a vector analysis of beckett's quad

P I O T R W O Y C I C K I

‘Mathematical Aesthetic’as a Strategy for Performance:

A Vector Analysis ofSamuel Beckett’s Quad

Stand up. Turn 90◦ left from your desk and walk 6 paces to B.Turn 135◦ to your left and walk 8 paces to D. Turn 135◦ to yourleft and walk 6 paces to A. Turn 135◦ to your left and walk 8paces to C. Turn 135◦ to your left and walk 6 paces to D. Turn135◦ to your left and walk 8 paces to B. Turn 135◦ to your leftand walk 6 paces to C. Turn 135◦ to your left and walk 8 pacesto A. Sit down. The above sequence of instructions from Beckett’sQuad marks a culmination of an aesthetic trend in Beckett’s pieces,an increasing focus on the use of mathematical patterns as aformal basis for structuring performance. In his detailed analysisof Samuel Beckett’s directorial notebooks S. E. Gontarski argues forthis trend:

Journal of Beckett Studies 21.2 (2012): 135–156Edinburgh University PressDOI: 10.3366/jobs.2012.0043© The editors, Journal of Beckett Studieswww.eupjournals.com/jobs

136 J O U R N A L O F B E C K E T T S T U D I E S

Revision is often toward a patterned disconnection, as motifsare organised not by causality but by some form of recurrenceand (near) symmetry. This process often entails the consciousdestruction of logical relations, the abandonment of linearargument, and the substitution for a more abstract pattern ofnumbers, music and so forth, to shape a work. (1985, 4)

What particularly interests me is how this trend towards thenumerical, the patterned, towards a ‘celebration of artificialstructures’ within Beckett’s plays becomes a major concept forperformance in his later works and in particular Quad (Dearlove,1982, 191). Arguably, in his earlier plays the use of geometricalpatterns, repetitions and other mathematical frameworks can beperceived as techniques used for undermining and reformulatingthe ‘traditional’, dramatic notions of character representation, in anattempt to free theatre from these sense-making frames. Examplesof this could be the peculiar geometric blocking of Endgame orthe symmetric, permutating narrative structures of Come and Go.However in his later plays, artificial structures become more of asubject matter in their own right, becoming a dominant aestheticwhich influences all aspects of theatricality and becomes more of aforeground of theatrical experience.

Historically mathematics has been the basis for developingcompositional tools and methodologies across a wide range ofart forms. Examples could be found in classical painting, musicand architecture but also in more contemporary forms such asstructural poetics, choreography, musical notation, film, and virtualtheatre. For instance in the classical era, the golden-section ruleand geometric figures were often used as aesthetic guidelines tostructure images and musical elements. The ‘Fibonacci Sequence’was used as a tool to establish proportions both within paintingand architecture, famously implemented by Michaelangelo inmany of his architectural works. Leonardo da Vinci was famousfor introducing perspective rules and mathematical proportionalityto painting. In some sense mathematical structures have beenlike a hidden ‘code’ within the Western cultural heritage, whichreinforced a continuous proliferation of certain formal qualities.They served as a formal spine, an inner structure that supporteddifferent elements of an artwork in question. In that sense these

A Vector Analysis of Samuel Beckett’s Quad 137

compositional rules were hidden patterns, ‘beneath’ the surfaceof emanation of a work of art. They comprised relations anddynamics designed to ensure a sense of beauty, balance, hierarchyand harmony which was to be apprehended on a more ‘intuitive’,qualitative level by the beholder. During the classical period theimplicit mathematical structures were never to become the subjectmatter of a work of art, nor were they were supposed to be exposed,unmasked or foregrounded on top of the structural hierarchyof a work of art. In the modernist age, however, there was amore explicit pronunciation of these compositional rules and themathematical structures comprising them. This is very visible inarchitecture for instance, where the logic of the buildings beganto accentuate rigid geometric forms, as in the works of Mies VanDer Rohe or Le Corbusier. Also in music, in the work of ArnoldSchönberg for instance, who applied set theory as a system fordefining and categorising harmonic relations; or in painting, wherePiet Mondrian made geometrical proportions the subject matter ofhis abstract paintings.

