NONLINEAR CHOREOGRAPHY

The distinction between improvisation, non-linear choreography and traditional choreography is often misleadingly discussed at a phenomenological level. Misleadingly because the question cannot be solved by approaching dance as a "phenomenon", that is in terms of its physical nature. The phenomenon 'Dance' is in fact inextricably interconnected with a vast number of other phenomena such as the body, human perception, cultural reference, language, etc; to name a few. Moreover, if it wasn't for the difficulty of coming to an agreement on any of these issues, we would be overcome by the difficulty of defining a clear, common context in which to protract phenomenological analysis. As we do not know, and cannot know, the ultimate nature of reality, we are forced to make subjective assumptions and choose which factors are relevant/important for us. In a sense, the discussion becomes more of an interesting, and certainly inspiring, mental exercise than anything else.
After all, on a phenomenological level there is no such thing as a linear process (1); even traditional choreographies possess aspects of non-linear systems and consequently endless ranges of permutations. To be clearer, let's consider these points: suppose that we choreograph a few dance steps precisely, in sequential order, and teach them to ten different dancers. We can be certain, without call for scientific analysis, that the so created dance sequence will never look, or better, be exactly the same when performed by each different dancer. This is common sense: phenomenologically the dance sequence exists only in relation to a physical body. Consequently its informational content cannot be manifested materially without a 'carrier medium', therefore by changing the carrier medium we are bound to change its physical essence, as phenomenologically the choreographic informational content is entangled or loaded with additional information represented by the body expressing it.
Not only this - and here please allow me some further rhetoric for the sake of clarity: as, in the above example, we refer to the human body then we have to consider that the word "human" is laden with a whole lot of further complications. For instance, if rather than ten different dancers, we have the same dancer to perform the same dance sequence repeatedly over time, we can confidently speculate that we will not observe exactly the same phenomenon twice. Tiny variations in detail; spacing, timing, dynamics, intentions, etc. will occur. We can decide to overlook these changes but still they exist. This can hardly be disputed, therefore we can return to the previous hypothesis: even a linear sequence of steps possesses an endless range of permutations and dance can only phenomenologically exist as 'perpetual novelty'.
This view of traditional, linear choreography manifests strong similarities to widely accepted views of improvisation and non-linear choreography. So why do we bother to use three distinct terms to define three processes that phenomenologically are, after all, not that different? Furthermore: do we really want to indulge in an ocean of considerations of similarity?
No. Given these considerations, it becomes clear that this distinction acquires meaning only when approached on an aesthetic level, where our subjectivity can rightfully go in search of patterns and differences without being ridiculed by the complexity of physical reality.
Aesthetics (2), being connected to perception on a more subjective level, is very much an art of definition in itself, based on decisions we make concerning which elements are or are not relevant. After all our sensorial perception of reality works in a similar way: we perceive forms and backgrounds, details or general patterns, isolated elements or relations; and we do so subjectively.
In the case of choreography we can make distinctions by focusing on the 'gestalt', rather than its 'micro-elements'. These patterns described in time and space can be considered independently as self-similar, without consideration for the endless tiny variations that arise from the phenomena of being. The aesthetic of choreographic structures focuses on this gestalt and it is only in this context that the distinction between open/closed choreographic systems makes sense.

Having clarified this important point, we can now move forward trying to identify those distinctions.
Let's start from traditional choreography, of which we have already mentioned something about its nature. We said that traditional choreography is intended as a linear sequence of movements (3) unfolding in time and space. Therefore choreography is, in a way, identifiable with a predictable chain of events: given a certain movement we can determine the previous and following one, and so on in a precise sequence of causes and effects. In the same way other general elements of choreography are "pre-carved" in the representation, making it equally possible to predict the overall flow of such elements. To be more precise, the dancer is not only able to predict the flow but strictly bound to it in a similar chain of causalities. The choreography in this way acquires the qualities of a crystal where every single atom is tightly held in place and resistant to external influences, therefore belonging to what could be defined as a closed system.

