1. Spring 2011 - ÇGIE 398 - lecture 41 lecture 4: complexity –parallel developments that are joining together: systems literature complexity literature –most systems of interest to IE/OR are complex –to understand the causes that gave rise to these developments we need to understand how science and the scientific method work

2. Spring 2011 - ÇGIE 398 - lecture 42 science and the scientific method ways to knowledge: – authoritarian and mystical mode versus the rational mode – the Enlightenment, Galileo and Newton – Newtonian mechanics aims of science – seeking reality and truth – explanation and prediction – understanding the scientific method - positivism – objectivity – the research cycle: theory-hypothesis-observation and experimentation-generalisation-theory

3. Spring 2011 - ÇGIE 398 - lecture 43 calculus and analytic functions – analysis – reduction the Newtonian paradigm – objective knowledge is possible: subject-object duality – cause and effect act linearly – nature is deterministic or predictable – reduction works Newtonian science has been a great success; it has created today’s technological society the Newtonian view of the world dominates our thinking even today

4. Spring 2011 - ÇGIE 398 - lecture 44 complexity quantum mechanics, biology, climatology etc Heisenberg’s principle of uncertainty insufficiency of analytical thinking failure of calculus in studying complex shapes realisation that nature is more complex than previously thought led to the development of the new field of complexity studies. complexity theory is as yet not fully developed its aim is to discover unified laws governing complex systems through interdisciplinary inquiry it is early to say whether this aim will be achieved

5. Spring 2011 - ÇGIE 398 - lecture 45 chaos nonlinear dynamics − phase-space – the two-body and the three-body problems – chaos in time : STIC, unpredictability the butterfly effect glasses, mountains, earthquakes etc. − predictability: edge-of-chaos; strange attractors – chaos in space : fractals – all nonlinear systems are chaotic in some regionof their phase-space – hence complexity implies chaos but chos can also occur in simple systems

6. complex systems have several scales; –chaos can be observed at a lower scale –but perhaps not at the higher scale above it to understand complexity and its relation to chaos we recall the laws of thermodynamics the first law of thermodynamics says that the total amount of energy remains unchanged in an isolated system if there is a gradient such as a difference of pressure or temparature in the system then work can be done but our ability to turn energy into work is reduced Spring 2011 - ÇGIE 398 - lecture 46

7. for example, work can be done when gas flows from a high pressure area to low pressure areas until there is no longer a pressure gradient; ie when the pressure gradient is reduced to zero there is no possibility of using it to do work when such a reduction takes place we say that “entropy has increased” gas will not flow back on its own and separate itself into high and low pressure ares; spontaneous change is irreversible, entropy always increases in an isolated system; this is the second law of thermodynamics energy is still there but we cannot use it again, only low entropy energy is useful to us such as electricity, which is energy of the highest grade Spring 2011 - ÇGIE 398 - lecture 47

8. the maximum amount of work that a system can do on its surroundings can be defined as exergy; it is the component of energy that can do useful work there are four types of exergy: –kinetic exergy associated with relative motion; –potential field exergy associated with gravitational or electromagnetic field gradients –physical exergy associated with pressure or temperature gradients, and –chemical exergy associated with chemical gradients exergy is non-zero when the system under consideration is distinguishable from its environment in one or more of these four dimensions; therefore exergy is the most general measure of distance from thermodynamic equilibrium or of the degree of distinguishability. Spring 2011 - ÇGIE 398 - lecture 48

9. distinguisibility here has the same sense as order, as structure, as differentiation or as organisation entropy on the other hand, is a measure of the degree of disorder of a system; or its degree of indistinguishability or disorganisation or lack of structure the state of maximum entropy therefore is a state of randomness, a case in which all states in the phase space have the same likelihood; when this happens the states in the phase-space are uniformly distributed open thermodynamic systems maintain a state of disequilibrium by the transport of material and energy across their boundary; such systems are known as dissipative structures Spring 2011 - ÇGIE 398 - lecture 49