In the theatre, Beckett progressively introduced mathematicalnotions to structure performance. In his later work therepresentational aspirations are reduced and this makes thestructural principles underlying performance more visible. Thismovement towards structural enunciation developed into astrategy that arguably became progressively dominant withinhis plays. I would like to analyse structural patterns thatconstitute Beckett’s mathematical strategies for performance fromthe perspective of mathematics and I will refer to them as the‘mathematical aesthetic’. This aesthetic can be broadly defined asan underlying set of principles, or an image often manifested by anoutward appearance or style of performance, where mathematicsprovides an especially succinct definition of the representationaland structural impulse. This is not to say that mathematics wasessentially at the heart of Beckett’s thinking behind aestheticchoices and dramaturgical strategies, even though it may bedifficult to avoid that impression with plays such as Quad.Furthermore Beckett’s experimentation with this ‘mathematicalaesthetic’ is not necessarily in line with a pursuit of an aestheticideal or the transcendental ‘real’. Despite its broad applicationin today’s society mathematics remains an abstract body of


knowledge that is often artificially imposed on reality in orderto yield models of representation/explanation and consequentlycontrol.

In this article I shall analyse the ‘mathematical aesthetic’ inBeckett’s Quad in terms of the play script and the possibilitiesit offers for performance. In the first instance I will explore therelationship between the mathematical choreography of Quad andits implementation in performance in terms of the significance thatit offers for the interpretation of the piece. I will argue that theuse of the ‘mathematical aesthetic’ in Quad works towards openingup a multiplicity of interpretations and hence I will elaboratehow it can be seen as negotiating various interpretations thathave been suggested in the past. In the second instance I willoffer a different approach to interpreting Quad. I will use JeanBaudrillard’s theory of simulation and treat Quad as a work ofconceptual art to show how the ‘mathematical aesthetic’ can beseen as a structural concept which effaces the author. I will contendthat by developing this aesthetic Beckett heralded the emergenceof performance simulation which finds an increasing applicationin contemporary virtual performance and CGI. I will demonstratethis by showing how the ‘mathematical aesthetic’ of Quad can beturned into a computer program capable of generating the script ofthe play ad infinitum.

Quad

Quad is a play built around the tension between an extremelyformal abstract choreographic system and its potential forimplementation as an actual live performance. As Steven Connorputs it, the play exhibits the ‘opposition between the living, theembodied, the concrete on the one hand, and the abstract, thesymbolic and the tangible on the other’ (1988, 140). The playconsists of four players moving within an area of a square whosesides are six paces long, with each player having a specificallydesignated path. Each of the players in essence performs the samepattern simply starting at different points in the square at differenttimes. This scheme can be likened to a baroque piece of musicwhere each instrument performs a complementary voice that is in a


different register to the other voices and is phased in time. Each ofthe players performs a journey that can be mathematically definedthrough a series of vectors.

Diagram 1 (Beckett, 1986, 451). Path ways for the movements of the fourplayers, within the square in Quad.

The vector Paths (see Diagram 1) are as follows:

Course 1: AC, CB, BA, AD, DB, BC, CD, DA

Course 2: BA, AD, DB, BC, CD, DA, AC, CB

Course 3: CD, DA, AC, CB, BA, AD, DB, BC

Course 4: DB, BC, CD, DA, AC, CB, BA, AD

The conceptual players seem to act as within a computerprogram, a machine that has created definite paths for their bodies.If we were to analyse this play from a dramatic perspective, or interms of what it potentially represents, then we are faced with analmost absurd situation since the play script offers little materialfor such an enquiry. From a dramatic perspective there is verylittle to read a subject/character from not to mention a plot ornarrative. Most of the dramatic notions of theatrical representationhave been reduced to a minimum and what is left is an almostpurely objective blueprint of movement that dictates the wholeperformance. Dimensions such as the use of spoken language,props and set are made substantially minimal or completely

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abandoned. All that remains is a dark void, a square and fourhooded human bodies.

A clear distinction must be made between Beckett’s aestheticstrategy and the way an audience may read and interpret it. Iwill problematise this distinction further on. For now I would liketo hone in on the specificity of the ‘mathematical aesthetic’ as acreative tactic in Quad. In order to illuminate the mathematicalconcepts, which are a blueprint for structuring the performanceof this play and seem to be at the heart of its substance, we mustfirst analyse the ‘mathematical aesthetic’ in detail. The script for theplay stipulates simply a series of vector movements for each playerto perform, within the square. On closer analysis, it becomes clearthat the whole sequence for the play consists of a repetition of twovector movements, one along a side of the square and the otherone across the diagonal. These two vectors form a core path foreach player. Once the path is completed, it is turned 90◦ clockwiseand repeated again. This consecutive repetition and re-mapping ofthe two vectors by a rotation of 90◦ forms the script for the play.In mathematical terms this could be described as a multiplicityof two vectors which are being re-mapped or multiplied by arotational matrix of 90◦ clockwise. Diagrams 2 to 6 explain thevector breakdown of movements in Quad.

