject, in an inflationary movement of self-projection and re-integration.

This idea can be broadly applied to processes of coding and decoding in which a programmatic identity takes the place of an originary identity, and in which the code-as-symptom can be viewed as structurally antecedent to itself within a sequence of metonymic substitutions. This antecedence (as a form of installation in advance), suggests another way in which programmatic emplacement operates what Joyce called a "paradox lust." That is, a way in which we might consider textual processes as programmed in advance–or as belonging to a program which has always already been installed and which cannot be disintricated from the machine/mechanism with which it will always have been integrated. In "Die Frage nach der Technik," Martin Heidegger likewise argues that the essence of technology (as Ge-stell or enframing, emplacement): "is an ordering of destining, as is every way of revealing. Bringing-forth, poiēsis, is also a destining in this sense."23 Similarly, Maurice Blanchot links discursive emplacement to a certain topology of the "fragment," as an element of metonymic recursion. According to Blanchot:

the fragment, as fragments, tends to dissolve the totality which it presupposes and which it carries off towards the dissolution from which it does not [...] form, but to which it exposes itself in order, disappearing–and along with it, all identity–to maintain itself as the energy of disappearing: a repetitive energy, the limit that bears upon limitation.24

This emplaced-fragmentation, without origin or derivation, would also describe the transversality of the "limit that bears upon limitation" as simultaneously the aporia of what Heidegger calls being placed. As the mark of discursive emplacement, this aporia of limits likewise describes a structural "hesitancy" between the fragmentary resemblance to a system in the process of emerging and to one in the process of dissolution. It suggests a mechanical lability, a technics of the fragmented tending simultaneously towards the infinitesimal and the monstrous through an interminable movement of autopoietic recursion. In place of the incomplete system it will always have seemed to imply, the fragment disseminates itself, engendering each of its elements as the fragmented-whole of which it is not even the whole-fragmented, mise en abyme.


In Structure and Motif, Clive Hart identifies two major patterns of organisation in the structure of Finnegans Wake. The first of these is a three-plus-one pattern which Joyce ostensibly borrowed from Giambattista Vico’s Principi di Scienza Nuova, of a cyclical model of history comprising three evolutionary stages and a ricorso. The second pattern consists of "Lesser Cycles" which "make up a four-plus-one quasi-Indian" pattern.25 As conceived by Hart, these models sustain the Wake’s overall double, cyclic structure: the "Major Viconian Cycle" describing the four books of the Wake, while within each of the "three Viconian Ages of Books I, II, and III, Joyce allows four four-chapter cycles to develop," and each of these lesser cycles also sustains an "implicit identification" with one of the four Western "classical elements" of earth, water, fire, and air:


Hart’s evolves an idea of a schemata function as not only organising but in fact conditioning the means and processes of textual production. That is to say, not merely as prototypical, but what we might call proto-tropic. The "model" of cyclicality in this way encompass a recursiveness both within and across signifying fields, between trope and schema, describing a "topological" relation–as in the example of book III.1 of Finnegans Wake, in whose organisation the 3+1 structure of the Wake as a whole is metonymically inscribed:

Cycle I
Age i (403.18-405.03):

Description of Shaun as a "picture primitive"; he does not speak (first Viconian Age).
Age ii (405.04-407.09):

Shaun has become a hero ("Bel of Beaus Walk"); there is an allusion to the heroic slaying of the Jabberwock and an entertaining Rabelaisian description of Shaun’s heroic eating habits.
Age iii (407.10-414.14):

Introduced by "Overture and beginners" this is the beginning of the Human Age, in which the gods can appear only in dramatic representation on stage; Shaun has become a popular representative ("vote of the Irish"); the word "Amen" brings to an end the group of three Ages forming the main part of this first Viconian cycle.
Age iv (414.14-414.18):

A short ricorso brings us back to the theocratic Age with the introduction to the Fable–Thunder (FW 414.19).26

Hart suggests that the overall structure of the Finnegans Wake–by the three-plus-one pattern and its four-plus-one schematic compliment–can also be understood in terms of the "cross of the quaternity" or Å symbol. This cross within a circle corresponds to the siglum in the Wake manuscripts used to designate what Hart refers to as the "highly important ninth question in I.6.9":

if a human being duly fatigued [...] having plenxty off time on his gouty hands [...] were [...] accorded [...] with an earsighted view of old hopinhaven [...] then what would that fargazer seem to seemself to seem seeming of, dimm it all?" [FW 143.4-27]27

The Wake’s answer: "A collideorscope" (FW 143.28), can be seen as one of the numerous mechanical terms with which Joyce’s text describes itself, and Hart contends that Joyce’s use of the Å symbol to designate a passage dealing with the structure of Finnegans Wake "suggests that in one structural sense, the whole book forms a mandala," which the Å symbol represents: "a quadripartite with diametrically inverted ornaments."28