10. dissipative systems dissipate gradients and maintain disequilibrium in a locally reduced entropy ­state this is done at the cost of increasing the entropy of the larger system in which the dissipative structure is imbedded dissipative systems self-organise into structures that dissipate gradients, ie. self-organisation is one way to counter and reduce gradients life itself can be viewed as a sophisticated dissipative structure away from equilibrium that has emerged to counter the gradient imposed by the sun; mainly by photosynthesis complexity can be defined as the degree to which the system maintains a thermodynamic disequilibrium Spring 2011 - ÇGIE 398 - lecture 410

11. complexity a complex system self-organises onto an attractor Baranger summarises the properties of complex systems as follows: 1.complex systems contain many constituents interacting nonlinearly 2.the constituents of a complex system are interdependent 3.a complex system possesses a structure spanning several scales 4.a complex system is capable of emergent behaviour Spring 2011 - ÇGIE 398 - lecture 411

12. Spring 2011 - ÇGIE 398 - lecture 412 – emergence is the fundamental property of systems – emergent behaviour at a higher level of scale arises from lower levels of scale although the mechanisms involved are difficult to comprehend – emergence can be complex or simple – emergent properties will be lost to reduction – if all states were equally likely then there would be no emergence – it appears that relatively few configurations are special or privileged in some way; these configurations are what we call attractors

13. − the combination of structure and emergence leads to self-organisation that occurs when emergent behaviour creates new structure 5.complexity involves an interplay between chaos and non-chaos: –while chaos may reign on a scale, the coarser scale above it may be self-organising, which in a sense is the opposite of chaos –complex systems, such as living organisms, manage to modify their environment so as to operate as much as possible at the edge-of-chaos, the place where self-organisation is most likely to occur Spring 2011 - ÇGIE 398 - lecture 413

14. –two way interaction between the system and the environment results in adaptation, or learning under changing conditions e.g. the stock market players acting on local information, consistent with Simon’s bounded rationality: individuals are unable to forecast the higher level consequences of their actions and so they optimise locally; yet the resultant behaviour has an emergent logic –evolution occurs as a result of collective adaptation over generations 6.complexity involves an interplay between cooperation and competition e.g. firms compete with each other in markets but they also cooperate and act collectively to prevent government intervention in markets Spring 2011 - ÇGIE 398 - lecture 414

15. Spring 2011 - ÇGIE 398 - lecture 415 measures of complexity – the degree of complexity can be expressed in terms of structural aspects, the complexity of structure – it can also be measured in terms of function – a mathematical measure of complexity is given by the amount of information needed to describe it – the length of the binary string that can contain 2 messages is 1; for 4 or 2 2 messages, it is 2; for 8 or 2 3 messages it is 3 where log 2 (8)=3 etc. – for a complex system with k possible states we need N bits of information where N = log 2 (k) – these ideas originated in communication theory and are relevant in combinatorial mathematics also as the problem of computational complexity

16. Spring 2011 - ÇGIE 398 - lecture 416 systems thinking and complexity many of the attributes that define complexity also define systems the commonalities between systems thinking and complexity studies are strong; especially because almost all human-activity systems are complex it is not clear yet if the mathematical constructs and results from complexity research can be directly applied to the study of socio-economic or socio- technical human systems

17. originally, OR searched for models and theories that could simplify the essence of the world so that we might capture a part of social reality for decision making although OR knew that the world was complex, the world also appeared to allow us produce robust models that could be used in applications with the growing realisation that, –complexity is more problematic to deal with than thought before –and that prediction appears to be getting out of reach –the concern of OR has been moving away from solving well defined problems towards structuring debate about a complex world Spring 2011 - ÇGIE 398 - lecture 417

18. many of the attributes of complex systems are certainly shared by human activity systems the fundamental generalisations about self- organisation and complex adaptive systems are especially relevant to OR hence an understanding of complexity can help us better understand human activity systems Spring 2011 - ÇGIE 398 - lecture 418