This core trajectory could be defined as the one of a multiplicityand looking at it from a purely theoretical structural perspectiveit is a mathematical, ideal multiplicity.1 The ‘one’ shape, beingthat of the two vectors, is being endlessly multiplied within thesame space. The endless quality is only there, if we accept thatthe play’s rudimentary symmetrical structure could be repeatedinfinitely. The reason why I want to make this clear is that this strictmathematical form has crucial implications for any performanceof the play and its witnessing by the audience. This mathematicalconcept for performance, where all paths, steps and actionsof the performers have been ascribed through a mathematicalstructure, naturally brings questions about the potential of itsrealisation in performance. Also intriguing are the reasons forsubjecting live performance to this finite mathematically controlledchoreography. The focus of the performance of Quad can beseen as a tension between two poles, the structural and theperformative, a tension which is arguably multifaceted. If we


The first two movement vectors, which then are rotated 90ºanti-clockwise to produce the character’s paths.

The second two vectors

The third two vectors





The fourth two vectors

When put together they form a full character path for Quad

Diagrams 2 to 6. Vector breakdown of movements in Quad.

were to compare the experience of reading or apprehending thisconcept with the spectating of its performance, then it can be saidthat the live performance, through the sheer detail and nuancedquality of a performer’s presence, has the potential to exceed orbe in excess of the minimalist conceptual structure from whichit derives. Arguably this excess results from the fact that thematerial stage body is never ideally performing the paths set outby the ‘mathematical aesthetic’; the live performance potentiallyfalls short of realising the concept, but also brings with it a




plethora of nuances that potentially come into tension with thepurely geometric choreography. These nuanced details may rangefrom subtle expressions of individual characteristics of performers,such as differences in walking pace, posture, minimal gestures,deliberately pronounced or not, to effects caused by exhaustionsuch as occasional slippages, uneven walking rhythm etc. As I willargue, it seems as if Beckett is setting up a theatrical experiment,where a potential tension will develop: a tension between animaginary aspiration towards a formal, aesthetic ideal and itsfailure of realisation in live performance.

In Quad I and Quad II, directed by Beckett for television in1982, actors performing the script internalise the inherent patternswithin it. When the performance starts, before the players enter, theaudience is faced with an empty void. Once the players enter andstart to move they start to map out all the vector patterns throughtheir movements. They plot the coordinates of the square andtheir regimented paths. For the players the script or the structurepre-exists the performance. For a witnessing audience, however,the mathematical structures and rules governing performance arenot clear from the start. The inscription of geometric patterns andfigures becomes apprehensible as they unfold from repetitionsduring the performance. Steve Connor remarks that ‘the shapeof the square becomes impermanent and has to be inscribed andanxiously re-inscribed by the pacing figures’ (1988, 144). Sooner orlater it becomes apparent for the spectator that there is a set of rulesgoverning and dictating the players’ paths. Each player has onephrase of movement which, as I have previously explained, couldbe seen as being made up of two vectors and a rotational matrix.As far as a potential for ‘character construction’ is concerned,this is what textually constitutes each player’s identity. This rigidrepetition may evoke the rejection of plot and character history.The repetitive movements of the players who have no memory,no defined past to develop from, assume the abstract structureinherent in their movement. There is no introduction or end totheir journeys, only a constant repetition of a mathematical form.The players seem to follow the idea of what could be defined as a‘liminal journey’, that Deleuze and Guattari defined as ‘proceedingfrom the middle, through the middle, coming and going ratherthan starting and finishing’ (1988, 25). If one tried to identify a plot,a progressive linear series of consequential events, then the circular


form of repetition would create a resistance. This is different thanin a play like Footfalls, an earlier play by Beckett heavily structuredaround mathematical permutations, where the repetition is se-quential and teasingly offers the possibility of a plot. In this contextQuad becomes more of a formal exercise. A process of attemptingto achieve an abstract mathematical aesthetic in performance.

Nonetheless it soon becomes apparent that this pure formalismis unachievable in performance since the live bodies resist theimposition of such rigid formal structures. And indeed Quad seemsto explore what becomes a failure of the human performer toembody them. Sidney Hoffman, who directed the BBC2 versionof Quad I and II combined, said that Quad I offers a ‘nightmarishworld’ for the actor, since there is almost no room for improvisation(1992, 41). Yet, it is the constant circular repetition of theseformal structures – which may prove annoying and tiresome towatch – that makes the audience seek out the detail, where theslightest movement or gesture starts to gain a new proportionof meaning. Sidney Homan comments on a rehearsal process forthe television version of Quad he directed, saying that despite therigid structure slight traces of character inevitably appear. This isinevitable since each actor has his/her own personality and certainsubtle habits which become more apparent as the formal structureis being repeated. As an audience we notice those personal touchesin ‘the form of a characteristic walk, a peculiar way of approachingthe corner, the very posture of the body, an expression on aface otherwise staring almost blindly ahead’ and ‘different moods. . . when only one player was present, or when all four weretogether’ (Hoffman, 1992, 29). It is out of these unprepossessingraw materials that Beckett generates a dramaturgy of which thesmallest detail may possess significance.

