[FW 293]

Hart's schematic ( 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.29

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 A(a), L(l), 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]30


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).31 Leibniz, in 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, A(a)-L(l).32 Amongst 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).


VESICA PISCIS

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 ("The aliments of jumeantry" [FW 286.L4]). 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 McHugh further remarks: "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."33

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.34

Elsewhere in the Wake the vesica 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 primitive, cyclical apparatus can also be seen as being structured as a symptom-a schematic of recursive aphanisis. In The Four Fundamental Concepts of Psychoanalysis, Lacan adopts a similar diagram in the presentation of his theory of alienation.35 For Lacan, the vel, or space bounded by both circles (the vesica), describes the condition between Being and Meaning, which is that of non-meaning:
LOUIS ARMAND

FROM SYMPTOM TO MACHINE: JAMES JOYCE &
THE PERVERSIONS OF THE TEXTUAL APPARATUS



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. (Jean-Michel Rabate)1



TEXTUAL MACHINES

In their 1979 book Autopoiesis and Cognition, cyberneticists Humberto Maturana and Francesco Varela coin the phrase "autopoietic machines" to describe a process of mechanised autoproduction. 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."2 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 autopoietic machines parallels what Victor Tausk conceived as "influencing machines," and what Gilles Deleuze and Félix Guattari term "desiring machines." For Deleuze and Guattari, the desiring-production of "desiring machines" coalesces about 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."3 This sense of a body-machine, produced "alongside" its parts, echoes Tausk's concept of an influencing apparatus as the terminal manifestation in a schizo 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.4 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 Deleuze and Guattari describe 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.5

This sense of "transverse communications" emerges in Finnegans Wake in terms of an overall apparatus, underwriting a general thematics of identity, autopoiesis, alchemy, duplicity, copyright, historicity and so on. In a key passage towards the end of Book I, Joyce describes Shem-the-Penman, the plagiarist-author figure of the Wake, 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 symbolically obscures the divisions between tropos and topos in a single act of autopoiesis. Or rather, this solipsistic reversion crosses between a topological space within language 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 'Two Words for Joyce,' terms "a hypermnesiac machine."6 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.

In Dissemination, 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,"7 an idea he further elaborates upon in 'Two Words for 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.8

The topological structure of the relationship described here, between two textual programmes, recalls what Derrida in The Truth in Painting terms 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."9 Elsewhere Derrida describes this process in terms of a supplementary "chain of substitutions," or as a "decentring," suggesting 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. For Russell, "whatever involves all of a collection must not [itself] be one of the collection."10

In the 'Mamafesta' episode 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") as a "metonymic dwarf" of Joyce's "nightbook" as a whole, in which the letters A.L.P. simultaneously describe the recurrent "vicious circle" of a Freudian repetition compulsion in which Alp is also 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."11

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.12

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 genetic processes of coding and decoding in which a programmatic identity takes the place of an originary identity, and in which the genetic code can be viewed as structurally antecedent to itself within a sequence of metonymic substitutions. Derrida links this idea to the principle of viral contamination:

It is precisely a principle of contamination, a law of impurity, a parasitic economy. In the code of set theories, if I may use it at least figuratively, I would speak of a sort of participation without belonging-a taking part in without taking part of, without having membership in a set. The trait that marks membership inevitably divides, the boundary of the set comes to form, by invagination, an internal pocket larger than the whole; and the outcome of this division and of this abandoning remain as it is limitless.13

This destining (as a form of installation in advance), suggests another way in which programmatic emplacement operates a type of "paradox lust." It also suggests 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 "hardware" with which it will always have been integrated. In 'The Question Concerning Technology,' Martin Heidegger likewise argues that the essence of technology (as Ge-stell or enframing): "is an ordering of destining, as is every way of revealing. Bringing-forth, poiesis, is also a destining in this sense."14 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.15

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.



HALTING MACHINES

The relation of the fragment to the organisation of semantic structures is also linked, through the material, typographical nature of the "book," to the technological concept of moveable type, echoing to a certain degree Plato's identification of the alphabet itself as a form of techne in Phaedrus. As Marshal McLuhan and others have pointed out, the invention of moveable type made Gutenberg's press one of the first Western machines of mass production.16 The limited set of variables required for the press (twenty six Latin characters, plus blank spaces, punctuation marks and diacriticals) provides a basic conception of a typographical grid or matrix, within which a virtually infinite number of permutations and combinations are possible-depending upon assumed conventions of grammar, syntax and orthography used to determine any particular typographical sequence. As Alan Turing has noted, however:

If we were to allow an infinity of symbols, then there would be symbols differing to an arbitrarily small extent. The effect of this restriction of the number of symbols is not very serious. It is always possible to use sequences of symbols in the place of single symbols. [...] Similarly in any European language words are treated as single symbols.17

The Turing "grid" provides a secondary means of organising language as a whole in terms of material combination and recombination, by assigning single values to entire terms, or to any linguistic, rhetorical or schematic unit whatsoever. In this way the cyclical notions of Giambattista Vico or Friedrich Nietzsche, or the structural repetitions of Homer's Odyssey and the Bible, can equally be thought of in acrostic terms.