According to Hart, the four quadrants of the circle constitute "the Wheel of Fortune, while Book IV lies at the ‘hub.’"29 An interesting corollary to this analysis arises from a consideration of the apparently "circular" structure of the Wake whereby the last line in the book is often considered as turning back upon the first line, so that the book itself becomes literally a circle (a "book of Doublends Jined" [FW 20.15-16]), through the "sentence":

A way a lone a last a loved a long the [|the outside of the book|] riverrun, past Eve and Adam’s, from swerve of shore to bend of bay, brings us by a commodius vicus of recirculation back to Howth Castle and Environs. [FW 628.15-16, 3.01-13]

But if this sentence belongs to both the first (I.1) and last (IV.1) chapters of Finnegans Wake, then there can be no simple divide between the first and last chapters. In his seminar "Joyce le symptôme I," Lacan suggests: "déjà son dernier mot ne peut se rejoindre qu’au premier, le the sur lequel il se termine se raccolant au riverrun dont il se débute, ce qui indique le circulaire?"30 Lacan goes on to argue that the structure of Finnegans Wake should, in fact, not be described as circular but rather as knotted, comparing the signifying relation of "the" and "riverrun" to the topological metaphor of the Borromean knot. Lacan further relates the idea of the knot back to the "circle and cross" of Hart’s mandalic Å schematisation, arguing that the function of this is not so much to render the Wake’s structure as a closed totality, but rather "à savoir l’ambiguïté du 3 et du 4, à savoir ce à quoi il restait collé, attaché, à l’interrogation de Vico."31

The exploration of the problem of Borromean knots represented Lacan’s attempt at elaborating a topology of the Real, Symbolic, and Imaginary,32 whose ambiguous structure, like Finnegans Wake, turns about the seemingly impossible equation 3=4, as a transition from the structure of the trinity to that of the quaternity. Which is also to say that if, according to conventional logics of scale, a sentence cannot be greater than a chapter, then the sentence "A way a lone [...] back to Howth Castle and Environs" belongs to one chapter, and the number of chapters in Finnegans Wake is not seventeen but sixteen, and the number of books is three and not four–or rather, there are both possibilities at once. In this way Book IV, the Wakean ricorso, the "hub" or "double axis" of the Wake’s mandalic Å structure, initiates this structural turn at the same time as this turning effaces it–providing a virtually schematic model of what Blanchot and Derrida describe as a de-centred structure.

Elsewhere in Finnegans Wake, this topological structuration recurs in the diagrammatical rendering of a doubly articulated "Viconian" mechanism, in which we might detect the solicitation of a particular "technology" of emplacement in the co-ordinates A.L.P.:


[FW 293]

Hart’s schematic Å model of the Wake in Structure and Motif in Finnegans Wake bears particular resemblances to this "vicociclometer." Describing a double chiasmatic movement between the four books of the Wake he argues that:

Around a central section, Book II, Joyce builds two opposing cycles consisting of Books I and III. In these two Books there is established a pattern of correspondences of the major events of each, those in Book III occurring in reverse order and having inverse characteristics. Whereas Book I begins with a rather obvious birth (28-9) and ends with a symbolic death (215-6), Book III begins with a death (403) and ends with a birth (590); "roads" and the meeting with the King (I.2) reappear in III.4, the trial of I.3-4 in III.3, the Letter of I.5 in III.1, and the fables of I.6 earlier in III.1. In his correspondence Joyce implicitly referred to this pattern.33

Such a Viconian "duplex" (FW 292.24) is also suggested in the above diagram (located approximately mid-way through book II) as describing a transversal along the co-ordinates Aa, lL, P(p), between a Trinitarian eschatology and an "Hystorical" (FW 567.31) cyclic re-birth, in the triangulated form of the vesica piscis–"between shift and shift ere the death he has lived through and the life he is to die into" (FW 293.003-05), becoming: "Uteralterance or / the Interplay of / Bones in the / Womb" (FW 293.L1).

In De monade, Giordano Bruno describes a similar figure of two intersecting circles–the Diadis figura. The plane of intersection, the monas, according to Bruno: "contains its opposite" (Immo bonum atque malum prima est ab origine fusum).34 Leibniz, elaborating the conception of monadology, similarly argued that "in the labyrinth of the continuous the smallest element is not the point but the fold," just as in Joyce’s diagram the plane of continuity describes itself through a fold, Aa–lL. Among other things, this diagram suggests a mechanism operating on the basis of a type of "paradox lust" whose structural topology (schematic or tropic) is not self-identical but a chiasmatic regeneration–an acrostic convergence of "anaglyptics" (419.10), where: "A is for Anna like L is for Liv. Aha hahah, Ante Ann you’re apt to ape aunty annalive! Dawn gives rise. Lo, lo, lives love! Eve takes fall. La, la, laugh leaves alass! Aiaiaiai, Antiann, we’re last to the lost, Loulou! Tis perfect" (FW 293.18-23).


