Complexity Theory

'... the snowflake's delicate sixfold symmetry tells us that order can arise without the benefit of natural selection.'
(Kaufmann, 2000, p1)

Complex systems are all around us and have always been. Ecology, evolution and the physical universe can be described as complex systems. Complex systems can contain networks of smaller complex systems, for example the weather within the earth or Gaia system, or they can contain a network of noncomplex elements. The particular non-linear manner in which the elements or smaller complex systems are connected/ related within larger complex systems effects the characteristics of the larger complex system. That is, a complex system is not simply a given result of the parts that constitute it, but is as much a function of the manner in which the parts are connected. The manner of relationship between the parts, the transitions and web of connections are vital to defining the complex system. The relationships are a relatively balanced mixture of randomness and order. Kirshbaum (2002) defines a complex system quite neatly (Quote 39) and can be viewed very much like Deleuze and Guatari's (1987) rhizomes and/or assemblages. Although complex systems abound around us, this perspective of the world / universe as complex system is a very recently contemporary phenomenon (thinking in networks).
Heylighen (1988) notes that analysis of complexity should include how a complex system evolves. He starts with a very obvious supposition: during a defined time frame within a system, certain parts will remain unchanged while others change. The parts of a system which are resistant to change can be perceived as substructures, which may also be substructures for systems other than the one in consideration (see Mutation and Recombination in Rhizomes). Change that occurs within a system can be categorised as two types: mutation or recombination, (Quote 35). Mutation is more likely to affect the substructure and thus the evolution of a new stable substructure, which may form the basis for new systems being built upon old ones. As the substructure is a foundation for more than one system, and these systems are interactive and part of a bigger complex whole, there will likely be a feedback mechanism of selection for substructures, which enhance a greater proportion of the systems. Feedback of the developments within one complex system affecting that same system and 'greater' others which comprise it, constitute cyclic relationships (see also hypertext) of interconnection. Complex systems are not a set of random connections, but can usually be described with the connections following patterns of part order (e.g. hierarchy... or linear cause and effect) and part chaos (e.g. loops of intraconnection /feedback cycles). Complex systems intraconnectedness allows for self-organisation, which is a defining characteristic. Heylighen (?) defines self-organisation as: 'the spontaneous creation of a globally coherent pattern out of local interactions' (Quote 62).
Heylighen suggests that this change through time of system within a complex of systems, because of the feedback loops, can function to create self-organisation (see also Kauffman. 1996). Self-organisation is a key characteristic of complex systems (Kirshbaum, 1999, Lucas,1997f).

Emergence another key characteristic of complex systems is a function of this self-organisation. Heylighen (1988) shows that evolution of a system will usually lead to increased complexity. There will be selection for invariant stable substructures and as new ones arise from change over time these new substructures may form building blocks, which by recombination favour higher-order systems to emerge.
So complex systems tend to be nonstable evolving forms, which Kauffman (2000) suggests necessarily give rise to increasing diversity of increasing dimensionality. That is a complex system expands into the adjacent possible with concommittant liklihood of expansion of complexity.

Kaufmann (2000) in discussing complex systems, which are autonomous agents or living systems

(i.e. 'a physical system, such as a bacterium, that can act on its own behalf in an environment...All free living cells and organisms are clearly autonomous agents.... A molecular autonomous agent is a self-reproducing molecular system able to carry out one or more thermodynamic work cycles.' p8.),

suggests that hierarchies of relationships are common in complex systems of autonomous agents. And further, that these are not simple linear hierarchies, but rather become a complex web with not only 'higher' autonomous agents built from 'lower' autonomous agents, but that these' higher' agents also affect the functioning and proliferation of the 'lower' agents. This I could see applies to Rhizomes as it evolves becoming ever more complex in hierarchical layers that contained feedback loops and interconnecting networks between the layers (see Rhizomopoly). Kaufmann's work is seminal as he discusses how investigating the notion of autonomous agents as a complex systems has lead to the idea that complex systems proliferate into ever increasing diversity as 'the adjacent possible' variations of current systems are realised into expression by recombination, mutation and a process of emergence of new higher levels in the hierarchy by combining lower complex systems. He suggests that the universe is steadily increasing in diversity and dimensionality (ibid. p149) at a rate, which falls just short of the whole complex universe system becoming chaotic. That is, variation in living systems is expanding at a maximum rate just below the threshold of chaos.

It has become clear to me that Rhizomes necessarily had to develop from a base line of first principles (researched in Phases I & II). We could not create our current level of complexity in the system by mutating and recombining an existing Contemporary 'Performance' piece. Each step of evolving Rhizomes in Phase III has also been an involved process of mutating and recombining our previous 'work' until an aesthetic sense in Curson or I resonates. We are (still ?) evolving Rhizomes into a 'performance' piece by slowly stepping through a series (or rather expanding network /ripple) of adjacent possibles.

The properties of complex systems are a dynamic relationship between order and randomness, non-linearity, emergence, and self-organisation.

QUOTE 1, QUOTE 12, QUOTE 13, QUOTE 34
2.0 Home Page, 'Beginning', Conclusion, Acknowledgements, References, Rhizomes Performances, Performances as References