Tracing Complexity TheoryFor ESD.83 – Research Seminar in Engineering SystemsSummary1 Ideas about Complex Systems2 Defining Complexity Theory3 Research Approach4 Current Applications and Research Topics5 Early History of Complexity, People and Institutions7 Assessment8 References9 BibliographyTracing Complexity Theoryby Pedro FerreiraFor ESD.83 – Research Seminar in Engineering SystemsFall 2001SummaryThis work traces the development of complexity theory as a field of study. Complexitytheory studies and analyzes complex systems and aims at understanding their structureand behavior. A complex system is characterized by emergent behavior resulting from theinteraction among its parts and, for that reason it cannot be fragmented without losing itsidentity and purposefulness. Therefore, complexity theory is at the heart of what systemsare today, and is concerned with the idea that a system is more than just assembling a setof machines together. To deal with this kind of systems, researchers use abstraction andrely heavily on computer simulation to derive steady-state information about the system,in form of invariants, limiting cycles and attractors. Complexity theory has a large scopeof application in today’s life mainly because real world systems are all complex. This document presents ideas, definitions and properties of complex systems andintroduces some of the tools and methods used in complexity theory. It also analyzes theorigins of this field of study and includes an assessment about its success and relevance.11 Ideas about Complex SystemsComplexity theory encompasses a body of knowledge aimed at analyzing complexsystems. Some views put up by researchers dealing with complex systems, compiled byJoseph Sussman1 in 2000, include the following ideas:- Joel Moses2 suggests that a complex system is composed of many parts thatinterconnect in intricate ways. In other words, the complexity of a system isrelated to the number of interconnections and to their nature. In addition, heargues that the amount of information in a system can be used as a proxy for theits degree of intricateness- Peter Senge3 refers to the concept of dynamic complexity. Dynamic Complexityoccurs when obvious interventions produce non-obvious consequences. Examplesof dynamic complexity are dramatically different short-run and long-run effectsand dramatically different local and global effects- Joseph Sussman suggests that a system is complex when it is composed of agroup of related units for which the degree and nature of the relationships isimperfectly known. In this case, emergent behavior is difficult to predict, evenwhen the behavior of every subsystem is readily predictable- Rechtin and Maier4 suggest that a complex system is a set of elements connectedin order to perform a unique function that cannot be achieved by any of the partsalone. In their view, a complex system may be approached at different levels ofabstraction, each with its own techniques for problem-solving1 Joseph Sussman is a Professor of Civil and Environmental Engineering and Engineering systems at MIT2 Joel Moses is a Professor of Computer Science and Artificial Intelligence at MIT3 Peter Senge is a Senior Lecturer at the MIT and Chairperson of the Society for Organizational Learning4 Eberhardt Rechtin and Mark W. Maier are Space Engineers at the National Academy of Sciences 2- David Levy5 argues that complexity and chaos theory attempt to reconcile theunpredictability of non-linear dynamic systems with a sense of order andstructure. He argues that, with this kind of systems, short-term predictability ispossible but long-term planning is impossible to achieveThese characteristics of complex systems are illustrated in Figure 1. A complex system iscomposed of many parts and exhibits emergent behavior. This emergent behavior cannotbe inferred directly from the behavior of the components. Complex systems may also exhibit hierarchy and self-organization resulting from thedynamic interaction of the parts. This suggests that a number of different scales maycharacterize a complex system and one can study complex systems by positioninghimself at one of these levels. Adding up to the concept of complexity, complex systemsevolve over time and small changes in the parameters of the system may easily result inchaotic behavior.Figure 1- Overview of the characteristics of complex systems.5 David Levy is a Science Editor since 1998 and one of the most successful comet discoverers in history3Other common-sense ideas related to complexity include size, ignorance, variety anddisorder. Size is an indication of the difficulty one might have in order to deal with asystem. The larger the system, the more complex it looks like. Ignorance tells us aboutthe lack of knowledge that one has about the system. A system is complex when one doesnot know about it. Variety is related to the different nature of the parts of a system.However, variety, just like size, is not enough for complexity. A system may be large andplenty of variety, but it can be very simple.Disorder is a very interesting concept associated with complex systems. For a visualexample, refer to Figure 2. A very simple system is not out-of-order. It is simple and onecan easily find an explanation for its operation. A random system is completely out-of-order and one cannot infer any information from of it. Complexity theory considerssystems in between, which are not simple but neither completely random, and thereforeencode some, potentially useful, information.ComplexityDisorderComplexityDisorderFigure 2- Relationship between complexity and disorder.Note that this has a very interesting relation to Shannon’s measure of entropy6. Shannon’smeasure of entropy of a system can be though of as a proxy for the information encodedin the system. It reaches its maximum value when all the events that can happen in theworld have the same probability. Therefore, Shannon’s entropy increases with the6 Shannon’s measure of entropy equals - pi.log(pi), where pi is the probability of occurrence of event i. This measure of entropy has been largely used in many research fields. For example, it can be used as a measure of inequality, as shown by Henry Theil in 1997 and analyzed by Amartia Sen in 1996, Nobel laureate in