Apart from occasional performance excess there is a far moreobvious moment in the play which illustrates the engendered‘escape’ in the structure of the ‘trace’. That is the moment wherethe directions given in the original script for Quad I fail toprevent players clashing at the centre of the square. The hot spotis the centre where there is a possibility of collision between theplayers. The centre E, also called the ‘danger zone’ by Beckett, isa problematic situation where the strict rules of the ‘trace’ have tobe compromised. The problem at the centre of the stage as Beckett


Diagram 7 (Beckett, 1986, 453). Beckett’s solution to the problem resultingat the center ‘E’.

suggests in his notes ‘could be exploited’. The ‘problem’ can be seenas a failure of the performers’ bodies to integrate themselves intothe pure mathematical system. Hence, the problem which can occurin the ‘danger’ zone of the play can also be seen as a manifestationof the subjective performance of the players. Beckett thus offersa plan B (see Diagram 7), which is precisely the manipulation ofthe players within the vector rules of their movement to solve theproblem.

Hans Hans Hiebel argues that

an audience that anticipates the subjective is astonished by therepetition of the jerky turn, the repeated and always recurringidentical frightened reaction of the performers in front of theterrifying centre of the quadrangle: “‘E”—the danger zone.The “danger zone”—“Abgrund” (Abyss). (1993, 339)

To further explore what is at stake between the mathematicaltext and the performance Ciane Fernandes’s insights into thenature of movement repetition in Pina Bausch’s theatre may beilluminating here. She points to the fact that performance createsa gap between the text or the interpretation and what is materiallyin front of us. She argues that the audience are faced with acrucial bodily function intensified by mechanisation. Repetition

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initially dismantles dance as spontaneous expression, positing it aspart of the ‘symbolic’. It then allows a temporary opening of the‘symbolic’ order into the real (Fernandes, 2001). This reveals ‘motormanifestations’ and experience. In the case of Quad, the ‘symbolic’is the mathematical structure. As we have seen, the repetitionof movements makes the audience spot the geometric pattern.However further down the process they may begin to notice themore subjective gestures of the players. The centre becomes a placeof friction, where the mathematical system collapses and has to bereinstated again. Beckett said that the centre:

marks the spot or moment of recognition of the void, thenothingness which seems to penetrate through the black holein the centre. Death, nothingness, misery, futility, ‘danger’ arevisible for a second, but are instantly forgotten or repressed.(Quoted in Hiebel, 1993, 339)

Hence, the temporary recognition of the void can also be seen asa manifestation of a deeply repressed conscience. Sidney Homanplayed with this idea in his production by having the last playerwalk into the centre and disappear. The lighting was adjusted insuch a way that the centre was a dark square.

Even though the play has no language, and its text seems to begeometry, it is not incapable of suggesting representations. SidneyHoffman suggests:

If we are an active audience in Beckett’s work, no matter whatmedium he chooses, here in the mimes we are even more so.The actions are devastatingly physical, [. . . ] and yet we cannotresist the self-imposed drive toward symbolism and meaning.(Quoted in Connor, 1988, 165)

For instance Connor argues in Quad that the ‘Anticlockwise andclockwise are the directions moved by the inhabitants of theInferno and Purgatory respectively in Dante’s Divine Comedy, tosignify movement away and towards God, away from and towardsfreedom’ (1988, 145). One can also read the play through MichelFoucault’s theory of the ‘panopticon’. The players act as within aprison but there are no walls, the barriers are within the players,the structure of surveillance has been internalised. The square


only exists through performance; it is thus the ‘performative map’.Foucault’s claim that ‘we are . . . in the panoptic machine’ can relatedirectly to the audience who watches the performance on a TVscreen, a private theatre and – given the notions of reality TVshows – also a system of surveillance (1979, 217). The Foucauldiantake on the play invites a political reading, along the lines of anOrwellian state, where all is controlled by an external all presentpower. Even though there is little possibility of traditional characterinteraction, the ‘mathematical aesthetic’ does offer a possibility forcharacter relations. Michael Guest states that: ‘Beckett’s vision ofhuman existence confined in a perpetual moment, no more livingthan not, has a philosophical affinity with Foucault’s project ofwriting a “history of the present”’ (1996). The rejection of historycalls for a creation of history in the ‘present’ or, in other words aform of community.

