Complexity

What do we mean when we say that something is complex? That it has many sides or aspects to it, needs many variables or parameters to describe it, or consists of many parts? Or that it is hard to understand, needs many words to explain, or is difficult to predict? Usually we mean an unspecified combination of some or all of these and similar definitions, with the emphasis depending on the particular case, but in one way or another, complexity is related to the number of parameters required to describe behavior.

Complexity

Complexity is a thoroughly human concept. Something is considered complex because it is difficult for us, as humans, to come to grips with and to work with; it has to do with the capabilities of our brain. It makes no sense to say that something is complex in itself, without putting it in the context of whatever entity is going to operate on it; what is complex to a human may be very simple for a computer, and vice versa. The difficulty we have in conceiving of something as a single entity once it has more than about seven parameters (Miller 1956) is a characteristic of the brain, and indeed, the success of our whole system design methodology will depend on how well it exploits the strengths and avoids the weaknesses of our brains.

System complexity arises in two fundamental forms, as identified by Peter Senge (Senge 1990); namely detail complexity and dynamic complexity. Detail complexity arises from the volume of systems, system elements and defined relationships. This complexity is related to the systems as they are; their static existence. Dynamic complexity, on the other hand, is related to the expected and even unexpected behavior of systems during their operation. These two forms of complexity can synonymously be referred to as structural complexity and behavioral complexity. The concept of the structure of a system was introduced in Topic 2.1.2, and with that description of interactions as links, a simple expression for the structural complexity is (Aslaksen 2004)

where ωi is the number of elements supporting i links to other elements.

The values of χ for four simple structures are Structure Structural Complexity Linear chain χ = 2(n-1)/n Closed chain (circle) χ = 2 Central element (e.g. broadcast) χ = 2(n-1)/n All-with-all (maximally connected) χ = n-1

However, in addition to the number elements and relationships, factors such as linearity or non-linearity in relationships, asymmetry of elements and relationships determine the degree of complexity.

Structural and/or behavioral system complexity is related to the systems themselves as well as how the systems are perceived by people, as noted above and also in the following quotation (Ashby 1973):

“… to a neurophysiologist the brain, as a feltwork of fibers and a soup of enzymes, is certainly complex: and equally the transmission of a detailed description of it would require much time. To a butcher the brain is simple, for he has to distinguish it from about thirty other “meats.”

Such factors as values and beliefs, interests, capabilities as well as notions and perceptions of systems are determinants of perceived complexity. Weaver provided an early viewpoint by categorizing complexity into organized simplicity, organized complexity and disorganized complexity (Weaver1948). These categories and later reflections by amongst others Flood and Carson (1993) and Lawson (2010) provide impetus for the following complexity categorization.

Organized simplicity occurs when there are a small number of essential factors and large number of less significant and/or insignificant factors. Initially a situation may seem to be complex, but on investigation the less significant and insignificant factors are taken out of the picture and the hidden simplicity is found. This is also the basis for the process of abstraction; creating systems of greater general applicability, but with lower level of detail.
Organized complexity is prevalent in defined physical and defined abstract systems where the structure of the system is organized in order to be understood and thus be amenable to scientists in describing complex behaviors as well as for structuring the engineering and life cycle management of complex systems (Braha et al. 2006). There is a richness that must not be over-simplified.
Disorganized complexity occurs when there are many variables that exhibit a high level of random behavior. It can also represent the product of not having adequate control over the structure of heterogeneous complex systems that have evolved due to inadequate architectural control over the system life cycle (complexity creep).
People-related complexity, where perception of any system fosters a feeling of complexity. In this context, humans become “observing systems”. We could also relate this category to systems in which people are elements and can well contribute to organized simplicity, organized complexity or disorganized complexity (Axelrod and Cohen 1999). The rational or irrational behavior of individuals in particular situations is of course a vital factor in respect to complexity (Kline 1995).

Emergence

Emergence is a central feature of the system concept, and while there is an ongoing debate about the exact nature of this feature, it is often summed up by the statement that “the whole is more than the sum of its parts”. That is, the system has properties that are not evident in any of its elements. Or, from another perspective, the properties of the system are determined not only by the properties of the elements, but also by the interactions between them. Much of the discussion about emergence is of a philosophical nature (Bickhard 2000); (Ryan 2008) contains a discussion of the application to engineering.

Based on the understanding of the system concept as a mode of description, there is no problem with defining the emergent properties of a system. Consider a given object. If it is described as a single object, it has no emergent properties; all its properties are simply the properties of the object. If we describe it as a system, i.e. a set of interacting elements, then the emergent properties are those that disappear when we turn off the interactions between the elements; in the limit of describing any object as a system of interacting atoms, all the object’s properties are emergent properties. Thus, the existence of emergent properties is simply a consequence of applying the system concept; they are not defined by the object itself.

However, of particular interest in the context of engineering is what might be considered the converse of describing a given object; predicting the properties that will emerge if a set of objects are combined in a certain way to form a particular system. The objects are combined so as to achieve a set of required properties, but how can one ascertain that there are no unintended properties? Determining the properties, in particular, the dynamic properties specifying the behaviour of a system under all circumstances, i.e. all combinations over time of all parameter values (inputs, environmental, operator actions, etc.) in both the design and testing phases rapidly becomes an impossible problem as the complexity of the system increases, so the approach can only be to reduce the uncertainty and the corresponding risk to acceptable levels. This risk must be handled within the design methodology in the same manner as acquisition cost and operating cost are handled, and in the design of complex systems, risk becomes itself a major design parameter. The uncertainty is handled by letting the functional parameters become stochastic variables, characterized by probability density functions, and the various measures of risk become expressions involving integrals of these functions (Aslaksen 2009).

References

Aslaksen, E.W. 2004, System Thermodynamics: A Model Illustrating Complexity Emerging from Simplicity, Systems Engineering, Vol. 7, No.3.

Aslaksen, E.W. 2009, Engineering Complex Systems: Foundations of Design in the Functional Domain, CRC Press, Boca Raton.

Ashby, W.R. 1956. An Introduction to Cybernetics, Chapman and Hall, London.

Axelrod, R. and M. Cohen, Harnessing Complexity: Organizational Implications of a Scientific Frontier, Simon and Schuster, 1999.

Bickhard, M.H. and D.T. Campbell 2000, Emergence, an interesting article with a large bibliography, available at http://www.lehigh.edu/~mhb0/emergence.html.

Braha, D., A. Minai, and Y. Bar-Yam, eds. Complex engineered systems: Science meets technology, Springer, 2006.

Flood, R. L., & Carson, E. R. 1993. Dealing with complexity: An introduction to the theory and application of systems science (2nd ed.). New York: Plenum Press.

Kline, S. 1995, Foundations of Multidisciplinary Thinking, Stanford University Press.

Lawson, H. W. 2010. A Journey Through the Systems Landscape, College Publications, Kings College, UK.

Miller, G.A. 1956, The Magical Number Seven, Plus of Minus Two: Some limits on Our Capacity for Processing Information, The Psychological Review, vol. 63, pp. 81-97, available online at www.well.com/user/smalin/miller.html. References to subsequent papers can be found at http://citeseer.nj.nec.com/context.

Ryan, A. 2007, Emergence is coupled to scope, not level, Complexity. A condensed version appeared in Insight, the newsletter of INCOSE, vol.11, no.1, January 2008, pp. 23,24.

Senge, P.M. 1990, The Fifth Discipline: The Art & Practice of The Learning Organization, Currency Doubleday, New York.

Weaver, W. 1948, Science and Complexity, American Science, 36 pp 536-544.

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