Chaos and Order on the Theatre Stage
Of all the arts, the concept of order (and its violation) is particularly important in the discussion of theatre, as it tends to include the tension between the planned and repeated (the rehearsed) and the performance as a one-time event, the "here and now" of a specific evening, in front of a specific audience. Moreover, theatre is a point of confluence for discussions of order and its violation in different fields: aesthetic, psychological, social, cultural, political, and also physical-mathematical, of course, being a material event in the world.
The artistic and experimental German theatre encompasses in its discourse a range of extremely varied and contrasting phenomena: it fluctuates between dramatic and post-dramatic theatre, and between theatre and performance art, while re-examining and challenging common distinctions about the relationship between actor and character, performer and spectator, and text and performance. In this article, I would like to describe the expression of mathematical-physical theoretical concepts of order and its violation in the German theatre of the 21st century. The theatrical scenography may be perceived as the meeting point between those theoretical terms and the realisation of a theatrical play with live persons, structures, and objects in the material world, as I shall show below.
The Geometric Order of Passion: Michael Thalheimer
A Greek legend tells of a plague suffered by the people of Delos. The poor residents turned to the Oracle of Apollo, and were told that the plague would disappear if they built Apollo a cube-shaped altar twice as big as the old one. The Delians then consulted Plato, who understood the mathematical problem (building a cube double in volume than a given cube) as a message from Apollo that they should dedicate themselves to mathematics and geometry to quell their passions. Plato reproached the Greek for their disrespect of pure mathematics and handed over the problem to the famed "academic mathematicians": Eudoxus of Cnidus, Archytas and Menaechmus. The three gave the problem a mechanical solution, which made Plato reproach them, too, for neglecting pure Geometry and deserting it in favour of simple mechanics.1 This legend incorporates some tensions that are important to our discussion of geometry here: the gap between abstract theoretical mathematics and concrete, practical arithmetic knowledge, but also, much later, the tension between the restraint of abstract mathematical subtleness and human desire.
The works of Michael Thalheimer encapsulate the tension between theory and practice, or order and passion, contained in geometrical abstraction. First, the stages in these works, designed by Olaf Altmann, are geometrical to the point of bidimensional abstraction. Second, the mise-en-scene emerges from the friction against these rigid sets, as if in an examination of the theorems derived from those strict rules.
These characteristics can be easily detected in his 2001 masterpiece Emilia Galotti, an adaptation of Lessing's classic drama, performed in 2002 at Germany's leading theatre festival, the Theatertreffen, and staged in the Deutsche Theatre until 2009. Thalheimer distils the play to its very essence, leaving only its minimal structure. Thus, a play which is originally three-hour-long or longer (not an abnormal length for German audiences) was cut down to a mere hour and a half. To do so, the plot was thinned down, some characters were left out, and the four first scenes, for example, were replaced by a short introduction of expressive, abstract theatre-dance portraying the relationship between the play's protagonists.
Stage designer Olaf Altman created a rectangular opening at the back of the stage, from which sides two walls gradually open towards the audience, creating a trapezoid-shaped floor. This abstract stage has a clear perspective, with the opening at the back acting as a vanishing point. But the interesting part is that the set's geometry seems to dictate the movement inside it. The actors move back and forth along the trapezoid's main axis, from the opening at the back downstage, as if on a runway. It is an abstract representation of the way one moves inside a church – which is where the prince meets Emilia Galotti – but it also translates religion into "fashion", as in the Vatican fashion show in Fellini's Roma (yet without the fashion items). The protagonists meet while moving along this axis: this is their sociological space, but also the law imposed upon them: a social law enforcing a clear, simple geometry of marching back and forth – even when they trip and fall, they do so along the runway.
The complete lack of furniture and props – except for one letter, and a pistol with which Emilia will eventually kill herself – further accentuates this radical minimalism, but it also accentuates what there is – the body is at the centre. Thalheimer's motto during rehearsals was "centerstage downstage" – there is no fourth wall, as in the realistic convention. Just like in a fashion show, this is manifestly a show – the actors face the audience, see it, and expose themselves. Yet once again, the permanent order dictated by the law is revered. Any violation of the movement along the "runway" or the frontal dialogue is intensely perceived. The geometric stage creates a "law", a language with clear-cut physical conditions, which greatly hinder the scenes' interpretation and their direction. But as Thalheimer makes clear, it is this very fraction between complete order and the human body and mise-en-scene which forces him and his actors into creativity.