Despite these multiple possibilities of interpretation, however,the abstractness of Quad and its sheer formality imply that almostany meaning within could be attributed to it. Many critics likeConnor see this play as ‘endlessly irresolvable, since one cannotimagine even some general overall direction for the players’(Connor, 1988, 145). Thus I would like to suggest a different wayof looking at Quad by looking at the ‘interinvolvement’ of its‘mathematical aesthetic’ and the performance text, not in terms ofwhat it represents, but rather by treating Quad as a conceptualwork of art which defies performativity. In that sense I would liketo contend that Quad is a beginning of a new era of theatricality.In the following part of my argument I will therefore extend theconcepts and issues suggested by Beckett’s work to point out someof the cultural, ethical and political issues with the progressivesystematisation and simulation of performance in contemporaryart and mainstream entertainment.

Beyond Quad: The Politics of The Mathematical

As I have argued, despite the heavily mathematised blueprint forperformance, the very fact that Quad is performed by live actorsallows for a wealth of interpretations beyond its structural core.Much like the multiplying vectors that constitute its text, it could


be said that Quad stimulates a multiplicity of interpretations andpotential instances of representation. But Quad can also be seen asa purely conceptual structure independent of live performance. Inthat context Quad could be seen as an extreme experiment to ‘efface’the live and the dramatic notion of the ‘human’ and consequentlyherald the removal of liveness from performance. I would like totake a step further and claim that Quad can also be seen as ‘effacing’the author. What is interesting about the concept and the text ofQuad is that it can be easily simulated and generated by a computerprogram. Once set in motion it becomes a sort of perpetuum mobile.

I have written a computer program which not only enactsthe key structure of Quad I and II but is essentially capable ofgenerating the set of instructions required for its performance.(A version of the program can be downloaded from www.wix.com/pwoycicki/Quad.) The program visualises and plots the pathof a player in Quad. The program contains the coordinates of thetwo vectors which comprise the path of a player. Then it has twoprocedures. One procedure transforms the initial vector blueprintfor a player’s movement by rotating it clockwise, very muchas described in the above Quad analysis. The second procedureanimates a square through six ‘paces’ according to the vectorcoordinates. As a result the avatar ‘square’ is moved through thepathways of Quad. The coordinates of the two vectors are storedin variables. Once they are multiplied and transfigured by thematrix, the new set of coordinates replaces the old ones and theyare stored again in the same variables. As a result, the programkeeps no record of its past trajectory and it generates its futureone as it goes along. This whole procedure is looped until the userhits ‘Esc’ and since no memory is accumulated as the coordinatesare constantly being ‘recycled’, in theory, the program could runforever. In essence this program can effectively generate the wholeof the play simply based on the two vectors and a matrix. The playscript is not necessary for it to plot all the pathways for the fourplayers, although one could also program it to write the script bymaking it write out all the vectors in sequence.

So what else can transforming Quad into a program like this tellus about the nature of this mysterious piece by Beckett? The mainsignificance of it is that it shows that Quad could be interpretedas a conceptually minimalist piece based on a mathematical,


computable aesthetic. Once the core of the concept is set in motion,the core being the two vectors and a rotational matrix, Quadconceptually becomes a simulation. Thus it can be argued thatby employing a mathematical aesthetic in such extensive waysBeckett was exploring the potential of performance simulation.This creates an interesting perceptual tension. On the one handQuad offers the potential for multiple readings when one considersthe abstractness and metaphorical nature of the piece. On theother hand the notion of a simulation becomes a strategy of theeffacement and decantation of a human subject. The potentialclash of these two perspectives through live performance, and theperceptual flux between the ‘creation’ of a human subject throughperformance and the ‘creation’ of an abstract mathematical objectwhich choreographs it, situates Beckett’s later work in relationto a society that was becoming progressively mathematised andtechnological.

To explore what is at stake in this dynamic further, JeanBaudrillard’s theory of the third order of simulacra can be helpfulhere as it gives insight into what happens to the sign in a societywhere sign production progresses towards simulation. Baudrillardcame up with three orders of the simulacra which, according tohim, define the way signs were and are produced since the ‘classicalperiod’ up to today. The first order is that of the counterfeit, thedominant schema of the ‘classical’ period where the signs areproduced in relation to an original. The second order is that ofproduction, which dominates in the industrial era, where the signproduction is derived from the production process, ‘technics’. Thethird order is that of simulation where the signs are governedby a mathematical code (Baudrillard, 1993, 50). Baudrillard statesthat we have already seen the signs of the first simulacra, withtheir complexity and wealth of illusion, changing into crude,dull, repetitive, functional and efficient signs. These orders arehistoricised and periodised to an extent. Baudrillard attributesthe domain of the first order to the classical age, the second tothe industrial and the third to post-modernity. Despite historicaldistinctions an argument is also put forward that these orders cancoalesce and are not specifically tied to their respective periods.