As Roland McHugh, in The Sigla of Finnegans Wake, reminds us, the construction of an equilateral triangle is the first proposition in Euclid’s Elements of Geometry. It is also the mystical figure par excellence, derived through esoteric Christian symbolism from the more geometrico of the neo-Platonist and Pythagorean cults. The equilateral triangle and its inverted double, moreover, combines the geometry of transcendence and the trinity with the generative principle symbolised by the female–as in the diagram which appears on page 293 of Finnegans Wake in which the vesica frames two opposing equilateral triangles (the Pythagorean Quintessence). McHugh further remarks that "the sexual interpretation of this figure has a precedent in the associations of the Vesica Piscis, or fish’s bladder, which is the central ovoid portion, where the circles overlap."35

It is know to both freemasons and architects that the mystical figure called the Vesica Piscis, so popular in the middle ages, and generally placed as the first proposition of Euclid, was a symbol applied by the masons in planning their temples […] the Vesica was also regarded as a baneful object under the name of the "Evil Eye," and the charm most employed to avert the dread effects of its fascination was the Phallus […]. In the East the Vesica was used as a symbol of the womb […]. To every Christian the Vesica is familiar from its constant use in early art, for not only was it an attribute of the Virgin and the feminine aspect of the Saviour as symbolised by the wound in his side, but it commonly surrounds the figure of Christ, as his throne when seated in glory.36

Elsewhere in the Wake the vesica (the triangulated vel described by the two overlapping circles in the vicociclometer diagram) is described as a "kind of a thinglike all traylogged then pubably it resymbles a pelvic or some kvind then props an acutebacked quadrangle" (FW 608.22-4). Joyce’s diagrammatic combination of Viconian and Platonic idealities ("Plutonic loveliaks twinnt Platonic yearlings–you must, how, in undivided reawlity draw the line somewhere" [292.30-32]) can be seen as describing a broader schematic function. But this dialectico-cyclical apparatus can also be seen as being structured as a symptom–a schematic of recursive aphanisis.

In Seminar XI (1964), The Four Fundamental Concepts of Psychoanalysis, Lacan proposes a schematic rendering of this topological shift from the 3 to the 4 in a projective theory of alienation.37 This similarly takes the form of two overlapping circles, describing a set theoretical relation of the "subject" (Being) and the "Other" (Meaning), which resymbles the Lacanian trinity of the Real, Symbolic and Imaginary. For Lacan, the vel, or space bounded by both circles, describes the condition between Being and Meaning, which is that of non-meaning, through which the mutually affective structure of Alientation is "dialectically" determined:


Being « Meaning

(the subject) (the Other)

According to Lacan, there is "no subject without, somewhere, aphanisis of the subject, and it is in this alienation, in this fundamental division, that the dialectic of the subject is established."38 Thus the sign of the lack, the "evil eye" (which is, again, the ana-glyph, the castrative eye of the Freudian Medusa), also becomes the emblem of what veils meaning: what elsewhere Lacan calls the mask of the Other, the concealment of the gaze, the mirror-illusion of the subject which conceals a "non-meaning." Nevertheless, "because of the vel, the sensitive point of balance, there is an emergence of the subject at the level of meaning […] from its aphanisis in the Other locus, which is that of the unconscious."39

Borrowing from Niels Bohr’s "complementary sets," Lacan describes the vel of alienation as "defined by the choice whose properties depend on this, that there is, in the joining, one element that, whatever the choice operating may be, has as its consequences a neither one, nor the other":

If we choose being, the subject disappears, it eludes us, it falls into non-meaning. If we choose meaning, the meaning survives only deprived of that part of non-meaning that is, strictly speaking, that which constitutes in the realisation of the subject, the unconscious. In other words, it is of the nature of this meaning, as it emerges from the field of the Other, to be in a large part of its field, eclipsed by the disappearance of being, induced by the very function of the signifier.40

This state of signification, of equivocity ("both and yet neither"), is given a more complex formulation in Lacan’s three major seminars on Finnegans Wake. In "Joyce le symptôme" I and II, and "Le sinthome, Séminaire du 18 novembre 1975," Lacan suggests that Finnegans Wake can be understood as a type of symptom which it is impossible to analyse. Following from its etymology (Gk. sumptōma: occurrence, phenomenon; from sumpiptein, to fall together, fall upon, happen), Lacan links the Freudian notion of "symptom" as a condition of the unconscious (of the Oedipal entanglement), to the notion of the unconscious as structured like a language, to the reversion of Joyce’s language and ultimately to Joyce himself (as "Shemptôme"), in whom all of these figures intersect as a kind of Borromean knot or "Borumoter" (FW 331.27)–"un nœud de signifiants"41 as symptom of J[ouissance] (as Lacan at least implies in the eighth chapter of Seminar XX, "Knowledge and Truth," in Encore–the diagram Lacan employs here closely resembling the Masonic pyramidal eye, with the letter J in place of the eye and the pyramid or equilateral triangle formed by three intersecting vectors, with the Imaginary forming the apex and the Symbolic and the Real describing the base):


A topological curiosity, the Borromean knot is in fact a set of three rings arranged in a symmetrical pattern, none of which are actually connected but which are intertwined so that they cannot be pulled apart, although with the condition that if any one of them is removed, then all three separate.42


