Complexity science studies systems which has a population of interacting entities. Theories in complexity complement classical mechanistic perceptions with the aim of explaining the broader phenomenon of a system or systems. Following the reductionist approach of René Descartes that the complexity of the world can be understood by reducing them to the interaction of parts or simpler things, the notion given by Sir Isaac Newton that “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things” and the idea of a ‘clockwork universe’ has influenced past scientific thinking. It was understood that once you have analysed phenomenon in their simplest components “their evolution will turn out to be perfectly regular, reversible and predictable, while the knowledge you gained will merely be a reflection of that pre-existing order”. As scientific explorations expanded into the study of living organisms and populations in different order however, the mechanistic conception has reached a limit in its ability to yield new knowledge, as far as complex systems are concerned.
“Complex” describes a system as consisting of many different and connected parts; it is a network, a group or a system of different entities that are linked in a close or complicated way – according to Oxford Dictionaries. Complex adaptive systems are present in every levels of the hierarchy of life – at the molecular level to individual organisms and metapopulation, and from community to the global environment. The intricate relationships at the micro level and the emergent behaviour found at the meso and the macro levels cannot be understood by analysing the microstates alone, for “the whole is more than the sum of its parts” (Aristotle, Metaphysica 10f-1045a). Complex systems require both a holistic and a reductionist approach in the epistemology; the latter is needed at least in the modelling of it, in order to understand the phenomena that are manifested in various levels of organisation. Although the variation of complex systems is vast, they share common characteristics such as emergence and self-organisation (De Wolf, 2005) that resulted from the interaction of simple rules. Complex systems are found at ‘the edge of chaos’ (Lewin, 1993), they exist between order and disorder, they are predictable and at times unpredictable; miniscule changes in initial conditions produces massive stochastic revolutions at spatial and temporal scales. These features may give us a ‘handle’ from which we can grasp illusive behaviour at the systemic level for creating models and for understanding phenomenon. How local communication between agents gives rise to collective behaviour is an important study area. At present however, the inner workings of many complex systems are yet unknown. Otherwise, issues related to epidemics, medical treatment, society, the economy, ecology, and etc. would have been resolved. Agent-based modelling and simulation can provide a platform from which phenomenon can be understood within our lifetime, at a flexible spatial and temporal magnitude, at liberty from ethical and environmental constraints, and free from noise. We must not forget that a model is a model, however, new information can be acquired and conclusions can be made from hypothesis generation and testing. The foundation of understanding complex systems requires computer modelling, for we are dealing with non-linear interactions within a population of entities. These interactions are mainly information and energy communications. They are difficult to model and predict with state-variable techniques (difference and differential equations) as changes occur at different levels and at certain resolutions.
Modelling complex systems necessarily implies that we are interested in determining the properties, functions, and principles associated with an individual entity, and how that entity interacts and communicates information with other entities and its environment. We must not however, observe behaviours at a local level only. The collective behaviour at multiple levels (micro-meso-macro) will need to be analysed. This is what is meant by the need for both a holistic and a reductionist approach. Such a modelling procedure reflects how complex systems in nature work, it is bottom-up (Resnick, 1994). This can be contrasted with ‘top-down approaches’ where models are governed by a central system which plans, arranges, and tunes patterns (See Ch’ng, 2009 for a survey of traditional statistical and predictive modelling methods).
My collection of articles and books which I thought was helpful in the Complexity concepts:
Bedau, M A. (2003). Artificial Life: Organization, adaptation and complexity from the bottom up. Trends in Cognitive Sciences, 7(11), 505–512.
Bedau, M. a. (1997). Emergent models of supple dynamics in life and mind. Brain and cognition, 34(1), 5–27. doi:10.1006/brcg.1997.0904
Bedau, Mark A. (n.d.). Weak Emergence. Philosophical Perspectives, 11, 375–399. Retrieved from http://philpapers.org/rec/BEDWE
Bertelle, C., Duchamp, G. H. E., & Kadri-Dahmani, H. (2009). Complex Systems and Self-Organization Modelling. Berlin, Heidelberg: Springer-Verlag.
Byrne, D. (1998). Complexity and the social sciences. London: Routledge.
Camazine, S., Deneubourg, J. L., Franks, N. R., Sneyd, J., Theraulaz, G., & Bonabeau, E. (2001). Self-Organization in Biological Systems. Princeton, NJ.: Princeton University Press.