If we go by this model one can draw a certain parallel ofhow sign production operates in Beckett’s theatrical works. In


his earlier plays there still seems to be a wealth of mimeticdevices and at times the audiences are lured into illusion andinvited to create, focalise, and indulge in these representations,while in the later plays those traditional dramatic devices becomeincreasingly replaced by mechanical or mathematical repetitions,which impose themselves on an increasing number of aspects thatmake up the theatrical event. The dramatic subject is systematicallyeffaced but not entirely. In that sense one could plot Beckett’suse of the theatrical sign against Baudrillard’s theory and findcorrespondence: ranging from the counterfeit and illusion of theearlier dramas such as Waiting for Godot (first order), through themore repetitive, ‘mechanic’ plays such as Come and Go (secondorder) and up to Quad which as I have argued borders on the notionof a simulation of a play (third order). Baudrillard’s thoughts onthe third order of simulacra seem to be a fitting description ofwhat is at stake in the ‘mathematical aesthetic’ of Quad. Baudrillardessentially sees the third stage of the simulacra as an overtaking ofall sign production by a model that no longer negotiates questionsand instead provides only answers. He says that in the third orderof simulacra:

At this level the question of signs, of their rational destination,their real or imaginary, their repression, their deviation, theillusion they create or that which they conceal, or their parallelmeanings - all of that is erased. We have already seen signsof the first order, complex signs and rich in illusion, change,with the machines, into crude signs, dull, industrial, repetitive,echoless, operational and efficacious. [Finally] there is a stillmore radical mutation as regards the code’s signals, whichbecome illegible, and for which no possible interpretation canbe provided, buried like programmatic matrices, [. . . ] End ofthe theatre of representation, the space of the conflicts andsilences of the sign: only the black box of the code remains.(Baudrillard, 1993, 57– 8)

By turning Quad into a computer program and looking at ithypothetically from a purely conceptual perspective with the liveperformance eliminated, the possibility of the undecidability ofthe theatrical sign, which for Baudrillard is an essential aspect


of signification, is lost. In this context there is a potential affinitybetween the nature of sign production in the third order ofsimulacra and Quad’s ‘mathematical aesthetic’. Where the liveperformance could still enable a potential interpretation of suchan origin, since the bodies in performance accumulate certaintraits, even if those are the tiredness of the players which canbring out certain performative nuances, the computer programhas no ‘history’ record as such. From a conceptual perspectiveit keeps no record of past or future. Baudrillard claims that thislack of ‘history’, evolution and trajectory at the heart of themathematical codes underlying sign production in the third orderof simulacra, leads to essentially cellular forms of perception. Heargues that ‘[e]ven space is no longer linear or one-dimensionalbut cellular, indefinitely generating the same signals like the lonelyand repetitive habits of a stir-crazy prisoner’ (Baudrillard, 1993,58). This can be again related to the concept of Quad where theplayers create their own space, but also their own prison. Themodel which is discreetly repeated in the program offers no ‘linesof flight’ to use Deleuze and Guattari’s terms, no possibility ofdeviation, mystery or ‘escape’ from its generative core. What iseven more interesting is that by viewing Quad through such anextreme conceptual framework not only the undecidability andmystery of the theatrical sign is effaced but so is the agency ofthe author or thespians involved. This is clearly emphasised bythe computer program which can reproduce itself to infinity byrepeating the mathematical core, thus ‘writing’ the concept ofthe play without the need for an author or performers once thevector model for its generation has been initiated. Baudrillard linksthis change in sign production with capitalist politics, claimingthat the reduction of all signs and knowledge to a binary codewill enable new means of controlling and organising society.Baudrillard’s argument has to be problematised here though, ashe in a way envisions the death of language. After all, the threeorders of simulacra co-exist and what Baudrillard proposes isa polarity, not an end state of total simulation. He proposes amovement towards a mathematised society with mathematisedforms of signification, rather than a complete ‘realisation’ thereof.A complete mathematisation of reality would be impossible but if itoccurred it would leave no more undecidability of meaning hence


no potential for creating signification. It would in a way be theend of science and all knowledge. The mystery of the sign is whatkeeps signification live. As long as language fails to define reality,mathematics can only be a system of approximation at any givenpoint in history, waiting to be re-inscribed into another system ofapproximation. Beckett’s work, and in a particularly abstract senseQuad, stages this failure of language. And thus if we look at itfrom the suggested philosophical perspective it stages the failureof a mathematised, technological society to set a definition of thehuman subject.

