Complexity
Complexity is one of the most important and difficult to define system concepts. Is a system's complexity in the eye of the beholder or is there inherent complexity? How should complexity be rigorously defined? How should it be measured? What are the consequences on systems engineering of dealing with higher complexity systems? Many questions abound. The knowledge about complexity is summarized in this article.
Defining System Complexity
Weaver (Weaver 1948) gives one of the earliest definitions as the degree of difficulty in predicting the properties of a system, if the properties of the system's parts are given. Does this simple definition describe a static property of a system artifact, or a dynamic property of systems in use to solve a problem? If complexity is related to an ability to understand systems, does it vary depending who is considering the system and why? How do these questions relate to the distinctions between natural systems , social systems and engineered systems or to the idea of a system context ?
According to (Sheard and Mostashari 2008) complexity sits on a spectrum somewhere between order and chaos. In common usage chaos is a state of disorder or unpredictability. A chaotic system has elements which are not interconnected and behave randomly with no adaptation or control. Chaos Theory (Kellert 1993) is applied to certain types of dynamic system (e.g. the weather) which, although they have structure and relationships, exhibit unpredictable behavior . These systems are deterministic; their future behavior is fully determined by their initial conditions with no random elements involved. However, their structure is such that (un-measurably) small perturbations in inputs or environmental conditions may result in unpredictable changes in behavior. This behavior is known as deterministic chaos, or simply chaos. Models of chaotic systems can be created and, with increases in computing power, reasonable predictions of behavior are possible at least some of the time. One might need to consider truly random or chaotic natural or social systems as part of the context of an engineered system, but such system cannot themselves be engineered.
Ordered systems have fixed relations between elements and are not adaptable. (Page 2009) cites a watch as an example of an ordered system. The components of a watch are based on similar technologies with a clear mapping between form and function. If the operating environment changes outside prescribed limits or one key component is removed, the watch will cease to perform its function. Although the watch may have many components, it can be regarded as complicated but not complex. Ordered systems occur as system components, and are the subject of traditional engineering. It is important to understand the limitations of such systems when using them in a complex system.
Complex systems sit between order and chaos with combinations of elements of different types arranged in relationships which provide more than one function. This can lead to multiple ways of achieving a given outcome. Complex systems adapt to environmental changes or the loss of some elements. For example, if one element such as a doctor, piece of equipment or building infrastructure is removed from a hospital surgical unit, the remaining elements will continue to function as a unit, albeit with reduced effectiveness. This would be considered a complex system.
The inclusion of people in a system is often a factor in their complexity, due to the variability of human behavior as part of a system and the perceptions of people out-side the system. (Sheard and Mostashari 2011) sort the attributes of complexity into causes and effects. Attributes that cause complexity include: many pieces, nonlinear, emergent, chaotic, adaptive, tightly coupled, self-organized, decentralized, open, political (vs. scientific), and multi-scale. The effects of those attributes which make a system seem complex, often as perceived by people, include: uncertain, difficult to understand, unclear cause and effect, unpredictable, uncontrollable, unstable, unrepairable and unmaintainable, costly, and takes too long to build. (Sillitto 2009) refers to these as Objective and Subjective complexity and associates both with problem situations and system solutions.
Thus, complexity is a measure of how difficult it is to understand how a system will behave or to predict the consequences of changing it. It occurs when there is no simple relationship between what an individual element does and what the system as a whole will do, and when the system includes some element of adaptation or problem solving to achieve its goals in different situations. It can be based on objective attributes of the system or on subjective perceptions of system observers. This view of complex systems is very much the kind of system for which a systems approach is essential.
Origins and Characteristics of Complexity
Many systems science authors have attempted to make sense of complexity; how does it differ from what is merely complicated or intricate, and how is it related to human perception or societal context? Weaver provided an early viewpoint categorizing organized and disorganized complexity (Weaver 1948). These categories and later reflections amongst others, such as (Flood and Carson 1993) and (Lawson 2010), provide the following complexity categorization:
- Organized simplicity occurs when there are a small number of essential factors and large number of less significant 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 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 physical and abstract systems where the structure of the system is organized in order to be understood and thus 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 oversimplified.
- 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 control over the system during its life (complexity creep).
- People-related complexity, where perception fosters a feeling of complexity. In this context, humans become “observing systems”. People can be viewed as system elements which contribute to the other types of 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).
(Senge 1990) identifies two fundamental forms of engineered systems complexity; namely, detail complexity and dynamic complexity. Detail complexity arises from the number of systems elements and 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 use in different problem scenarios.