For Lacan, the Borromean knot describes the relationship between symptom and a certain perversion (or hérésie of the R[eal], S[ymbolic], and I[maginary]), which he relates to the Freudian drama of triangulated desiredefined in the Oedipus complex. As Lacan argues:

The Oedipal complex is such a symptom. It is in this sense that the Name-of-the-Father is also the Father of the name.43

This chiasmatic turn describes a perversion in the relation to the father-scriptor "in as much as perversion has the meaning of a translation or transference directed at the Father [version vers le père], and that in sum the Father is a symptom, or a sinthome."44 This relation has to do with the stratification of the individual as subject according to the relation of the Real, Symbolic and Imaginary in which the genealogy of this subject describes a topological formulation. What the topological metaphor of the Borromean knot suggests, then, is the synthetic nature of the psychoanalytic subject, which, as subject, is the unique "solution" to the problem of the incomensurability of what is named by these three terms. Moreover, it is only by virtue of this synthesis that the subject can be said to exist qua subject. In this way, Lacan argues: "It is not the division of the imaginary, symbolic and real which defines perversion, but rather that they are already distinct."45

Like Joyce’s investigation of Vico’s theory of cyclical historical recursion or "vicociclometer" (Å ), Lacan’s formulation of the Borromean knot hinges upon a similar figure described by the vesica, or vel, between the co-ordinate figures R, S and I ("vous savez qu’avec ce cercle et cette croix je déssin le nœud borroméan"). In this case, however, the vesica (the symbol of lac) is roughly bisected, so that the points at which the three rings initially overlap also describe a triangle, which may tentatively be posed as a figure of the Lacanian symptom (as the "perversion" between le Nom-du-Père and le Père du nom: as, for example, between Joyce [Freud] and jouissance). As a consequence, it is necessary to posit the Borromean knot in a doubly fourfold manner: as the symptomatic topos of the encounter of the Real, Symbolic and Imaginary, and as their tropological linkage (the double or ghost of the dialectical lapsus, 3® 4). It is this tropological counterpart of the symptom that Lacan refers to as le sinthome:

If you find a place […] which schematises the relationship between the imaginary, symbolic, and the real (as long as they remain separated from one another) you have already–in my preceding drawings, in which this relationship has been clearly set down–the possibility of linking them, but by what? By the sinthome. It is necessary for you to see this: it is the re-folding of the capitalised S–that is, of what affirms itself in the consistency of the symbolic.46

The ex-istence of the symptom is implicated by the position of this "enigmatic link" of the Real, Symbolic and Imaginary, which Lacan describes in the following diagrams:


For Lacan, when we attempt to untie the knot of the Real (R), the Symbolic (S), Imaginary (I), and le sinthome (S ), and thus divide it into four separate parts, the following figure is invariably formed:


The topological entanglement of these four elements is consequently regarded as describing (by a process of metonymy) the radical condition of language as such (and exemplified for Lacan by the paronomasia of Finnegans Wake). In this way, the chiasmatic perversion of symptom and sinthome also marks a form of transversal, across which each of the relations described above is expressly interchangeable. Mirroring the subjective determinacy of the "dialectic of identification," the movement from position 1 to position 2 can be reversed, as 2 to 1, while 3 to 4 can be reversed, as 4 to 3–just as the imaginary identification of the mirror stage operates a reversal mechanism across the Other-locus in the emergence of the signifier as marking the subject’s "entrance" into the symbolic order. In other words, both the symbol and the symptom present themselves in such a fashion that either of the two terms (S or S) takes them in their entirety, "so that the other passes over the one which is above and under the one which is below." Following from René Thom’s theory of topological folds, Lacan argues that this doubled chiasmus is thus accorded an immanence as "the figure we regularly obtain when we attempt to separate the Borromean knot into its four parts."47

The topological relations mapped out by Lacan by means of his exploration of Borromean knots are in many respects anticipated in the work of Philippe Sollers, author, theorist and editor of the avant-garde journal Tel Quel. Sollers’s 1968 text Nombres, discussed in some detail in Derrida’s Dissemination (1972), contains a sequence of diagrams at times intriguingly similar to those which later appear in Lacan’s seminar on Joyce. This may in itself be more than mere coincidence. The emphasis Lacan places upon the "perversion" of the nom-du-Père in that seminar (the implicit relation between the name Joyce as a "translation" of Freud, as well as the significance of Lacan’s name in this context) finds a parallel in Sollers’s own name-playing–between the sun-like non-de-plume (Sollers) and the occulted, "original" name of the author, Joyeux (which suggests both jeux and jouissance, as well as Joyce–which Sollers’s himself deals with explicitly in his later novel Femmes).