Improvisation, on the other hand, is like the weather. Certainly there are laws governing the weather, yet we are still baffled as to what these might be, and whether to discover them would make much of a difference. Certainly we can make probabilistic predictions, but the truth is that we can never be sure of what the atmospheric conditions will be at any given time in any given place. Furthermore, we all know as performers do, that improvisation imitates the weather in other ways too: some days it is good, some days it is bad. One of the aesthetic purposes of improvised performance, after all, is the quest for unpredictability, even if improvised sessions are often structured, that is some choreographic elements are pre-established (for instance, it is common to establish relations in a group improvisation).
With improvised performance then, the main contrast to traditional choreography remains in the fact that its information content is never pre-determined, being created instead in 'real-time' during the unfolding of the performance. The pre-established structure therefore acts by channelling the (sub)conscious responses of the performers, who respond in turn to the unfolding of events and attempt to relate back to those same unfolding events according to a general pattern represented by this structure. I can see that this is in a way another chain of causes and effects as traditional choreography is. The difference being that the performers themselves cannot possibly anticipate the "improvised relations" and are forced to devise personal strategies at each moment. This observation however is slowly bringing us back to the phenomenological problem from which I am trying to abstain. Instead, it is important to stress that the most fundamental distinction between traditional choreography and improvisation is the way in which the "represented" information (the time-space bodily pattern) is generated. In fact we might as well steal the "elemental structure" of a traditional choreography and improvise the movements within it, with a good dose of subjective interpretations in so doing (4). Here another important point emerges: in improvisation the performer's subjectivity is fundamental, in traditional choreography it is not, at least not in terms of general choreographic patterns (5). In the first the leading figure is the dancer in the latter the choreographer.

In some aspects, non-linear choreography occupies a space between traditional choreography and improvisation but is much more than simply a mix of the two. Metaphorically we could picture it as a flowing river. We might follow its course, we might reshape its shores, we might even redirect its flow by digging for it a new bed, but we will never be in complete control of its own dynamics: its currents, its speed, its tides, or even flooding. Obviously through observation and experience we can build a general idea of these dynamics and devise structures able to channel them in one direction rather than another, without ever gaining complete control of them.
In non-linear choreography we proceed in a similar way, we create dynamic flows and tweak some parameters in order to achieve the emergence of specific choreographic features.
Metaphors are useful to give a sense of the process, yet they don't say much about the process itself. To give a better insight into what we mean by non-linear choreography, let's approach the task semantically, explaining why we use the words 'non-linear' and 'choreography'.

The term non-linear is used in a variety of different fields, from mathematics, physics, chemistry, and biology, to engineering, economics, and medicine; but it has also made its way into practically any aspect of our culture. A quick web search will probably bring you to sites ranging from philosophy, history, literature and poetry to music composition, visual arts and, now, choreography! Each time the term seems to carry a slightly different meaning, but, on the contrary, it has brought together what have been for centuries, totally disconnected subjects (6). At closer inspection it becomes in fact clear that the presence of a common 'leit-motiv', identifiable with certain qualities, such as a "structured openness" in its dynamics or the fact that the whole is always more than the sum of its parts. To go into lengthy scientific explanations about non-linear processes would be non-sense from me, especially when I am trying to avoid falling into the phenomenological trap, and particularly because I am not qualify to do so (7). Better to make clear that my observations are purely artistic, even when referring to scientific issues. I will rather limit myself to giving a few examples of how 'non-linear' is described in different fields, trying to give a sense of similarities and differences.
In algebra the term is applied to systems or components for which the output for the sum of two input signals, A and B, is not the sum of what would be obtained if the two inputs were processed separately: f(A + B) [not equal to] f(A) + f(B), where f represents the effect of the system or component. The effects of the component on a complex signal (for example, an amplifier on a voice recording) cannot be predicted by breaking the signal up into simpler signals (the individual frequencies making up the voice) and looking at the effect of the system on those separately. Or like systems with a threshold below which output is = 0 and above which output = 1. Furthermore, while we can enumerate the linear objects, non-linear ones are non-denumerable (8).
In chemistry the term refers to reactions that never settle in a state of equilibrium or that produce runaway effects. An example is auto-catalysis. Catalysts initiate or increase the rate of a chemical reaction without being consumed in the process. In auto-catalysis the catalyst is one of the products of the reaction, resulting in an increase in the rate of further reactions. Another example could be when the result of a reaction it is not a self-catalyst but rather a catalyst for a different chemical process whose reaction could in turn create a new type of catalyst for yet another type of reaction, and so on.
In physics non-linear is normally used to refer to open, non-equilibrium dynamic systems. These adjectives describe systems that continuously evolve in time and whose behaviour is dictated by a range of interacting variables, making therefore long term predictions virtually impossible.
And here allow me to stop my non-linear quest, in order not to make it unnecessarily complicated. Let me just point out that, during the last few decades, non-linear physics has brought about the emergence of Chaos theories and Complexity Science. The latter being the major source of inspiration, on a practical and theoretical level, for the current developments of non-linear choreography, which my colleagues (Michael Klien & Nicholas Mortimore) and I are still in the process of exploring and defining. (9)