Thus Quad could also be seen as addressing a contemporarypolitical climate, by means of a theatrical manifestation of the‘human’ within a dominant mathematical framework. ConsideringQuad as a computer program, a simulation can also helpus to understand how this play relates to the progressivemathematisation of politics and culture that was becoming evidentin the 1980s and extends to this very day. Obviously Quadwas intended to be performed by human performers, live ortelevised, since what is at stake in Quad is the tension betweenthe human performance and the mathematised aesthetic. Thisperspective of simulation can also negotiate a difference betweentheatrical performance and simulated electronic performance.Theatrical presence has been often referred to as ephermal, fleeting,metaphorical, pointing to something beyond itself, beyond itsphysical matter of the here and now. In the context of Baudrillard’sanalysis the theatrical sign remains a mystery, it is unstable andindefinable. By extension so is the identity and the origin of thehuman if one were to consider more general terms. In contrastto this, a simulated sign in a simulated performance is ultimatelyand completely reducible to the code which generates. There isno more mystery but an empty vacuous definition of identitythrough a mathematical genus. Within this context Quad could beseen as negotiating the relationship between the theatrical signof live performance and the simulated choreographical structuresimposed upon it.

Quad can also be seen as a prototype of a simulated virtualperformance, despite the fact that it was intended to be performedby live performers after all, and in that heralding and exemplifyinga trend both in contemporary arts and mainstream arts, where


the mathematical codes and simulations are steadily taking overand ‘colonising’ live performance. For example Susan Broadhurst’sBlue Bloodshot Flowers (2001) where an avatar was programmedwith an “emotion engine”, capable of simulating a wide spectrumof performative behaviours and reactions. In mainstream artcomputer simulations have been extensively used to generatevirtual performance in films and computer games. The animationprocess mainly consists of the animator key-framing avatars, oranimating them by using mathematical tools to define movement.2

At times motion capture is used to source movement into thevirtual avatars. In all of the above cases we still have humaninput and directorial control. Even though everything is ultimatelyreduced to a binary code, we still get a human source which makeseach character different. Peter Jackson’s film Lord of the Rings: TheReturn of the King used a revolutionary sequence. One of the battlesequences demanded that over 10,000 characters be animated. Thisposed a workload problem for the animators working to a tightproduction schedule. A program was designed that could takea character animation conceived by an animator and multiplyit so as to generate a whole legion. However to avoid an exactreplica which would seem non-naturalistic the program woulduse a set of matrices with which it multiplied vectors definingthe movements of characters thus modulating them and changingtheir movements. This process would differentiate characters andgive each one a personal dimension. The program would alsoanimate fights between different characters, differentiating everyfight, randomly deciding on the outcome of a fight based on anoverall statistic given by the programmer. In other words it wasa battle simulator which had a certain degree of autonomy. Ina way the program generated new material and thus could beviewed as an author-director of some of the things we see on thescreen.

My program of Quad is a more primitive version since it does notcreate an illusion of difference; however, the basics are similar.It has a set of initial instructions, vectors which work likeBaudrillard’s model which it then multiplies to create a perfor-mance. A lot of contemporary culture exemplifies a progressivemathematisation of performance, which is essentially becominggenerated by computer simulations. The human being as an origin


and generator of performance is being replaced by mathematicalmodels. In that sense contemporary culture can be said to carryaspects of a post-human condition. Beckett’s Quad is not so muchan exemplification of this in the way that the above examples offilms and computer programs are, but it can be seen as an attemptto articulate the ‘human’ in performance within a progressivelymathematised culture.

Advocating The ‘Live’

In the light of this cultural shift, we could reflect upon Beckett’slater drama as advocating the ‘live’, giving his audience a lessonin measure. Thus does Beckett’s advocating of ‘live’ presence,make him the last humanist? Or as Martin Esslin put it, does heshow us the ‘courage to face the ultimate void [and] produces acatharsis and intimation of the sublime, hence after all, somethingthat lifts us above the void’ (1993, 20)? So far, and partiallythrough recourse to Baudrillard, I have implied that the eminenceof mathematical structures in our contemporary culture and age issomething negative and soulless, essentially inhuman and set inopposition to the ‘live’ posing a threat of its effacement. It is alsotrue that the age of post-humanism is often portrayed as a negativeand progressively catastrophic time, leading to the creation of anaustere technological civilisation with which our engagement willbecome severely compromised in all aspects of life. But this is onlyone side of the argument which assumes a stance of pessimism.In many ways such an approach is fitting to the evaluation ofthe ‘interinvolvement’ of live performance and the ‘mathematicalaesthetic’ in Quad, since Beckett’s dramatic world is often perceivedas absurdly pessimistic and cynical. However the implementationof mathematics can be perceived here in a more positive sense. Thepursuit of mathematical ontology and idealism in art reflects theoldest human aspiration, the aspiration towards ideal objectivityand by extension a representation of the human in the light ofthis ideal. In a classical sense: beauty. Alain Badiou advocatesthe beauty of mathematics by quoting a short poem by ÁlvaroDe Campos, one of the heteronyms used by the Portuguese poet