Moreover, Thalheimer's mise-en-scene consists of a language of repeated gestures, and his direction may be viewed as an orchestration and composition of "notes". An arm stretched forward, yearning for touch, is a gesture repeated by different characters, gaining significance as the work progresses. While the realism of Ibsen or Chekov concentrated its gradually accumulated meanings around a symbol (the wild duck, the seagull), here it is a dance-like gesture. This is not only a difference of quality – replacing the image (semiotic representation) with the body (a live bodily gesture) – these gestures also become the framework for the entire work, dictated by the strict physical environment of the stage.
The music, too, obeys unmistakable regularity. A single motif is being repeated throughout the work: "Yumeji's Theme" by Shigeru Umebayashi, from Wong Kar-wai's In the Mood for Love. The music expresses the tension in the play between law and passion: it is constructed of endless repetitions of a triple-timed dance, but in slight variations, and with abrupt and significant stops. On this repetitive background, the freedom of the violin solo makes it almost sounds improvised. Against the geometric regularity governing all aspects of the show, and even the actors' bodies, the physical-singular-particular love and passion of the unprogrammable gap is being thrust upon the audience. Derrida's Différance, if you like, or Lakan's Real.
This geometric stage design, which imposes a particular organisation and order, is typical to Thalheimer's works. In his Oresteia, a flat wall blocks the stage. The only furniture are two narrow platforms, placed one on top of the other. The actors are drenched in blood, which is being splashed onto the wall as they move about – the play is thus "painted" on this "canvas", which bears a silent testimony to the play's violence.
In Die Ratten, the space consists of a very thick wall and ceiling, about a metre and a half apart, so that the actors must remain bent.
Even when staging a play as realistic as Ibsen's The Wild Duck, Thalheimer uses a revolving stage, made of a cylinder cut in diagonal.
The Thermodynamic Shift: Dimiter Gotscheff
In his essay, "Turner Translates Carnot", Michel Serres establishes an analogy between two major shifts in the 19th century: one in art history, the other in physics. In art history, we see a transition from the aesthetics of the Age of Enlightenment, when painting centred on solid geometric shapes and geometric compositions, to the aesthetics of Romanticism, aiming to capture fluids and gases, as in the works of Wiliam Turner: clouds, the steam of trains, the smoke of a fire, the flow of water. In Physics, there is a transition from the straight, round, hyperbolic and parabolic trajectories and solid objects of Newton's theory, to the research of liquids and gases in thermodynamics. This is an extreme transition from researching regular phenomena to researching random, irregular phenomena.2

In Dimiter Gotscheff's plays, this thermodynamic shift reaches a performative realisation. In his remarkable version for Chekov's Ivanov from 2005, staged in the Volksbühne theatre and also invited to the Theatertreffen festival, there is no "set", so to speak. At the beginning of the play, Ivanov himself turns on a fog machine, and the fog gradually fills the bare stage (designed by Katrin Brack). The actors become submerged in this fog and get lost inside it, so that they must emerge towards the audience to see and be seen.
Whereas painting strives to represent flow and randomness, here they materialise in front of the audience, with the crucial element of time. The fog becomes increasingly hard to control; its operator, who sits in the first row, does his best, but the cloud naturally reaches the first rows, uniting the audience with the play. The dimension of visibility here stands in contrast to Thalheimer's works. Whereas the actors of Thalheimer's play are fully seen and exposed the minute they set their foot on the stage, here the very concept of theatre as a "place for seeing" (according to its Greek etymology) is challenged – as the very ability to see is being questioned.
Moreover, the very perception of man in the world is necessarily different, with the challenge to the body's limits and to the categorical distinction between body and material. The actors, who are supposed to "have the stage to themselves", are in fact subject to the fog's arbitrary movement, and in each performance must improvise so as to find a spot where they can be seen. They are like large bodies in Brownian motion3 inside a gas. They have free will – yet it is limited by the arbitrariness of the fog. Once again, the identity of the object of seeing is unclear, as the cloud itself takes up so much space that it is hard to describe it apart from the actors' bodies, or define the "limits" of movement in the play. Like in Thalheimer, it becomes itself the body of the play, together with the actors. In other words, the play demonstrates the interactive relationship between man and the world – not a man in the world, but a man and a world in an endless feedback loop – as well as the crucial indeterministic element of the improvisation in that common existence.
This same sort of language may be found in some other of Gottshaff's works, which were also created in collaboration with designer Katrin Brack. In his Ubu Roi, the stage is filled with a huge collection of balloons in various sizes. Fans move the balloons a little, but the actors must constantly push them away if they wish to have eye contact with the audience. In Tartuffe a constant rain of colourful confetti descends on the stage, while in Das große Fressen (La Grande Bouffe) it is foam. Katrin Brack has designed similar stages for other directors, too: heavy rain for Armin Petras's The Prince of Homburg or constant snow for the entire four hours of Luk Perceval's Molière.
