Part of my education was in mathematics, so it was only natural for me to apply some ideas from mathematics to dance and choreography. When I first became interested in complexity theory in the mid-nineties I could instantly see how it might apply to dance, although it took some time to work out my ideas.
The basic motivation is that a choreographer can only overlook a certain amount of complexity, which is why the spatial organization of most choreographed ballets is more or less the same. With more time it is possible to create more intricate patterns but even then spatial variability is limited by the fact that relations between dancers have to be communicated to the dancers.
Complexity theory has shown that a central governing agent is not necessary for the emergence of intricate patterns or cooperative behavior. However, simply transferring the rules that govern for instance the flocking of birds or traffic jams to dance doesn't work. These rules only apply under certain conditions. One would therefore have to develop rules specific to dance. I should emphasize that ANY choreography is governed by a set of IMPLICIT rules. By making those rules EXPLICIT their hidden potential in the form of alternative forms of organization can be revealed.
But what is complex? And what is a complex system? A complex system can be defined as a system in which many different components interact, whereby the properties of the individual components do not fully explain the properties of the system as a whole. A principal characteristic of complex systems is the coupling between component parts and system, or between individual and group.
There is an alternative definition of complexity: the (algorithmic) complexity of an object is defined as the length of the shortest program (or description) which generates the object. For example: 0000000000 and 0101010101. The first sequence can be succintly described as a sequence of ten zeroes while the second can be described as five alternating 0's and 1's. Now take a look at the following sequence: 0010111101100. The shortest possible description of this sequence is the sequence itself. This last sequence can therefore be called the most complex.
If we apply this to movements it follows that constantly moving every conceivable part of the body may at first look complex, but is in fact quite simple: the task move every part of the body will produce a series of sequences that all look more or less the same.
But why does complexity matter? This is where my interest in complex systems, self-organization and neuroaesthetics come together. In general it has been argued and demonstrated that people tend to find novel and/or complex objects, scenes and so on interesting, as long as it is not too complex or totally novel.
The more complex a system becomes, the more information is needed to describe it, in terms of a choreography: the more instructions one has to give to the dancers. With more time it is certainly possible to create more complex works, but even then there are limits as to what can be tried out. Although history provides a starting point each individual will first have to arrive at the complexity of previous works before being able to transcend it.
The literature on complex systems offers a different paradigm for bringing about complexity. This is what I have termed Emergent Choreography
The collective motion of birds, fish and bacteria, the movements of large crowds of people, traffic jams, etc. can be modelled using models consisting of a number of individual agents with some simple rules guiding their individual behavior and their interactions with other agents.
Instead of applying complexity theory to dance, one would have to design a complexity theory of dance. Models of crowding or flocking reduce multi organ organisms to dots on a screen. Under some conditions this modelling approach may apply to groups of humans, but in dance dancers will instantly be at a loss as to what to do. The rules are underspecified (HOW to walk, move etc.).
My own approach has been to extract rules from the interaction of dancers and to then re-apply those rules to the dance and to see where a conflict or a "decision void" arises.
Hagendoorn, I.G. (2002), Emergent patterns in dance improvisation and choreography. In: Minai, A.A. and Bar-Yam, Y. [Eds.]. Unifying Themes in Complex Systems Vol. IV. Proceedings of the Fourth International Conference on Complex Systems, 183-195.
Hagendoorn, I.G. (2004), De wereld als wiskundig netwerk. De Academische Boekengids (in Dutch).
Gell-Mann, M. (2002). Plectics: The study of simplicity and complexity. Europhysics News Vol. 33 No. 1.
Barabási, A.-L. (2009). Scale-Free Networks: A Decade and Beyond. Science 325, 412-413.
Barabási, A.-L. and Bonabeau, E. (2003). Scale-free networks. Scientific American 288, 60-69.
Strogatz, S. H. (2001). Exploring complex networks. Nature 410: 268-276.
Mitchell, M. (2009). Complexity. A Guided Tour. Oxford: Oxford University Press.
Strogatz, S. (2003). Sync. The Emerging Science of Spontaneous Order. London: Penguin.
Holland, J. (1996). Hidden Order. How Adaptation Builds Complexity. Reading, MA: Helix Books.
Barabasi, A.-L. (2002). Linked. The New Science of Networks. Cambridge, MA: Perseus Publishing.
Communications from the Lab. The labyrinth scene is based on a limited set of movements and some simple rules.
An excerpt from Koyaanisqatsi.