Cornings, P. A. (2002). The Re-Emergence of “Emergence”: A Venerable Concept in Search of a Theory. Complexity, 7(6), 18–30.
De Wolf, T., & Holvoet, T. (2005). Emergence Versus Self-Organisation: Different Concepts but Promising When Combined. LNCS, 3464(2005), 1–15.
Gajardo, A., Moreira, A., & Goles, E. (2002). Complexity of Langton’s ant. Discrete Applied Mathematics, 117(1-3), 41–50.
Goldstein, J. (1999). Emergence as a Construct: History and Issues. 1, 1, 49–72.
Halley, J. D., & Winkler, D. A. (2008). Classification of emergence and its relation to self-organization. Complex., 13(5), 10–15. doi:10.1002/cplx.v13:5
Holland, J H. (1995). Hidden Order: How adaptation builds complexity. Reading, MA: Helix Books, Addison-Wesley Publishing.
Holland, J. (1998). Emergence: From Chaos to Order. Redwood City, California: Addison-Wesley.
Holland, John H. (2006). Studying complex adaptive systems. Journal of Systems Science and Complexity, 19(1), 1–8.
Holland, John H. (2012). Signals and Boundaries: Building Blocks for Complex Adaptive Systems. MIT Press.
Johnson, S. (2002). Emergence: The Connected Lives of Ants, Brains, Cities, and Software. Sribner.
Kauffman, S. A. (1993). The Origins of Order: Self-Organization and Selection in Evolution. Oxford: Oxford University Press.
Kauffman, S. A. (1996). At Home in the Universe: The search for laws of self-organisation and complexity. Harmondsworth: Penguin.
Lewin, R. (1993). Complexity: Life on the Edge of Chaos. London: Phoenix.
Mainzer, K. (1994). Thinking in Complexity: The complex dynamics of matter, mind, and mankind. Berlin: Springer-Verlag.
McLaughlin, B. P. (1992). The Rise and Fall of British Emergentism. Emergence or Reduction?: Essays on the Prospects of Nonreductive Physicalism. Berlin: Walter de Gruyter.
Mihata, K. (1997). The Persistence of “Emergence”. In A. E. Raymond Horsfall, S., Lee., M.E. (Ed.), Chaos, Complexity & Sociology: Myths, Models & Theories (pp. 30–38). California: Sage: Thousand Oaks.
Miller, J. H., & Page, S. E. (2007). Complex Adaptive Systems: An Introduction to Computational Models of Social Life (Princeton Studies in Complexity). Princeton: NJ: Princeton University Press.
Mingers, J. (1995). Self-Producing Systems: Implications and Applications of Autopoiesis. New York and London: Plenum Press.
Mitchell, M. (2009). Complexity: A Guided Tour. New York: NY: Oxford University Press.
Page, S. E. (2010). Diversity and complexity. Princeton University Press.
Pagels, H. R. (1988). The dreams of reason: The computer and the rise of the sciences of complexity. Simon and Schuster New York.
Resnick Silverman, B., M. (1996). The Facts of Life. MIT Media Laboratory. Retrieved from http://llk.media.mit.edu/projects/emergence/life-intro.html
Rietman, E. (1993). Creating Artificial Life: Self Organization. Blue Ridge Summit, PA: Windcrest Books/McGraw Hill.
Simon, H. A. (1962). The architecture of complexity. Proceedings of the American philosophical society, 106(6), 467–482.
Sipper, M. (1998). Fifty years of research on self-replication: an overview. Artificial Life, 4, 237–257.
Sole, R., & Goodwin, B. C. (2002). Signs of Life: How Complexity Pervades Biology. The Perseus Books Group.
Stacey, R. (1996). Complexity and Creativity in Organizations. San Francisco: Berrett-Koehler.
Von Neumann Burks, A.W., J. (1966). Theory of Self-Reproducing Automata. Urbana IL: University of Illinois Press.
Waldrop, M. (2008). Big data: wikiomics. Nature, 455(7209), 22.
Waldrop, M. M. (1993). Complexity: The Emerging Science at the Edge of Order and Chaos. London: Viking.
Weaver, W. (1948). Science and complexity. American scientist, 36(4), 536–544.
Weaver, W. (1949). Problems of organized complexity. American Scientist, 36, 143–156.
Wolfram, S. (1986). Theory and applications of cellular automata.