One of the questions raised by Joyce's writing, however, is how to account for the possibility of this acrostic grid exceeding its own rules. In other words, how to account for the assigning of multiple values to individual terms, or to the multiplication of terms within the same grid-space? Moreover, the apparently mechanical nature of the acrostic grid poses questions similar to those raised by Noam Chomsky about the relatedness of such things as grammar and syntax to semantic coherence. This question is partly answered by the contingency of contextuality, or the way in which the acrostic grid motivates a multi-dimensional connectivity between each of its elements. Each connection provides a trajectory of possible interpretation, such that we can say each term is in place within its particular context(s).

A simple example of this is the referential function of an index or concordance, in which a basic system of co-ordinates employing two sets of variables (word or phrase and numerical page reference) provides a type of basic hypertextual site map or primitive cybernetic apparatus. In most cases, the first term remains constant for a variable number of second terms. "Plotted" against two-axes on a Cartesian plane, any set of co-ordinates sharing the first term will describe a straight line. The indexical value of the first term thus appears strictly linear.
The difficulty arises with a classic Wittgensteinian problem of determining the relative value of the first term, which without appearing to differ, also does not remain constant across all of the contexts in which it appears (which is not its indexical value). Plotting the set of co-ordinates as a point-to-point vector across the body of the text, however, will produce a very different diagram-a transversal passing through a topological, "acrostic" space, whose values are not linear in any straightforward sense of that term. Other means of plotting these co-ordinates can also be determined to produce different hypertextual configurations, evolving the acrostic possibilities of the textual co-ordinates in increasingly elaborate ways. As Joyce himself suggests:

The proteiform graph itself is a polyhedron of scripture. There was a time when naif alphabetters would have written it down the tracing of a purely deliquescent recidivist, possibly ambidextorous, snubnosed probably and presenting a strangely profound rainbow in his (or her) occiput. [FW 107.08-12]

But while such acrostic possibilities are conceivably infinite, they do pose questions of formal significance which ask whether or not an apparently random constellation of texts whose resemblance is always fractional can exert mutual simultaneous influence at a level which is not merely trivial or at best a fabulation ("a strangely profound rainbow").18


VICOCICLOMETRY

In Structure and Motif, 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 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.19 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:


Major Viconian Cycle                             Lesser Cycle

1. Book I (Birth) ..............................      I.1-4: Male, H.C.E
                                                                I.5-8: Female, A.L.P.

2. Book II (Marriage) ........................... II-Male and Female
                                                                 battles; fire

3. Book III (Death) ..............................  III-Male cycle; Shaun as
                                                                 Earwicker's spirit; air



Where Hart's work touches closest on contemporary genetic approaches to Joyce's text is his idea of schemata functioning as prototypical models of different levels of textual production-although where Hart focuses on how these emerge within Joyce's text along more traditional lines of character and narrative, genetics tends to focus on how these schemata emerge from different points in the history of the text's composition. The following analysis of III.1 provides an example of how Hart sees Joyce's text as putting "cyclic ideas to work" in organising individual chapters:


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 illusion 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).20



Hart suggests that the overall structure of the 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 ( symbol. This cross within a circle corresponds to the siglum in the Finnegans 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]21

The Wake's answer: "A collideorscope" (FW 143.28), can be seen as one of the many terms with which Joyce's text describes itself, and Hart contends that Joyce's use of the ( 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 (+) symbol represents ("a quadripartite with diametrically inverted ornaments").22 This symbol can also be taken as defining a shift across scale, between trope and schema, describing an implicitly hypertextual relation:
                                                        Being  <---->  Meaning           
                                                              (the subject)              (the Other)
                                                                                       non-
                                                                                  meaning


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."36 Thus the sign of the lack, the "evil eye" (which is, again, the feminine, 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.37

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.38

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. sumptoma: 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 (incestuous) 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).39