Fernando Pessoa: ‘Newton’s binomial is as beautiful as the Venusde Milo. The truth is few people notice it’ (quoted in Badiou, 2004,20). In this sense the application of the ‘mathematical aesthetic’in Quad, with its strict, yet elegant pattern can be perceived asmesmerising and simply beautiful, like a musical prelude or anunfolding architectural rosette. Thus the sublime emerges out ofthe anticipation of the formal mathematical pattern that never quitecomes about in performance.

The key concept here again is failure, the inevitable failureof living up to the ideal. A polish conductor, Jerzy Maksymiuk,known for his strict and structural yet somewhat extravagantapproach to music, once said that art is born out of error. Thusthe lesson taught by Beckett lies in failure. This perhaps shouldnot be seen as a dark irony but as part of the process ofengaging with structures that we see as dominating our reality. Thetransgression of the mathematical model by the human performersets in motion the fluidity of the subject-object relation. Both theformal mathematical patterns and the unexpected qualities anddetails of live performance become negotiated in Quad. Such isthe image in Quad: four bodies resonating with a mathematicalstructure and a mathematical structure resonating through them.And in this context Quad can be seen as a play which demarcatesa space for the ‘failure’ of the ‘live’ within the structures ofthe mathematical, hence negotiating this relationship betweenlive performance and the ‘mathematical aesthetic’, not as one ofopposition and irreducibility, but one of ‘interinvolvement’.

N O T E S

1. A pattern or in this case a sequence of movements denoted byvectors, which multiplies (repeats itself through a constant rotationaltransformation) ad infinitum.

2. Key framing is when an animator sets up a series of positions,tableaux, on a timeline that an avatar will assume during the course of ananimation. The computer program calculates all the positions in betweenso that a fluidity of 30 frames per second is achieved.


W O R K S C I T E D

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Badiou, Alain (2004), Theoretical Writings, London and New York:Continuum.

Baudrillard, Jean [1976] (1993), Symbolic Exchange and Death, trans. I.Hamilton Grant, London: Sage Publications.

Baudrillard, Jean (1994), Simulacra and Simulation, trans. S. F. Glaser, USA:The University of Michigan.

Beckett, Samuel (1986), The Complete Dramatic Works, London: Faber andFaber.

Connor, Steven (1988), Samuel Beckett: Repetition, Theory and Text, Oxford:Basil Blackwell.

Deleuze, Gilles and Félix Guattari [1980] (1988), A Thousand Plateaus:Capitalism and Schizophrenia, trans. B. Massumi, London: Athlone Press.

Deleuze, Gilles and Félix Guattari [1972] (1984), Anti-Oedipus: Capitalismand Schizophrenia, trans. R. Hurley, M. Seem and H. R. Lane, London:Continuum.

Dearlove, J. E. (1982), Accomodating the Chaos: Samuel Beckett’s NonrelationalArt, Durham: Duke University Press.

Dürrenmatt, Firedrich (1982), Plays and Essays, New York: ContinuumPublishing Company.

Esslin, Martin (1993), ‘WHAT BECKETT TEACHES ME: His MinimalistApproach to Ethics’, Samuel Beckett, Today / Ajourd’hui Beckett in the 1990s,II, pp. 13–20.

Fernandes, Ciane (2001), Pina Bausch and the Wuppertal Dance Theater:The Aesthetics of Repetition and Transformation, New York: Peter Lang.

Foucault, Michel (1979), Discipline and Punish, London: Penguin Books.Gontarski, S. E. (1985), The Intent of Undoing in Samuel Beckett’s Dramatic

Texts, Bloomington: Indiana University Press.Gontarski, S. E. (ed.) (1999), The Shorter Plays: With Revised Texts for Footfalls,

Come and Go, and What Where, New York: Grove Press.Guest, M. (1996), Beckett and Foucault: Some Affinities,

http://www.levity.com/corduroy/beckettf.htm.Hiebel, H. H. (1993), ‘Quadrat 1 + 2 as a Television Play’, Samuel Beckett,

Today / Ajourd’hui Beckett in the 1990s II, pp. 335–341.Hoffman, Sidney (1992), Filming Beckett’s Television Plays, London:

Associated University Press.The Lord of the Rings: Return of the King, film, Peter Jackson (director),

London: New Line Home Entertainment, 2004.

a vector analysis of beckett's quad

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