(Sheard and Mostashari 2011) describe Structural, Dynamic and Socio-political complexity. Structural complexity looks at the system elements and relationships. In particular, structural complexity looks at how many different ways system elements can be combined, and thus the potential for the system to adapt to external needs. Dynamic Complexity considers the complexity which can be observed when systems are used to perform particular tasks in an environment. There is a time element to dynamic complexity. The ways in which systems interact in the short term is directly related to system behavior ; the longer term affects of using systems in an environment is related to system evolution. Finally, Socio-political complexity considers the affect of individuals or groups of people on complexity. This will include the cognitive behavior of people in the system, multiple stakeholder viewpoints within a system context and social or cultural biases which add to the wider influences on a system context.
Characteristics of Complex Systems
According to (Page 2009), there are four characteristics of complex systems:
- Independence of system elements. That is, making their own decisions; although these decisions may be influenced by information from other elements and the adaptability algorithms it carries with it. (Sheard and Mostashari 2008) refer to this characteristic as “autonomous” components.
- Interconnectedness: between system elements. This may be via a physical connection, shared data or simply a visual awareness of where the other elements are and what they are doing as in the case of the flock of geese or the squadron of aircraft.
- Diversity simply means that system elements are different in some way, technologically or functionally. Element may be carrying different adaptability algorithms, for example.
- Adaptability is generally considered to be the most important characteristic of the elements of a complex system. Adaptability means that each element can do what it wants to do to support itself or the entire system. In the case of the human pilots, each pilot can make his or her own decisions to adjust to the mission of the whole squadron. (Sheard and Mostashari 2008) refer to this characteristic as self-organizing. Sheard and Mostashari also say that complex systems adapt to their environment. Adaptability can also be achieved with software. (Pollock and Hodgson 2004) describe how this can be done in a variety of complex system types including power grids and enterprise systems.
Complexity is also in many ways a human concept. Looking at a hospital surgical unit from the perspective of an experienced nurse, a member of the cleaning staff, a software engineer designing code for a piece of medical equipment, a typically educated patient or a patient from an African village flown into the hospital after a natural disaster, it is clear that the education, experience and knowledge of each person may radically change their understanding of the same system. Such factors as human values and beliefs, interests, capabilities as well as notions and perceptions of systems are determinants of complexity.
(Warfield 2006) developed a powerful methodology for addressing complex issues, particularly in the socio-economic field, based on a relevant group of people developing an understanding of the issue in the form of a set of interacting problems - what he called the “problematique”. The complexity is then characterized by several measures, such as the number of significant problems, their interactions, and the degree of consensus about the nature of the problems. Thus, what becomes clear that how, why, where and by whom a system is used may all contribute to its complexity.
Some of this complexity can be reduced by education, training or familiarity with a system; some must be managed as part of a problem or solution. (Checkland 1999) argues that a group of stakeholders will have its own world views which lead them to form different, but equally valid, understandings of a system context. These differences cannot be explained away or analyzed out, but must be understood and considered in the formulation of problems or the creation of potential solutions.
Complexity and Context
The views of complexity are not independent when considered across a system hierarchy . system context is a concept used to focus on an engineered system-of-interest, while still considering wider holistic system and environmental relationships. Problem situations and potential solutions may contain both subjective and objective complexity, while structural complexity at one level will be related to dynamic complexity at higher levels. People are involved in most system contexts, as system elements and as part of the operating environment. People are also involved with systems throughout the lifetimes of those systems.
(Sillitto 2009) considers the link between the types of complexity and system architectures, but this can be generalized to consider how to deal with complexity in the applications of a Systems Approach (see Applying the Systems Approach). Sheard and Mostashari 2011) also show how the different views of complexity map onto product systems , service systems and enterprise systems ; and to associated Development and Sustainment systems and Project organizations.
The definition of system complexity used in the SEBoK covers two views of complexity within a system context: the structural complexity of the system-of-interest and wider system; and the dynamic complexity when the system-of-interest is used as part of the wider system in different problem scenarios. The differing perceptions of this complexity by both individuals and social groups of people involved in creating, using or interacting with a system is recognized. In many ways the Systems Approach exists to deal with these complexity issues.
References
Works Cited
Axelrod, R. and M. Cohen. 1999. Harnessing Complexity: Organizational Implications of a Scientific Frontier. New York, NY, USA: Simon and Schuster.
Braha, D., A. Minai, and Y. Bar-Yam (eds.). 2006. Complex Engineered Systems: Science Meets Technology. New York, NY, USA: Springer.
