Abstract
Complexity is another key concept in understanding systems, but it is not an easy concept to define. There are many approaches to understanding complexity and we will review several representatives. However, we make a commitment to a definition that we feel is most compatible with the breadth of systems science, Herb Simon’s (The science of the artificial. The MIT Press, Cambridge, MA, 1996) concept of a decomposable hierarchy (as explained in Chap. 3). Systems that have many levels of organization are, generally speaking, more complex. This definition will come into play in later chapters, especially Chaps. 10 and 11 where we look at how complexity increases over time. Toward the end of the chapter, we examine some of the downside of higher complexity, especially as it affects modern civilization.
“I shall not today attempt further to define the kinds of material I understand to be embraced … [b]ut I know it when I see it …”
United States Supreme Court Justice Potter Stewart, 1964
“…complexity frequently takes the form of hierarchy and… hierarchic systems have some common properties independent of their specific content.”
Herbert A. Simon (1996. The science of the artificial, The MIT Press, Cambridge MA, p 184)
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Notes
- 1.
The subject of chaos theory will be explored in Chap. 6, Dynamics. We mention it here because of its triggering effect in kicking off the quest for understanding the nature of complexity .
- 2.
- 3.
Remember, for our way of thinking, this is actually a redundant phrase since we claim all systems, even so-called abstract ones, have physical embodiment in one form or another.
- 4.
This is the case for cellular automata (see http://en.wikipedia.org/wiki/Cellular_automaton). Wolframn (2002) suggests cellular automata rules may be the law of the universe . We will say more about cellular automata and variants in the realm of “artificial life ” later in the chapter.
- 5.
- 6.
Technically we would not be able to call this figure a “system. ” The blue dashed oval outline could represent a boundary , in which case this might be a potential system, as covered below.
- 7.
In elemental atoms the electrons distribute in shell-like orbitals around the nucleus. These shells are governed by quantum laws of energy. The outermost shell of any atom may contain fewer electrons than quantum laws allow and that is the basis for chemical interactions such as covalent or ionic bonding. See http://en.wikipedia.org/wiki/Electron_configuration.
- 8.
Or at least consider Moore (2003).
- 9.
It gets even worse if you consider the field of exobiology! This is the study of life not on this Earth. Biologists are now convinced that life is not a purely chance phenomenon on this one little planet, but a natural consequence of the properties of the planet. Recently astronomers have discovered many planets orbiting many different stars, including some coming very close to Earthlike properties such as distance from their star, mass, etc. The current thinking is that life will arise naturally on any Earthlike planet, but it might reflect very different variations based on random conditions. Ergo, biology becomes an even more complex subject. If we find life on Mars, it will get very interesting. See Chaps. 10 and 11 for more about life emerging from chemical bases.
- 10.
Margulis and Sagan (2000, chapter 5). Also see the Theory of Endosymbiosis: http://en.wikipedia.org/wiki/Endosymbiotic_theory. The creation of eukaryotic cells in this fashion is actually a reflection of the point made in the section above on the need to “reduce” complexity by introducing a coordination control system .
- 11.
See Taxonomic rank: http://en.wikipedia.org/wiki/Taxonomic_rank.
- 12.
Here a computing device is any combination of circuits that accomplish a computational function . For example, the central processing unit (CPU) is a computational device even though it is only useful when combined with other devices like memory and input/output devices to produce a working computer.
- 13.
Intermittent means they come and go. Sporadic implies they do not occur regularly. And episodic implies that when they occur, they last for a while and may have varying amplitudes of strength during an episode. What all of this implies is that many kinds of connections introduce a great deal of uncertainty into system structures.
- 14.
Actually these days we also are concerned with energy consumed by computation , not just how big or how fast the computer is!
- 15.
This isn’t really what NP stands for, but the explanation would require far more space than we can afford to take. And, unless you plan on going into theoretical computer science, you wouldn’t really appreciate it.
- 16.