In a series of passages dealing with the numerological, geometrical and dialectical significance of the numbers 1,2,3 and 4 (trinity and quaternity: a two-fold structure which underlies the entire book, itself divided into 4 sets of 10 subsets: 1+2+3+4=10), Sollers’s introduces three diagrams which describe a certain shift "d’un ensemble à l’autre, d’un blanc au blanc redoublé"48:


In these first two diagrams, an open sided square figure is shown undergoing a series of inversions (in the first instance) and rotations (in the second). These squares (vectors) can be considered, among other things, as roughly analogous to Lacan’s schematic of the stade du miroir: a stage with an open "fourth wall." The mirror motif reappears later in Sollers’s text, and the ideas of "reflection" and "transmission" are clearly related here to those of inversion and rotation in the above diagrams. These parallel transpositions "d’un ensemble à l’autre, d’un blanc au blanc redoublé," also suggest a linguistic dimension–the metaphoric and metonymic axes elaborated in the work of Roman Jakobson and later reformulated in the work of Lacan in terms of the quasi-Sausurean algorithms S/s (metaphor) and S……S' (metonymy).49 The topological entanglement of these composite trajectories is at least one of the renderings implied in Sollers’s third diagram:


How this reflects upon Lacan’s later work on Borromean knots may be gauged in the play of "imaginary" inversion which accompanies Lacan’s notion of perversion, which itself describes a particular mirroring apparatus (nom-du-Père/Père du nom). This may otherwise be thought as the inversion of the symbolic and imaginary in the proposition of the Real (the mechanism which comes to bind, however surrepticiously, the structure of the subject to that of the sinthome). The open-sidedness of Sollers’s diagram also makes clear, where Lacan’s perhaps does not, that above all the symptom is the other side of a model of a particular détournement, to which it constantly defers without ever refering. This doubling of the 3+1 figure of the open dialectic implies, then, another fold, a topological "surface" in which the (4), the sinthome, is bracketted of (through a type of mimetic détournement) in the figure of the Viconian mandala Å –where the + implies both the imaginary overlap of non-communicating vectors, as well as their crossed-out centre (d’un ensemble à l’autre, d’un blanc au blanc redoublé).

On page 45 of Nombres, Sollers introduces a fourth diagram, this time itself in the form of a "cross" (en-abyme, almost)–a type of "tick-tack-toe" diagram suggesting an open-sided cube unfolded onto a two-dimensional plane:


Cut out and assembled, this cube would nevertheless remain open on one of its sides–"these 4 surfaces which appear to be filled in, fold back onto a centre which isn’t there–which doesn’t count in any sense as part of the competed figure." The blank central panel again suggests that containment (it is the only square bounded on all sides by the others, constituting a series of folds, a structural hub on which the entire structure hinges) "defines" an empty centre whose location is subsumed into a series of interfaces ("Le carré que nous parcourons ici est la terre, mes ces quatre surfaces remplies renvoient à un centre qui n’est pas là, qui ne compte pas de telle sorte que la figure complète […] comporte une case vide pour l’instant impossible à vivre, le sort").50 This leads to a further transformation:

the construction is presented thus: three visible sides, three walls if you like, on which the sequences are in reality inscribed–transitions, articulations, intervals, words–, and one absence of side or wall defined by the three others but enabling one to observe them from their point of view.


This forth surface is in a sense carved out of the air: it enables speeches to make themselves heard, bodies to let themselves be seen: consequently, it is easily forgotten, and that is doubtless where illusion and error lie.51

Here, then, Sollers provides the topological extension by which we may make sense of Lacan’s diagramatic metamorphoses between the mirror dialectic and his later preoccupation with the Borromean knots. By substituting the terms Real, Symbolic, Imaginary and Sinthome for the numerical features of Sollers’s diagrams, it is possible to make somewhat clearer sense of the way in which the "figure" of the Lacanian subject is inextricably linked to these topological/tropological antinomies (both as symptom and as sinthome, or perhaps synthomme).

Moreover, as a type of stade du miroir, Sollers’s model points towards an entire thematics of apprehension in the production of (subjective) signifying relations. But whilst Lacan first adopts a material dialectical model of identification as the basis for this, Sollers implies a mirroring relation external to dialectics in a movement which "sublates" the 3 within the (parenthetical) fourth term. Like the ricorsi storici of Vico’s Scienza Nuova, this fourth term stands in an open relation to the other three and may in fact be said to inscribe them as a movement of signifying recursion–recalling Hegel’s statement that the "triplicity" of the dialectic is its "external, superficial side."52 On page 75 of Nombres, the following text and diagram appear:

(et ainsi, vous êtes comme devant le portique de l’istoire elle-même, sur sa scène brusquement redresée et illuminée


et votre forme est désormais affrontée à ce risque, à cette tension qui vous tient debout, éveillé …53