Chaos: Frank Castorf
I will finish my presentation of the paradigms of order with one final example, representing a contemporary aspect in the debate between order and disorder: chaos theory, which aims to find order in phenomena that seem purely random and irregular, such as stock price fluctuations. This is a local order, manifested in regular repetition in varying scales. This is how fractals are created, for instance. The Koch snowflake is constructed from recursive iterations of a triangle: the triangle's edge is divided in three, and the triangle constructed on its middle segment is therefore smaller by one third.
It turns out nature is brimming with fractals: the shorelines of continents and islands, the structure of a cauliflower and our blood circulatory system are but few examples. In painting, we can see such recursive and gradually diminished regularity in Caspar David Friedrich's trees: the trunk splits into main branches, which divide into secondary branches, which split into small branches, and so on.
Frank Castorf is the well-known director of Berlin's Volksbühne theatre. For the 2002 production of Dostoevsky's The Idiot, he and set designer Bert Neumann radically transformed the entire space of the theatre. A 'Neustadt' (new city) was built over the stalls, a reference to the Modernist architectural utopian views of Berlin. A commercial area, including an active cinema, a hairdresser (with running water), and a travel agency replaced the staircase. Three apartment buildings, each of them three- or four-story-high, were erected around the stage, and the audience watched the play from a three-story "hotel" constructed on a revolving stage, which allowed a view of different sections of the city as required by the play. The separation between commercial and residential areas, as well as the geometric outline, echoes modern functionalistic perceptions of the city: the city as a machine, as in Le Corbusier's vision.

But all over this city, this vision is violated by signs: green neon Chinese letters at the entrance; "Romantic World Hotel" inscribed in fluorescent purple above the spectators' "hotel"; and a huge "Las Vegas" sign above a bar – perhaps referring to the origin of it all, the emblem of the post-modern city as described in the 1968 book, Learning from Las Vegas. Its writers, Robert Venturi, Denise Scott Brown and Steven Izenour, had tried to examine existing reality, instead of forcing theoretical models upon it, as in the new cities envisioned by modern utopias. Some of their book's radicality lies in the authors' decision to turn their gaze to a reality considered ugly and dull: the confused mixture of the city's signs. Ugliness and dullness are considered characteristics of disorder, whereas order or an internal regularity are an expression of wisdom and delight; yet altering this perception can allow the discovery of a fascinating phenomenon.
The signs are a result of the need for immediate communication. This leads to another phenomenon: ornamentation, which is considered an absolute taboo in Modernism. Adolf Loos, in his Ornament and Crime, defines it as spiritual pollution. I would like to propose a mathematical basis for the rejection of ornamentation and signs: according to Loos, Modernism sanctifies the three dimensions of space. Ornamentation focuses on the bidimensional surface (the decoration of a shoe, in the example given by Loos), the decorations of a carpet or simply a bidimensional sign. Ornamentation and signs are rich in details, but only on the surface. Why? Loos explains it by an urge – to him, a loathsome, primitive urge – to decorate as a form of communication. Learning from Las Vegas confirms this urge and sets it free, but the pre-imposed order strikes back at it, and the result is a superposition of the two powers, a battle between bidimensional ornamentation and signage and the modernist geometric elements of the three-dimensional city. In this sense, the dimension of the city is somewhere between two and three (2D and 3D) – like the fractured dimension of a fractal.
The fractal is present in this work in an additional sense. Castorf incorporates live video shootings, which are screened to the audience, as he does in many of his works. The question of visibility is being addressed from a different angle: the actors/protagonists withdraw to their rooms, behind closed curtains, shutters, doors and windows. Yet the cameras keep following them: video surveillance installed in the rooms, as well as camera crews moving around the stage. The entire set seems like a giant television or cinema set, with the content immediately broadcasted to the multiple televisions and screens all around: a huge screen above the city's cinema, television sets inside the apartments, television sets in the "hotel" for the spectators. Not only that the three-dimensional body is repetitiously screened in its bidimensional representation, it is screened in varying scales: from enormous screens to small television sets. The entire space is a fractal.
1 Leonid Zhmud. The Origin of the History of Science in Classical Antiquity. (Berlin: Walter de Gruyter, 2006).
2 Michel Serres, “Turner Translates Carnot,” in: Hermes: Literature, Science, Philosophy, Josué V. Harrari and David F. Bell, trs. (Baltimore: John Hopkins University Press, 1982), pp. 54-62.
3 British botanist Robert Brown examined the jittery motion of pollen immersed in water through a microscope in 1827, and was the first to prove that it must have a physical (and not a biological) explanation (until then, their random motion was explained as a result of the pollen's life force). Albert Einstein provided the physical model for this phenomenon in 1905, predicting the exact motion pattern of atoms in his article about Brownian motion.