Random number generators in computers are really pseudorandom number generators. That is, the sequence of numbers generated appears to be random with a uniform distribution. But in fact if you run the same program over and over, using the same “seed” value, you will get exactly the same sequence of pseudorandom numbers. Generating truly random numbers in computers requires special electronic circuits that produce white noise and that is used to generate random numbers. Even then there is some philosophical debate about what the meaning of this randomness really is; much more so than we care to get into here.
- 17.
See Wikipedia—Cellular Automaton, http://en.wikipedia.org/wiki/Cellular_automaton.
- 18.
Langton CG et al. (eds) (1992. Also see Wikipedia—Artificial Life, http://en.wikipedia.org/wiki/Artificial_life. Additionally, John Conway’s Game of Life, http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life.
- 19.
Mandelbrot (1982). Also see Fractals, http://en.wikipedia.org/wiki/Fractal.
- 20.
See Mandelbrot Set: http://en.wikipedia.org/wiki/Mandelbrot_set .
- 21.
See Chaos Theory: http://en.wikipedia.org/wiki/Chaos_theory.
- 22.
Weaver , W. (1948). “Science and complexity,” in American Scientist, 36: 536–544. Accessed online at: http://philoscience.unibe.ch/documents/uk/weaver1948.pdf, Jan. 2013.
- 23.
These kinds of events are called “black swans” by Nassim Nicholas Taleb. They are unexpected or of exceedingly low probability and so are not anticipated while the system is in development, i.e., no provision for resiliency is included in the structures and functions.
- 24.
Today, modern computer designs are moving toward more redundancy in components, at least at a high level of organization . Such redundancy, such as what are known as multiple core CPUs, allows a computer to continue working even if one component fails at that level. Of course the system then operates at a reduced level of performance because the component cannot, at the present state of technology, be repaired in situ.
- 25.
See descriptions of these civilizations and their histories in Joseph A. Tainter ’s The Collapse of Complex Societies, Cambridge University Press, 1988.
- 26.
Thomas Homer-Dixon, “The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization,” Island Press, 2006. Homer-Dixon was interested in not just collapse but also how such collapses freed up resources, especially human ingenuity, that then became the seeds for new civilizations.
Bibliography and Further Reading
Casti JL (1994) Complexification: explaining a paradoxical world through the science of surprise. Harper Collins, New York
Fuster JM (1995) Memory in the cerebral cortex. The MIT Press, Cambridge, MA
Gleick J (1987) Chaos: making a new science. Penguin, New York
Gribbin J (2004) Deep simplicity: bringing order out of chaos and complexity. Random House, New York
Langton CG et al (eds) (1992) Artificial life. Addison-Wesley Publishing Co., New York
Mandelbrot BB (1982) The fractal geometry of nature. W. H. Freeman and Co., New York
Margulis L, Sagan D (2000) What is life?. University of California Press, Los Angeles, CA
Mitchell M (2009) Complexity: a guided tour. Oxford University Press, New York
Moore J (2003) Chemistry for dummies. Wiley Publications, New York
Morowitz HJ (1992) Beginnings of cellular life: metabolism recapitulates biogenesis. Yale University Press, New Haven, CT
Nicolis G, Prigogine I (1989) Exploring complexity: an introduction. W.H. Freeman & Company, New York
Prigogine I, Stengers I (1984) Order out of chaos: man’s new dialogue with nature. Bantam Books, New York
Simon HA (1996) The science of the artificial. The MIT Press, Cambridge, MA
Striedter GF (2005) Principles of brain evolution. Sinauer Associates, Inc., Sunderland, MA
Tainter JA (1988) The collapse of complex societies. Cambridge University Press, Cambridge, MA
Weaver W (1948) Science and complexity. Am Sci 36:536–544. http://philoscience.unibe.ch/documents/uk/weaver1948.pdf. Accessed Jan 2013
Wolfram S (2002) A new kind of science. Wolfram Media Inc., Champaign, IL
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Mobus, G.E., Kalton, M.C. (2015). Complexity. In: Principles of Systems Science. Understanding Complex Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1920-8_5
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