Here the open-sided square is itself bracketed off, the square "circled" and in whose circling the 4 predominates, we might say, as a figure of an unexpressed relation (the 4 literally unfolded would describe the figure beneath which it lies and in this sense "mirrors," just as elsewhere this 4 out of 3 takes the form of a figure shaped like the letter Y).54 Given this it would be inviting to speculate that, for Sollers, the 3+1 relation likewise implies a "mirror stage" whose mechanics of revelation, apocalyptō or Aufhebung, disclose a hypothetical present or presence-to-self which is in fact a surface effect: "Whence the impression of witnessing a projection, whereas it is ultimately a matter of the very product of the surface." This surface effect (we might also say, arithmetical effect) is itself likened, by a process of metonymic substitutions, to the technics of mechanical reproduction and of the "camera," as a "darkroom transformed into a surface."55 This darkroom or camera obscura provides a metaphor for a type of "hidden stage" upon which "theoretical" demons perform the mechanical tasks of "processing" textual images, as a type of mnemotechnics or "ghostwriting":

Indeed, what is thus too easily taken to be the opening of a stage is nonetheless a panel that distorts, an invisible, impalpable, opaque veil that plays towards the other three sides the role of a mirror or reflector, and towards the outside […] the role of a negative developer on which the inscriptions simultaneously produced on the other planes appear inverted, righted, fixed. As if the hypothetical actors came and traced or pronounced their text backwards, in front of you, without your being aware of it.56

This structural matrix or textual apparatus likewise describes, as Joyce says, a "polyhedron of all scripture," its supposed fourth surface opening onto a representational space of indefinite dimension ("the superposition of scenes, the emergence and progressive articulation" of competing structural ensembles, linkages, détournements). But also, as an other-matrix, it stands in place of the ineffable renversement of what Derrida, in Résistances de la psychanalyse (1996), terms "woman between three and four."57 This "third-forth person" likewise describes a topological relation of the sinthome, "between the three and the four," whose surface effect describes an internal difference with itself which effectively organises the apparatus which it at once screens, mediates, translates, interprets and metaphorises, as an apparatus of disclosure. Once again, this apparatus is given in the form of a mise-en-scène, a theatrical stage [scène] whose forth wall or fons scænæ is apparantly substituted by a glace-sans-tain or double mirror. In the chapter on Sollers in Dissemination, Derrida elaborates further along these lines:

this mirror will have been turned toward the back of the stage […] offering us only the site of its tain.

Which would (not) be anything if the tain were not transparent, or rather transformative of what it lets through. The tain of this mirror thus reflects–imperfectly–what comes to it–imperfectly–from the other three sides and lets through–precisely–the ghost of what it reflects.58

What the mirror gives, what it transmits by means of the imaginary fourth wall of the stage, its tain, is a "deformation irreducible to any form."59 This mirror-effect, or error-effect, of the stade du miroir underwrites of type of "ghosting" which Derrida elsewhere calls a "gift without the least memory of itself,"60 that nevertheless marks an "impossible past" of something that has never been present, has never been, what both is and is not a Being-there in the Heideggerean sense: "over ‘there,’ in a distant past, a lost memory of what is no longer here. Was it ever?"61

Transposed onto the mirror apparatus of the stade du miroir, the technics of this "ghosting" apparatus describes a structural matrix, an apparatus or programme in which the ghost writing of the signifier in the illusion of a signified marks a schematics of destination: an horizon effect of the mirror which gives the subject’s desire back to it under the guise of the translated image of its own truth (as specular double). This "mirror-stage," far from being simply, or literally, a means of representation of a displaced exterior, "limits" the domain of speculative thought, though in such a way that it extends the speculative field itself indefinitely.62

This itself may be viewed in analogously material terms–that is to say, as an extension into the signifying relation of the Real, Symbolic and Imaginary that the stade du miroir gives an expression to, of a probability quotient which founds chance upon a requirement of structural finitude (signifying substitutability). In this way not only does chance relate in figure of the subject, but does so in a manner we can describe as t(r)opoligical (the shift from the 3 to the 4). Lacan’s dialectical transcription of the opening of "the subject" thus situates within the locus of chance or possibility the matrix of the sign belonging to philosophical tradition which links the verbal image of "language" presentation to the visual image of object presentation, and thus subjects it to the same paradoxical forces to which the ego in its Cartesian formulation is subjected.

This apparent antinomy, in which signification becomes fatally fascinated with itself (le moi illusion), also describes a circuit of autopoiesis. As a product of autopoiesis, the mirroring effect gives the impression of a dumbshow masked by a type of projectionism, or rather a template of desiring affectation as the horizon of subjective self-knowledge. The theatrical metaphor thus provides for unlimited substitutability in the staging of this specular relation, underwritten by a form of deus ex machina. This "ghost in the machine," as a confusion of archē and mimēsis, suggests a form of signifying dissimulation at the "origin" of textual production. At the same time this originary dissimulation can be said to make signification possible in the "first place," while nevertheless circumventing closure in the form of mimēsis or adæquatio. As such, this machine functions upon a principle of "duplicity," which would not be reducible beyond a deus ex machina as an apparatus in the service of an ideality or "ideal text," and whose form and operations it would simply "mimic" through a type of mirror-play or speculative dialectics. Such a machine would instead operate as a schemato-tropic transposition of signifying elements mirroring the t(r)opological shift from the 3 to the 4 ("trinity" to the "quaternity") in its model of structuring recursion.