BORROMEAN KNOTS

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.40
According to Hart, the four quadrants of the circle constitute "the Wheel of Fortune, while Book IV lies at the 'hub.'"23 One 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 the Wake, then there can be no simple divide between the first and last chapters. In his seminar 'Joyce le symptôme,' Lacan suggests:

déja 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?24

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 Borromean knots. Lacan further relates the idea of the knot back to the "circle and cross" of Hart's mandalic schematisation of the Wake,25 arguing that the function of this is not so much to render the Wake's structure as a closed totality, but rather:

a savoir l'ambiguité du 3 et du 4, a savoir ce a quoi il restait collé, attaché, a l'interrogation de Vico.26

The exploration of the problem of Borromean knots represented Lacan's attempt at elaborating a topology of the symbolic, imaginary and real,27 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 four28-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 ( 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.:
HJS
volume 3, issue 1, 2002
For Lacan, when we attempt to untie the knot of the imaginary (I), the symbolic (S), the real (R), and le sinthome (Z), 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 basic condition of Joyce's language in 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 (Z 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."45

In Lacan's view, the "figure" of Joyce is inextricably linked to this topological/tropological antinomy (both as symptom and as sinthome, synthomme if not "Saint Homme": "Joyce n'est pas un Saint").46 Moreover, what Lacan situates as the perversion of Joyce's writing in A Portrait and Ulysses, with respect to the Name-of-the-Father (Dedalus, artificer), serves to aver in the language of Finnegans Wake a certain Joyce as Father of the name. The translational play between Joyce and Freud also implies, as a subtext to Lacan's seminar, a further transferential play between the name of Lacan and the lac against which this "literalising" discourse is projected.

In the chapter of her biography of Lacan entitled 'Mathemes and Borromean Knots,' Elizabeth Roudinesco describes how in his later years Lacan was known to be quite passionately concerned with Borromean knots, and discusses his interest in topological puzzles in collaboration with Pierre Soury, Rene Thom and several other French mathematicians. What she relates bears a peculiar resemblance to certain key aspects of Finnegans Wake:

Soury's teaching, both in private and in public, aimed at constructing a mathematical mould that would facilitate the study of Lacan's logical and topological preoccupations: "What was our point of departure? There was the transition from knot to braid in the special case of the Borromean knot." [...] The solving of the great casse-tete took the form of a long correspondence between Lacan and the inhabitants of the planet Borromeo: first with Soury and Thom alone, and then with Christian Léger, who joined them in 1977. There were fifty letters from Lacan, a hundred and fifty from his colleagues: a veritable epic made up of suffering and melancholy, in which everyone involved exhausted themselves in the attempt to solve the riddle of the unconscious by means of telegrams, pneumatiques, and ordinary letters. [...] When they all got together for a discussion, it turned on the possibility of making a knot consisting of four clover leaves, or trefoils, and the transition from the knot to the braid.47


In this curious epistolary drama, in which Lacan ties himself in knots attempting to unravel the mysteries of the Borromean puzzle, we can perhaps see a return of the spectre of Joyce-le-symptôme: "the Shemptôme and the Shaun," or Shem the penman and Shaun ("Joyce Shaunise") the postman, inscribing here anew, in the vel or lack of this "circular" relation, the open mystery of yet another "purloined letter."48 Joyce's lettristic machine, or synth-tome, described through a metonymic reversion of the name "Joyce," turns back upon its Lacanian symptomatology a figure of "Lacan" as Freudian asymptote. The joie de livre in the symptom of the machine.


NOTES
1  Rabaté, Jean-Michel. '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  Maturana, Humberto and Francisco Varela. Autopoiesis and Cognition. Boston: Reidal, 1979.

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

4  Tausk, Victor. 'The Influencing Machine,' trans. Dorian Feigenbaum. Incorporations, eds. Jonathan Crary and Sanford Kwinter. New York: Zone Books, 1992: 551-2.

5  Deleuze and Guattari, Anti-Oedipus, 43.

6  Derrida, Jacques. 'Two Words for Joyce.' Post-structuralist Joyce: Essays from the French, eds. Derek Attridge and Daniel Ferrer. Cambridge: Cambridge University Press, 1984: 147.

7  Derrida, Jacques. 'The Double Sessions.' Dissemination, trans. Barbara Johnson. Baltimore: Johns Hopkins University Press, 1981: 221.

8  Derrida, 'Two Words for Joyce,' 148.

9  Derrida, Jacques. The Truth in Painting, trans. Geoffrey Bennington and Ian McLeod. Chicago: Chicago University Press, 1987: 27. This metaphor describes a two-fold relation that suggests, also, 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."