Having outlined the basic points of non-linearity, let's move on to choreography. Why choreography? Earlier I have described these systems as virtually unpredictable in the long term, doesn't this express a contradiction in terms; doesn't this bring us to improvisation rather than choreography? It does not. Paradoxically, it is the very nature of these systems that brings us to choreography. Complex systems normally require the presence of building blocks or a network of agents acting in parallel. In this case, we use precisely choreographed dance sequences - that we define 'primitives' - as bricks from which to build emerging dynamics. These will be subsequently manipulated according to a series of pre-determined procedures, while the dancers act as interacting agents in the so created virtual choreographic environment (10).
Aesthetically this is a very important similarity with traditional choreography, in the sense that we can retain a complete control of dance style and technique, giving to the choreographer an important role during the creative phase. Furthermore the role of the choreographer goes well beyond the simple creation of steps. He is also responsible for channelling the dynamics in the desired direction through the construction of appropriate models of the show. Modelling and mapping procedures are at the core of non-linear compositional practises; that is, in my opinion, the truly innovative challenge of such a choreographic approach, a qualitative leap in the conception of arranging bodily information in time and space.
We could now ask: if starting with a precisely set information content, how much unpredictability remains, moreover what is the common ground shared with improvisation? First of all it all depends on what we mean by 'precisely'. While the choreographic building blocks are set, the nature of the work as a whole remains 'open'. It is also true that even if procedures or models regulate the interactive dynamics, they remain unspecified in the details, bringing about in real terms an endless range of possible permutations. These possible configurations will be dependent on factual circumstances and decision making by the dancers, bringing during the actualisation of a performance, an emphasis on the acting subject as in improvisation. Furthermore, the dancers are constantly rearranging and revising their building blocks during the unfolding of events, a process involving subjective interpretations and responses. Yet, while it is true that the emphasis swings from the choreographer, during creation, to the dancers during execution, it is also true that the presence of the choreographer remains on all levels, almost built into the structure regulating the dynamic processes (11). The dancers are immersed in a pre-ordered reality, with its own laws and chains of causalities, where still there remains room for the expression of a "free will". This implies a decentralisation of the 'locus of control' that, in my opinion, is one of the most important characteristics of non-linear choreography.
In traditional choreography the choreographer structurally retains a total control and responsibility over what will be performed on stage by the dancers; even in those cases where the process of creation is partially developed in collaboration with the dancers or through improvisation sessions, the choreographer still retains - at least as potential, as an implicit possibility to be acted upon - the opportunity of exerting univocal decisions upon every aspect of the final product.
In improvisation this 'locus of control' is less easy to pinpoint. At an initial, intuitive level we could be led to believe that control is as dispersed as in non-linear choreography, if not more so. Yet, with closer observation, this intuition is proven wrong: the individual bringing life to the dance is also the one bearing the full responsability of it. Even in the case of a group session, where the performers may react to each other and where a basic structure has been laid down, the defining nature of the improvised material relies solely on "I". The control is not dispersed as a whole; it is rather splintered into self-regulating cells, into independent wills. When creating open choreographic systems, these independent wills are truly bridged together as the manifestation of a single dynamic channelled by the will of the choreographer. They are immersed in a fluid context, which acts as the 'carrier medium' for their decisions.
These differences are fully manifested, both aesthetically and poetically, when looking at what is left behind; what are the traces left in history?
Traditionally what remains is a rigidly defined entity, an artwork in the way that we are used to thinking about a sculpture or a painting. Something for the posterity to re-build putting together piece after piece, as it used to be. We leave behind a precise chain of events that we can record making, even less transient, its memory. Contrarily, improvisation is ephemeral; it disappears when the bodies leave the space. There are only traces left in our personal, individual memories, impressions that were purposefully exclusive to a specific moment. Such works cannot be re-staged without transforming them into something else. In non-linear choreography we have a map of dynamics, precise choreographic landscapes wherein the dancers can freely move. Its topography and basic informational content can be formally encoded, yet we can only predict its general flow, never its combination in detail. We are left with de-crystallised order.

NOTES

(1) Linearity is a rather special mathematical abstraction to which we have become familiar through years of Euclidean geometry and algebra taught at school. In the real world there is no such thing as a truly linear system, therefore all linear models are exclusively simplified approximations.