Prague, August 2002


1. Jean-Michel Rabaté, "Lapsus ex machina," trans. Elizabeth Guild, Post-structuralist Joyce: Essays from the French, eds. Derek Attridge and Daniel Ferrer (London: Cambridge University Press, 1984) 79.

2. Jacques Lacan, "A Materialist Definition of the Phenomenon of Consciousness," The Seminar of Jacques Lacan. Book II: The Ego in Freud’s Theory and in the Technique of Psychoanalysis 1954-1955, trans. S. Tomaselli (London: Cambridge University Press, 1988) 46-7.

3. Lacan, "A Materialist Definition," 47.

4. Lacan, "A Materialist Definition," 47; 49.

5. Georges Canguilhem, "Machine and Organism," Incorporations, ed. Jonathan Crary and Sanford Kwinter (New York: Zone Books, 1992) 53. Cf. "Sixth Meditation" in Philosophical Works of Descartes, trans. Elizabeth S. Haldane and G.R.T. Ross (Cambridge: Cambridge University Press, 1967).

6. Lacan, "A Materialist Definition," 52.

7. Sigmund Freud, Beyond the Pleasure Principle, trans. C.J.M. Hubback (London: The Hogarth Press, 1922) 14ff.

8. Jacques Lacan, "On a Question Preliminary to any Possible Treatment of Psychosis," Écrits: A Selection, trans. Alan Sheridon (New York: Norton, 1977) 215.

9. Lacan, "The Agency of the Letter in the Unconscious," Écrits, 167.

10. Jacques Lacan, The Four Fundamental Concepts of Psychoanalysis, ed. Jacques-Alain Miller, trans. Alan Sheridon (London: Hogarth Press, 1977) 177-8.

11. Heidegger, "The Question Concerning Technology," 336.

12. Jacques Lacan, "La logiqe du fantasme," Autre écrits (Paris: Seuil, 2001) 323. Cf. Jacques Derrida, The Truth in Painting, trans. G. Bennington and I. McLeod (Chicago: Chicago University Press, 1987), back cover (paperback edition): "parergon (for example the frame) is neither in the work (ergon) nor outside it. As soon as the parergon takes place, it dismantles the most reassuring conceptual oppositions." Also Derrida, "Lammata," ibid., 9: "the insistent atopics of the parergon: neither work (ergon) nor outside the work [hors d’ouvre], neither inside nor outside, neither above nor below, it disconcerts any opposition […] and it gives rise to the work."

13. Humberto Maturana and Francisco Varela, Autopoiesis and Cognition (Boston: Reidal, 1979).

14. Gilles Deleuze and Félix Guattari, Anti-Oedipus: Capitalism and Schizophrenia, trans. R. Hurley, M. Seem, and H.R. Lane (New York: Viking, 1977) 43.

15. Viktor Tausk, "The Influencing Machine," trans. Dorian Feigenbaum, Incorporations, eds. Jonathan Crary and Sanford Kwinter (New York: Zone Books, 1992) 551-2.

16. Deleuze and Guattari, Anti-Oedipus, 43.

17. Jacques Derrida, "Two Words for Joyce," trans. Geoffrey Bennington, Post-structuralist Joyce, 147.

18. Jacques Derrida, "The Double Session," Dissemination, trans. Barbara Johnson (Baltimore: Johns Hopkins University Press, 1981) 221.

19. Derrida, "Two Words for Joyce," 148.

20. Derrida, The Truth in Painting, 27. This metaphor describes a two-fold relation contiguous to Georg Cantor’s set continuum problem, which also came to pre-occupy Gottlob Frege and Bertram Russell. The first is the ambivalent set between two writing/translation softwares, in which one is a "minute" and "metonymic dwarf" which is nonetheless "detached from" and able to "exploit" the other. The second is the equivalent set of relations between two softwares in which both are a "detached fragment of a software" and, simultaneously, a "software more powerful than the other" and a "part larger than the whole of which it is a part."

21. Bertram Russell, "Mathematical Logic as Based on the Theory of Types," American Journal of Mathematics 30 (1908): 222-62. Repr. in Bertram Russell, Logic and Knowledge (London: Allen and Unwin, 1956) 59-102.

22. Rabaté, "Lapsus ex machina," 79.

23. Heidegger, "The Question Concerning Technology," 330.

24. Maurice Blanchot, The Writing of the Disaster, trans. Ann Smock (Lincoln: University of Nebraska Press, 1995) 60-61.

25. Clive Hart, Structure and Motif in Finnegans Wake (London: Faber and Faber, 1962) 62.

26. Hart, Structure and Motif, 58. Hart then analyses the following sections of the book along the same lines and demonstrates that Cycle IV brings III.1 "to a conclusion with a prayer [...] to Shaun the god-figure, who is to be resurrected in the next chapter" (60).