Checkland, P. 1999. Systems Thinking, Systems Practice. New York, NY, USA: John Wiley & Sons.
Flood, R. L., and E.R. Carson. 1993. Dealing with Complexity: An Introduction to The Theory and Application of Systems Science", 2nd ed.. New York, NY, USA: Plenum Press.
Lawson, H. W. 2010. A Journey Through the Systems Landscape. Kings College, UK: College Publications.
Kellert, S. 1993. In the Wake of Chaos: Unpredictable Order in Dynamical Systems, Chicago, IL, USA: University of Chicago Press. p. 32.
Kline, S. 1995. Foundations of Multidisciplinary Thinking. Stanford, CA, USA: Stanford University Press.
Page, Scott E. 2009. Understanding Complexity. Chantilly, VA, USA: The Teaching Company.
Pollock, J.T. and R. Hodgson. 2004. Adaptive Information. Hoboken, NJ, USA: John Wiley & Sons.
Senge, P.M. 1990. The Fifth Discipline: The Art & Practice of The Learning Organization. New York, NY, USA: Doubleday/Currency.
Sheard, S.A. and A. Mostashari. 2008. "Principles of Complex Systems for Systems Engineering." Systems Engineering, 12(4): 295-311.
Sheard, SA. and A. Mostashari. 2011. "Complexity Types: From Science to Systems Engineering." Proceedings of the 21st Annual of the International Council on Systems Engineering (INCOSE) International Symposium, 20-23 June 2011, Denver, Colorado, USA.
Sillitto H.G. 2009. "On Systems Architects and Systems Architecting: Some Thoughts on Explaining The Art and Science of System Architecting." Proceedings of the 19th Annual International Council on Systems Engineering (INCOSE) International Symposium, 20-23 July 2009, Singapore.
Weaver, W. 1948. "Science and Complexity." American Science. 36: 536-544.
Warfield, J.N. 2006. An Introduction to Systems Science. London, UK: World Scientific Publishing.
Primary References
Page, Scott E. 2009. Understanding Complexity. Chantilly, VA, USA: The Teaching Company.
Flood, R. L., & E.R. Carson. 1993. Dealing with Complexity: An Introduction to The Theory and Application of Systems Science, 2nd ed. New York, NY, USA: Plenum Press.
Sheard, S.A. and A. Mostashari. 2008. "Principles of Complex Systems for Systems Engineering". Systems Engineering, 12(4): 295-311.
Additional References
Ashby, W.R. 1956. An Introduction to Cybernetics. London, UK: Chapman and Hall.
Aslaksen, E.W. 2004. "System Thermodynamics: A Model Illustrating Complexity Emerging from Simplicity". Systems Engineering, 7(3). Hoboken, NJ, USA: Wiley.
Aslaksen, E.W. 2009. Engineering Complex Systems: Foundations of Design in the Functional Domain. Boca Raton, FL, USA: CRC Press.
Aslaksen, E.W. 2011. "Elements of a Systems Engineering Ontology". Proceedings of SETE 2011, Canberra, Australia.
Eisner, H. 2005. Managing Complex Systems: Thinking Outside the Box. Hoboken, NJ, USA: John Wiley & Sons.
Jackson, S., D. Hitchins, and H. Eisner. 2010. What is the Systems Approach? INCOSE Insight 13(1) (April 2010): 41-43.
MITRE. 2011. "Systems Engineering Strategies for Uncertainty and Complexity." Systems Engineering Guide. Accessed 9 March 2011 at [[1]].
Ryan, A. 2007. "Emergence Is Coupled to Scope, Not Level, Complexity". A condensed version appeared in INCOSE Insight, 11(1) (January 2008): 23-24.
SEBoK Discussion
Please provide your comments and feedback on the SEBoK below. You will need to log in to DISQUS using an existing account (e.g. Yahoo, Google, Facebook, Twitter, etc.) or create a DISQUS account. Simply type your comment in the text field below and DISQUS will guide you through the login or registration steps. Feedback will be archived and used for future updates to the SEBoK. If you provided a comment that is no longer listed, that comment has been adjudicated. You can view adjudication for comments submitted prior to SEBoK v. 1.0 at SEBoK Review and Adjudication. Later comments are addressed and changes are summarized in the Letter from the Editor and Acknowledgements and Release History.
If you would like to provide edits on this article, recommend new content, or make comments on the SEBoK as a whole, please see the SEBoK Sandbox.
blog comments powered by Disqus