The Complexity of Complexity
There is a determination by many theorists to show that complexity is the new unifying interdisciplinarity – even bridging the science–society gap. But the case is not yet proven, and it may be that there are different types of complexities in different realms. As suggested above although computation can now produce lifelike simulations, perhaps complexity is usually associated with living things – bacteria, brains, languages.
In Figure 6, this complexity is but one column. There are three other terms – two of a lower order complexity, and a fourth which is of higher order (Table 1).
The divisions between the four columns are important. On the left in 'complication' we stay firmly within the domain of physics and chemistry, and the realm of reductionist explanation. The next column 'complification' is the world of artifice – the machines of mankind that obey the laws of physics and chemistry, but which have not been observed to occur spontaneously, and about which systems theory and operations research may have much to say. Although all these machines and buildings perform, in so far as they do, according to nonteleological explanation, their existence is understood in teleological and ecological terms – they are invented and built by man for man's own purposes. They are therefore split from the biological world by the 'purpose' divide. They have an exterior teleology. Mostly (to date) they have the property that they should not behave chaotically. Cars should not wobble erratically, nor should they behave differently according to their individual histories. For their operational success, fractal landscapes are replaced by smooth continuously curved roads.
The divisions between the inanimate world and the world of biology can be made on several grounds. The most immediate one is self reproduction perhaps one definition of life itself. Many people subscribe to the idea that sexual reproduction and genetic mixing is more complex than the dripping tap modeled by a theoretician of chaos. The next division is between the world of physical existence – world 1 – and the worlds of conscious and reflexive thought – worlds 2 (individual thought) and 3 (social epistemology). Note that the brain therefore simultaneously exists as an organ in world 1, and as thinking in world 2. The relationship between physical substance and the emergence of consciousness was highlighted above. Complexity theory is the product of the human brain, and is part of how we 'choose' to describe some phenomena. Its categorization of nature may or may not prove to be better than disciplinary ones currently on offer.
In sum, the interdisciplinary unity of complexity is debatable.
Systems which are perfectly organized (ordered) do not evolve, unless by outside intervention. Systems composed of individuals which exhibit purely random behavior, like molecules of gas in a cylinder, do not evolve, and are best described in terms of their aggregate properties. Poised between randomness and order are other systems. Of biological ones we can state, we the observers, think they have the following properties: They have a large number of elements, because when the number of elements rise, formal description of relations between elements cease to give an understanding of the whole; there are dynamic interactions among this large number of elements, and many of these interactions are nonlinear; there is feedback within the system; they have a history; and every element of the system is ignorant of the behavior of the whole. With regard to even more complex (complexification) reflexive social systems, none of the mappings between these conditions and the 'real world' is as yet unambiguous.
With reference to human geography, complexity has made an impact as a metaphor, the value of which Thrift (1999) has compared with actor network theory – where again there are many parts not fully aware of the way their behavior is mediated by the network. Harris (2007) has used insights drawn from complexity theory to grapple with the interface between society and planet in the quest for sustainable development. In more applied terms, agent based models are used to study system evolution, for example, with regard to cities by Allen (1997) and Batty (2007), and dynamics on networks, for example, with respect to traffic flows in cities by Transims (Los Alamos National Laboratory, USA). These models may provide us with lots of insights into how systems can behave, and how they might behave, but very little by way of predicting their exact behavior. The most certain prediction is that they will be unpredictable, because of sensitivity to initial conditions and bifurcation points.