27. Cited in Alan Roughley, James Joyce and Critical Theory: An Introduction (London: Harvester, 1991) 11.

28. Cf. Roland McHugh, The Sigla of Finnegans Wake (London: Edward Arnold, 1976) 118. For McHugh the ‰ symbol "denotes the mental sensation of contemplating the mandala of Finnegans Wake, a tranquil equipoise at the hub of time" (121). There has been considerable speculation on the relationship between Finnegans Wake’s schematic structures and Jung’s conception of archetypes and collective unconscious (in which Jung employed the mandala symbol). Although Joyce was acquainted with Jung (who treated his daughter, Lucia, for part of her illness), and made several references to Jung in the Wake ("Jungfraud’s" [FW 460.20]), he was more clearly drawn to the ideas of Vico, Freud and the British anthropologist Sir J.G. Frazer.

29. Hart, Structure and Motif in Finnegans Wake, 77.

30. Jacques Lacan, "Joyce le symptôme I," Joyce avec Lacan, ed. Jacques Aubert (Paris: Navarin Éditeur, 1987) 29.

31. Lacan, "Joyce le symptôme I," 28.

32. See Jacques Lacan, "Seminaire," Scilicet 6.7 (1976) 40.

33. Hart, Structure and Motif, 66-7.

34. Cf. Jordani Bruni Nolani Opera Latine Conscripta, ed. F. Fiorentino (Napoli, 1879-91); facsimile reprint by F. Fromman (Stuttgart-Bad Cannstatt: Verlag Gunther Holzboog, 1962). Op. cit. is De Monade Numero et Figura, Secretioris Nempe Physicæ, Mathematicæ et Metaphysicæ Elementa.

35. McHugh, The Sigla of Finnegans Wake, 68.

36. William Sterling, The Canon (1897; London: Garnstone Press, 1974) 11-14; cited in McHugh, The Sigla of Finnegans Wake, 68.

37. Lacan, The Four Fundamental Concepts of Psychoanalysis, 211.

38. Lacan, The Four Fundamental Concepts of Psychoanalysis, 221.

39. Lacan, The Four Fundamental Concepts of Psychoanalysis, 221.

40. Lacan, The Four Fundamental Concepts of Psychoanalysis, 211.

41. Lacan, "Joyce le symptôme I," 24; Lacan, "Télévision," Autre écrits, 516.

42. The term "Borromean" comes from the Borromeo family of Renaissance Italy, who used the three interlocking circles on their coat of arms. There is another interesting historical context in which the image of the rings arises. The diagram was found in picture-stones on Gotland, an island in the Baltic sea off the south-east coast of Sweden. These are dated to some period in the ninth-century and are thought to record tales from the Norse myths. To the Norse people of Scandinavia, a drawing of the Borromean knot using triangles instead of rings is known as "Odin’s triangle" or the "Walknot" (or "valknut," the knot of the slain). The symbol was also carved on bedposts used in sea burials.

43. Lacan, "La Sinthome," Joyce avec Lacan, 46.

44. Lacan, "La Sinthome," 44-5.

45. Lacan, "La Sinthome," 44.

46. Lacan, "La Sinthome," 45.

47. Lacan, "La Sinthome," 46.

48. Philippe Sollers, Nombers (Paris: Seuil, 1968) page 81.

49. Lacan, "The Agency of the Letter," Écrits, 164.

50. Sollers, Nombres, section 4.24.

51. Sollers, Nombers, 4.8.

52. Cited in Julia Kristeva, Revolution in Poetic Language, trans. Margaret Waller (New York: Columbia University Press, 1984) 109.

53. Sollers, Nombres, 4.48.

54. Sollers, Nombers, 3.19.

55. Sollers, Nombers, 4.8.

56. Sollers, Nombers, 4.8.

57. Jacques Derrida, Resistance of Psychoanalysis, trans. Peggy Kamuf, Pascale-Anne Brault and Michael Naas (Stanford: Stanford University Press, 1994) 8.

58. Derrida, "Dissemination," 314.

59. Derrida, "Dissemination," 314.

60. Jacques Derrida, Cinders, trans. Ned Lukacher (Lincoln: University of Nebraska Press, 1992) 77.51. Derrida’s notion of the gift here, as elsewhere, follows from Mauss and Lacan. Bataille similarly develops this idea of the gift or potlach as inequation or dissymmetry (of expenditure versus exchange). Cf. Marcel Mauss, "Essai sur le don. Forme et raison de l’échange dans les sociétés archaïques," L’Année sociologique (1923-1924): 30-186; rpr. Sociologie et Anthropologie (Paris: Presses Universitaires de France, 1950) 143-27. "The ideal would be to give a potlach and it not be reciprocated"; cited in Georges Bataille, Œuvres complètes, 8 vols. (Paris: Gallimard, 1971-1988) 1:310.

61. Derrida, Cinders, 31.3.

62. This mirror does not constitute a rigid boundary, rather is marks a scene of play, of what Derrida elsewhere terms "rupture": "the moment when language invaded the universal problematic, the moment when, in the absence of a centre or origin everything became discourse. […]. The absence of the transcendental signified extends the domain and the play of signification indefinitely." Derrida, "Structure, Sign and Play," 279-80.

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