(2) By Aesthetics I mean the study of structures, patterns and elements belonging to certain specific phenomena and of how they relate to human perception and cultural references. In this approach the relevance resides not so much in the physical nature of this phenomena as on the 'symbolic referents' and 'emerging features' that subjective human perception and interpretation discover in them. Consequently, this is also related to concepts such as 'proportions', 'beauty' and 'style'; but in my opinion those are in a way derived issues rather than the core of aesthetics.

(3) With 'movement' I consciously make a rough generalisation which includes various elements that comprise choreography such as: actions, positions, timing, spacing, dynamics, relations, intentions, etc. Everybody has a different list of "meaningful" elements, but in this context this is a matter to overlook.

(4) To push the instance to an extreme level: we could decide to improvise within the structure of a classic such as Petipa's "La Bayadère". In this extravaganza we could keep most of the elements of the original ballet, not only choreographic but also scenic (costumes, plot, dramaturgy, etc), and give freedom to the dancers to improvise the steps as the story unfolds… actually one day we might give it a try.

(5) Of course, even in traditional choreography the performing subject is relevant in relation to other contexts, for example in relation to the public, to personal interpretation, etc, but as said this does not enter in the pursued line of argument.

(6) The Santa Fe Institute is probably the best and most successful example, even if it focuses on a more specific aspect of non-linear dynamics: complexity. Complexity studies a class of behaviours in which the components of the system never reach a static equilibrium and never quite dissolve into turbulence, either

(7) There exists a huge library of excellent books dealing with the topic. In particular I recommend: Jack Cohen & Ian Stewart - The Collapse Of Chaos: discovering simplicity in a complex world - Penguin Books Ltd -

(8) Normally this non-denumerability is expressed as a 'phase space', that is the collection of possible states of a dynamic system (for instance, ideally the toss of a coin has two states: heads and tails; in reality the phase space would also describe all possible trajectories when flipping in the air).

(9) Some of you might still be wondering how more humanistic studies deal with non-linearity. Philosophy does so by putting aside the determinism and mechanistic conceptions that came into their own through DeCartes and the Positivists of the 17th Century. Non-linear philosophy examines reality as phenomena connected through a complex web of interactive dynamics. History shifts the focus from individual historical characters and specific facts to more general cultural-politic configurations and dynamics. The global acquires a predominant importance on the localised. Visual Arts' approach is somehow less easy to define. The most obvious examples are computer generated animations and graphics. In poetry there are several examples dating back more than a century and some of them presenting ties with the tradition of the 'free verse' but being distinct from it. Most of the time the descriptions arise from the method used for creating the verses, from random procedures and free associations, to morphing structures; Dada and Surrealists poets are well known for having used such techniques. I am of the opinion that G. Apollinaire's work is one of the best examples, also popular enough to find in any library. In literature non-linearity has been at times achieved by using 'hyper-text', allowing for multi-ordered readability through the unfolding of a story or a book.

(10) Probably for those among you familiar with the scientific quest of Artificial Intelligence (AI), this will sound like nothing new. Using similar methods, AI has been trying for decades to recreate intelligent behaviours and, more ambitiously, life, into the virtual word of digital computers. The quest has been so far unsuccessful but it remains an exciting prospective. I say this to make a light hearted comment about what in comparison seems to be an advantage of working with choreography: we already have intelligence and life integrated into our world. While AI uses strings of programs to simulate interacting agents, we can directly rely on one of the most complex adaptive forms in the universe: human beings. The human factor makes the process extremely difficult to control if not on very broad scales, but in a way this is the main point of complexity: the irrelevance of details, the highly dispersed control and the predominance of emergence.

(11) To use a gratuitous metaphor, therefore declassified to footnote: non-linear choreography is neither anarchic as improvisation nor dictatorial as traditional choreography; it is rather a regulated society of free individuals.

REFERENCES:

• Steve Grand, Creation: Life and how to make it, Weidenfeld & Nicolson, 2000.

• M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos, Penguin Books, 1994.

• Duane P. Schultz - Sydney E. Shultz, A Histrory of Modern Psychology, Harcourt Brace College Pubblishers, 1996.

• Valerie Preston-Dunlop, Dance Words, Harwood Academic Publishers, 1998.

• Roselee Goldeberg, Performance Art: From Futurism To The Present, Thames &Hudson, 2001.

• Clive Cazeaux, The Continental Aesthetics Reader, Routledge, 2000.

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Usual thanks to Nicholas Mortimore and Michael Klien for their vital contribution to this script and to Christoph Hoelscher for his precious feed-back and suggestions.