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

11  Rabaté, 'Lapsus ex machina,' 79.

12  See Russell, Bertram. The Principles of Mathematics. Cambridge: Cambridge University Press, 1903. Cf. Russell, Bertram and Alfred North Whitehead. Principia Mathematica. 3 vols. Cambridge: Cambridge University Press, 1910.

13  Derrida, Jacques. 'The Law of Genre,' trans. Avital Ronell. Glyph 7. Baltimore: Johns Hopkins University Press, 1980: 207.

14  Heidegger, Martin. 'The Question Concerning Technology,' Basic Writings: From Being and Time (1927) to The Task of Thinking (1964), ed. David Farrell Krell. Revised edition. London: Routledge, 1993: 330.

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

16  Cf. McLuhan, Marshall. The Gutenberg Galaxy: The Making of Typographical Man. Toronto: The University of Toronto Press, 1962: passim.

17  Turing, Alan. On Computable Numbers, with an Application to the Entscheidungsproblem,' Proceedings, London Mathematical Society, 2.42 (1936): 249-50.

18  Cf. FW 140-1. The letters A B C and D function here, as elsewhere, as subsectional "indices" of a series of questions, to which it is required "to harmonise your abecedeed responses" (FW 140.14).

19  Hart, Clive. Structure and Motif in Finnegans Wake. London: Faber and Faber, 1962: 62.

20  Hart, Structure and Motif in Finnegans Wake, 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).

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

22  Cf. McHugh, Roland. 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" (ibid., 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 and, to a less certain extent, Freud and the British anthropologist Sir J.G. Frazer.

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

24  Lacan, Jacques. 'Joyce le symptôme I,' Joyce avec Lacan, ed. Jacques Aubert. Paris: Navarin Éditeur, 1987: 29.

25  Lacan, 'Joyce le symptôme I,' 28.

26  Lacan, 'Joyce le symptôme I,' 28.

27  See Lacan. 'Seminaire.' Scilicet 6.7 (1976) 40.

28  Cf. Roughley, James Joyce and Critical Theory, 279.

29  Hart, Structure and Motif, 66-7.

30  Cf. Theall, Donald. James Joyce's Techno-Poetics. Toronto: Toronto University Press, 1997: 134f.

31  Fiorentino, F., ed. Jordani Bruni Nolani Opera Latine Conscripta. Neapoli, 1879-91; facsimile reprint by F. Fromman. Stuttgart-Bad Cannstatt: Verlag Gunther Holzboog, 1962 (op. cit. is De Monade Numero et Figura, Secretioris Nempe Physica, Mathematica et Metaphysica Elementa).

32  Eisenman, Peter. 'Unfolding Events,' Incorporations, 425.

33  McHugh, The Sigla of Finnegans Wake, 68.

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

35  Lacan, Jacques. The Four Fundamental Concepts of Psychoanalysis, ed. Jacques-Alain Miller, trans. Alan Sheridon. London: The Hogarth Press, 1977: 211.

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

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

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

39  Lacan, 'Joyce le symptôme I,' 24.

40  The term "Borromean" comes from the Borromeo family of Renaissance Italy, who used the three interlocking circles on their coat of arms. Cf. The Mathematical Intelligencer, 17.1 (Winter 1995). 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.

41  Lacan, 'La Sinthome,' Joyce avec Lacan, 46.

42  Lacan, 'La Sinthome,' 44-5.

43  Lacan, 'La Sinthome,' 44.

44  Lacan, 'La Sinthome,' 45.

45  Lacan, 'La Sinthome,' 46.

46  Lacan, 'Joyce le symptôme II,' Joyce avec Lacan, 33.

47  Roudenesco, Elizabeth. Jacques Lacan: Esquisse d'une vie, histoire d'un systeme de pensée. Paris: Fayard, 1993: 366-67.

48  Lacan, 'Joyce le symptôme I,' 24.


©
Louis Armand
For Lacan, the Borromean knot describes the relationship between symptom and a certain perversion, which he relates to the Freudian drama of triangulated desire defined 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.41

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 pere], and that in sum the Father is a symptom, or a sinthome."42 This relation has to do with the stratification of the individual as subject according to the relation of the symbolic, imaginary and real in which the genealogy of the 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."43

Recalling the Joycean "vicociclometer," Lacan's formulation of the Borromean knot hinges upon the figure described by the vesica, or vel, although in this case the vesica itself 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-Pere and le Pere du nom). 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 imaginary, symbolic and real, and as their tropological linkage. 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.44

The ex-istence of the symptom is implicated by the position of this "enigmatic link" of the imaginary, symbolic and real, which Lacan describes in the following diagrams:
1