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Complexity A new perspective for the 21st century "I think the next century will be the century of complexity.” Professor Stephen Hawking Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Complexity A new perspective for the 21st century • Welcome and Introductions • A Short History of Science • Order and Chaos • Fractals • Power Law Distributions • Small World Networks • Complex Adaptive Systems • Other connections • Discussions Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Victor MacGill • MA (Chaos, Complexity and Creativity) (UWS) • Two published papers in the peer reviewed journal, Emergence • Attended 4 international conferences on Complexity – presented four papers • Complexity website with over 47,000 visits Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Complexity A new perspective for the 21st century Introductions • Introduce yourself • Give some personal background if you wish • What was appealing about attending a workshop on complexity? • What do you hope to gain from the workshop? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions A Short History of Science Gallileo Gallilei Johannes Kepler Sir Isaac Newton Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions A Short History of Science Reductionist Science • Science usually works by breaking things into smaller and smaller pieces until each piece can be accurately analysed. • To find out how a car works, we examine the parts and understand them and then gain an understanding of how a car works. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions A Short History of Science F=ma F=GMm/r2 Sir Isaac Newton saw the universe like a clock set by God and thought his mathematical laws could predict what would happen in the future, if only we could measure it accurately enough. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions A Short History of Science Henri Poincaré and the three body problem Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions A Short History of Science • If we can’t even understand a system with three interacting bodies, how can we ever imagine understanding the complexity of life? • Using reductionist methods often means we lose the overall picture. Dissecting a rat tells us much about dead rats, but cannot explain a living rat. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions A Short History of Science • Complexity Theory looks at systems that are too complex to predict future states but nevertheless exhibit useful patterns. • Because of the large amount of data number of calculations generally required to investigate complex systems, the real development of complexity really only began with the advent of computers. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Chaos Theory Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Chaos Theory How do we best describe our world? Divide into two groups and discuss. • Random • Chaotic • In equilibrium • Ordered • Pre-determined Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos What is the difference between random events and chaotic events? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos Divide into two groups. One group will look at the advantages and disadvantages of order in our world and the other will look similarly at chaos. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos • An ordered system is predictable and structured. • In a totally ordered system all the agents act just the same. There are limited ways of acting, and the system loses flexibility. • A chaotic system allows novelty and diversity. • When a complex system is too chaotic the system lacks enough structure to be effective. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos • Everything in our world moves between order and chaos. • When we learn we start in a position of order, but then enter the unknown and the chaotic as we take on something we do not know about. As we become familiar with the new knowledge, we return to order. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Feedback Loops • Complex systems often have feedback loops • Positive Feedback Loops • (Fold a piece of paper 50 times. How big is the pile?) • Negative Feedback Loops Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Butterfly Effect Ed Lorenz, 1963 Lypanov time for chaotic •dx/dt=-10x+10y systems •dy/dt=30x-y-xz Increased energy for longer •dz/dt=-3z+xy predictability Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Butterfly Effect Sensitivity to initial conditions “Predictability: Does the Flap of a Butterfly’s Wing in Brazil Set off a Tornado in Texas?”, 1979 What other systems might be sensitive to initial conditions? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Butterfly Effect Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Attractors • Point attractor • Cyclic attractor (limit cycle) fish in a lake Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Attractors • Chaotic attractor or strange attractor • far from equilibrium, maintains its own structure Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Strange Attractors The Fitness Landscape – Bifurcation – Catastrophe Theory - Renee Thom Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Edge of Chaos A strange attractor can move to a point called the “Edge of Chaos” where there is just enough order to maintain structure, and just enough chaos to allow for diversity and novelty. At this point the system takes on a “magical” life of its own. Chris Langton Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos • A juggler is an example of a complex system at the Edge of Chaos. The balls seem to be thrown chaotically in the air, but there is an underlying order so the balls move in a way that could not have been predicted before. The system has a dynamic balance rather than a static balance. •The dynamic balance is only maintained as long as the juggler keeps juggling. A moment’s inattention and the system lapses into chaos. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos • A runner can also be at the edge of chaos. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Emergence When conditions reach a critical state in a complex system, as at the Edge of Chaos, we may see emergent properties appear. Emergence occurs when properties not apparent when looking at individual agents “magically” appear as a result of the complex interactions of the agents. They involve system wide co-ordination at a whole new level of complexity. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Order and Chaos Read this short article from the website of the City Council of Littleton, Colorado. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Edge of Chaos Further examples of complex systems at the Edge of Chaos are: • heart beat • the free market • ant colonies • earthquakes • population dynamics Does life tend towards the Edge of Chaos? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Swarms Many autonomous agents with minimal individual abilities • Maintain the same speed • Not too close, not too far from others Boids1 Boids2 • Average direction of nearby agents Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Swarms Ant colonies Bee hives Practical Uses Movies Trucking companies Telephone rerouting Military robots Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals A scale free landscape Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Scale free Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractal Coastlines • The coastline is scale free. • In groups, take one of the maps and use the string provided to find the length of the coastline. • How long is the coastline of the South Island? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractal Dimensions Natural Pattern Fractal Dimension South African coast 1.05 Norwegian coast 1.52 Galaxies 1.23 Wood, plants, trees 1.25-1.55 Waves 1.3 Clouds 1.3 - 1.33 Snowflakes 1.7 Retina blood vessels 1.7 Bacterial growth patterns 1.7 Lightning 1.75 Mineral patterns 1.78 Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals •Scale free shapes are called fractals. The word fractal was coined by Benoit Mandelbrot from the Latin “fractus” or broken. •Fractals are shapes where the basic pattern of the whole shape is repeated at smaller and smaller levels within the main shape. A twig is similar in shape to a whole tree. •How might be the basic shape for a tree that is repeated at smaller and smaller levels? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals How does a tree grow to become a fractal pattern? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Look at this fractal generated by a computer Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Examples of real world fractals Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Turbulence Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions More Fractals Sierpinski’s Triangle Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions More Fractals Koch Snowflake Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Mandelbrot Set Pure fractals can be created mathematically. The best known example is the Mandelbrot Set. It is infinitely complex. • The Mandelbrot Set was discovered by Prof Benoit Mandelbrot • The formula is: z iterates to z2+c Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Mandelbrot Set Zooming in on Mandelbrot Set Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Exercise: The electricity grid is down, but the telephone lines are still working. The mayor has come to you to create a telephone tree to get messages out to all citizens as effectively as possible. How will you design the telephone tree? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Equal proportions between levels. X XX XXXX XXXXXXXX XXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Pareto’s Law •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions • Power law systems have a few agents at extreme high levels, middle numbers at middle levels, and large numbers at low levels. • Other examples of power law distributions are city sizes, life span of businesses, crime levels, word frequency, time waiting in traffic jams, sand falling off a sand pile, interacting organisms in an ecology, people killed in wars, number of sexual partners in a lifetime, people’s income levels. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions • Does this explain why communism could not have worked? The more we try to make people equal, as soon as they interact, higher and lower levels will automatically arise. • Does it explain why crime won’t go away? If we catch the worst criminals, do we just create opportunities for other criminals to take their place? •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Luke 19: 12-27 (abridged) “A nobleman summoned ten of his slaves and gave them ten minas, and said, ‘Do business with these until I come back.’ When he returned, he summoned the slaves to whom he had given the money. The first one came before him and said, ‘Sir, your mina has made ten minas more.’ And the king said to him, ‘Well done, good slave! Because you have been faithful in a very small matter, you will have authority over ten cities.’ Then the second one came and said, ‘Sir, your mina has made five minas.’ The king said to him, ‘And you are to be over five cities.’ Then another slave came and said, ‘Sir, here is your mina that I put away for safekeeping in a piece of cloth. I was afraid of you, because you are a severe man. You withdraw what you did not deposit and reap what you did not sow.’ Why then didn’t you put my money in the bank, so that when I returned I could have collected it with interest?’ He said to his attendants, ‘Take the mina from him, and give it to the one who has ten.’ But they said to him, ‘Sir, he has ten minas already!’ ‘I tell you that everyone who has will be given more, but from the one who does not have, even what he has will be taken away.” •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions In practice many real world power law distributions drop off at the lower end of the scale. This might be because of: Limits to scale: (i.e.) The amount of many in bank accounts has a lower limit because there is a lower income limit a person can survive on. Natural limitations E.g. in a fern root, there is a limit to how small the basic pattern can be reproduced •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Zipf’s Law • The population of cities in a country follow the following law. • The population of the city is the population of the city divided by its ranking in that country. Pn=P1/na • Take the data about city populations and draw a graph with the city populations and the population as predicted by George Zipf. It also works for word frequency. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Fat tail graph •Why are we so surprised by large scale catastrophes? •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Note the link between fractals and power law distributions. Both repeat a basic pattern at different levels increasing or decreasing each level by the same proportion. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions • If we look at a tree. The trunk branches into smaller and smaller each branch being roughly the same reduction in thickness at all levels • If we look at a cauliflower or the alveoli in our lungs, we see a similar pattern of reducing proportions. Why does nature create power law systems? •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions • When we have a large flow coming into the system, (air, nutrients, etc.) needing to be distributed evenly over a wide area as efficiently as possible, the best way is using power laws. • Even our roadways are the same; big multi-lane highways branching off into smaller and smaller streets as you go into the suburbs. It works the other way round for getting from the suburbs to the highway. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions Rivers catch water from a widely distributed area of land and take it efficiently to one river mouth. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Complexity Theory •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks A Small World Network is a network of nodes which are joined by links. Nodes could be people, places, computers, fish, telephones or even atoms. Autonomy and connectivity The nodes are free to make their own decisions, but need to co-operate with other nodes •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks Create a small word network diagram of this group. Link people you have met before and put a stronger line the longer you have known each other. Create another small world network diagram based on how much you are following the World Cup. Rate yourself between 1-10. Work out the difference between you and others. 0-3 strong link 4-6 medium link over 6 weak link •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks How might a network be most effectively linked? • Random • Hierarchical • Sparse links • Heavily linked •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks Social Network Analysis •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks If there are too few links the network does not operate very effectively. If there are too many links communication is clogged and it is also not efficient. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks • Small world networks natural tend to be fractal and are power law systems. • For example, in a human group, a small number of people have an extraordinary number of social contacts, while most of us have a smaller group of contacts. • Other examples are the power grid, ant colonies, brains, animal groups •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks A Small World Network has hubs - critical points which link to clusters of agents. The clusters are fractal (I.e. they are mini versions of the whole network). This makes them very efficient. As well, the network has other random connections between agents making it even more effective. In social groups we tend to stick within our cluster - people we know well, but we have many other links to people we don’t know as well in other clusters, that can be very useful. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks What are the strengths and weaknesses of a small world network? The importance of strong and weak links. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks The human brain works as a small world network. It organises itself into clusters or modules with specific tasks, but also has many interconnections between the clusters. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks There is no brain cell or part of the brain that is in charge. The intense interactions between brain cells allows the brain’s activity to self-organise, enabling the emergence of thoughts and feelings, a sense of self and other qualities of our mind. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks Artificial Intelligence If the brain is really just an extremely complex complex adaptive system, maybe we can replicate some or all of the brains functions in a computer or on a machine. A small world network can make computations! 2015 has been set as the target date to build a computer of equal complexity to the human brain. Much work is being done combining carbon based living tissue and silicon based technology. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks How do international airline network works? It is not efficient to have direct flights from Dunedin NZ to Dunedin, Florida. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Small World Networks We move first to increasingly larger hubs: From Dunedin, New Zealand to Auckland to Los Angeles and then to decreasing airports to Tampa to Clearwater and then drive to Dunedin, Florida. The same is true of postal networks, telephone networks, computer networks, terrorist networks, drug networks, etc. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Six Degrees of Separation The most efficient network structure to get from one point in the network to any other is a power law small world network. This happens by moving from the outside to larger and larger hubs in the network, then going out to smaller and smaller hubs until the other point is reached. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Six Degrees of Separation Stanley Milgram gave people living in the middle of the US an envelope and instructed them to get it to an accountant in New York. They had to send the envelope to someone they knew personally, who would be more likely to know how to get the letter to the accountant. The letter was passed on person at a time until it arrived. He found on average it took only six steps to reach the accountant. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Six Degrees of Separation The Bacon Game Following from Stanley Milgram’s work, the Bacon game measures the number of steps of Hollywood actors from Kevin Bacon. Anyone who has been in a movie with Kevin Bacon has a “Bacon number” of 0. Someone who has acted with a person with a 0 Bacon number has a number of 1. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Six Degrees of Separation Erdős Number Paul Erdős was a Hungarian Mathematician who did important pioneering work on small world networks. Scientists calculate their Erdős number By the number of links through collaborated research papers to get back to Paul Erdős. Benoit Mandelbrot is a 2 Stephen Hawking is a 3 •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points If you take agents out of a small world network one by one, at first it makes little difference, because the network can find other ways to fulfill its function. As you continue to take out agents you reach the tipping point, where it just cannot find other ways of sustaining itself and it collapses quickly. E.g. power sub-station failures causing other sub- stations to fail. Sometimes we want a system to collapse. E.g. kill so many opossums that they die out, or sometimes want to stop them from reaching the tipping point. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points At other times we want a new dynamics to form in a network, so we want the number of agents to reach the tipping point. (E.g. getting a new business known in the market or spread an idea). At other times again, we want avoid new network to start. We do not want the avian bird flu or a computer virus to reach its tipping point, because it would then spread very rapidly. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points What factors would make a new dynamic more likely (or less likely) to spread through a network? •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points • How easily is the dynamic spread? (It may only need one transmission) • How easily does it move out of a local hub? • What external factors are evident (Baltimore STD 1995 and Housing estates) • How sticky is it? •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points Since complex systems can be very sensitive to even small changes, I.e. the butterfly event. Small changes can start domino effects that take it to its tipping point. E.g the power grid, one tree falling on a line can knock out a sub- station. If the rest of the network is at a critical point there can be a domino effect affecting the whole grid like the black-outs in New York. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points Coronation Street Harry Potter Bill Gates and Microsoft •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points Fax machines could not reach a tipping point until, enough people owned a fax machine. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points Sometimes there are competing systems in an environment. A very small advantage can make one the dominant system and send the other to extinction very quickly. Do you remember VHS and Beta video recorders? Both were trying to become the industry standard. Beta was recognised as being better technologically, but VHS became perceived as the one likely to become the standard. Immediately VHS sales skyrocketed, while Beta quickly became extinct. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Tipping Points Could this be why the dinosaurs died? We usually think big effects must have big causes, like the big meteorite landing in the sea off Mexico. Chaos Theory tells us a small causes, such as a small change in the food chain could have been sufficient for the demise of the dinosaurs. •Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Tipping Point Malcolm Gladwell Mavens – trend setters Connectors – know lots of people Sales people – Sells ideas Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Wolfram Classes Class 1 Point Attractor Class 2 Cyclic Attractor Class 3 Strange Attractor (Chaotic attractor) Class 4 Complex Adaptive System All living systems are complex adaptive systems. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Santa Fe Institute established in the 1980s Chris Langton Stuart Kaufmann Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems So, What is Life….? Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Entropy If you place a plate of fruit out for a month, it will decay. This tendency for objects to move to the lowest, most disordered state is called entropy. Life must find energy to overcome entropy. At death, the forces of entropy again become stronger. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Dissipative Structures They take energy from the outside environment - food, water, warmth, metals, oil, money, ideas, images etc. and release waste and/or products back to the environment. Ilya Prigogine Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Complex Adaptive Systems are complex systems that can adapt themselves to cope better in their environment. A complex Adaptive System can learn in order to become more efficient. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Properties They create their own boundary. A cell has a cell body, a city has a city boundary, a tribe has tribal boundaries, a herd of cows has membership boundaries even an idea or a concept. The system allows some things to come inside the boundary and excludes others. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems. Properties The agents are bounded by simple rules to maintain group cohesion (simple traffic rules allow complex traffic flows). It takes on a life of its own we could not predict from just looking at the individual agents. Self-organisation occurs. (i.e. the system organises itself rather than needing organisation to be imposed from outside.) Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems. Properties • Nested Complex Adaptive Systems • Nesting occur as self-organisation. It is bottom up not top down • Forms hierarchies, but there are mutual interlinkings between layers. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Organisational Complexity If we looked at an organisation as a complex adaptive system in its own right, what might be factors we might like to include in order to make it more likely that it can self organise to new levels of complexity? Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions From a Complexity perspective an efficient organisation would: • encourage individual autonomy • encourage reasonable risk taking and chaos • encourage diversity and novelty • encourage openness and full participation and interaction of all members • have effective communication links through hubs and random links Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions • encourage strong bottom-up interaction and inter-level interaction as well as top down hierarchy. • acknowledge each full person (physical,emotional, intellectual,spiritual, relationships) • project a clear identity and have clear simple rules everyone can understand • know that small changes can transform a whole organisation • uses dominant story and recessive story. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Evolution and Complex Adaptive Systems When we combine natural selection and the property of emergence, we have powerful ways of describing evolution. • Sensitivity to initial conditions means small changes in the environment can mean large evolutionary changes • Small advantages between competing species can have a large effect on their fitness (feedback loops) Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Evolution and Complex Adaptive Systems • There are chemical dissipative systems (that is, the edge between life and non- life is blurred) • A complex adaptive system can change its structure over time to become more effective in its environment. • New levels of evolutionary complexity can “just” emerge. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Evolution and Complex Adaptive Systems • An environment is typically filled with many different structurally coupled complex adaptive systems, each one is generally nested. • Species tend to compete with other species, but co-operate amongst themselves. They also often form symbiotic relationships (e.g. pilot fish) • Order Chaos • Autonomy Connectivity • Competition Co-operation. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex Adaptive Systems Autopoiesis • Humberto Maturana and Francisco Varela • Mind - body - environment • Structural Coupling • The observer affects the system. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complex patterns in the flow of human history Spiral Dynamics Human societies evolve through distinct levels of complexity as a nested hierarchy Generational Dynamics (Fourth Turning) A limit cycle of around eighty years that plots times when the economy is more likely to be buoyant, social unrest is more likely and wars are more likely. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic Aristotle’s law of the excluded middle Every proposition must either be True or False, A or not-A, either this or not this. For example, a typical rose is either red or not red. It cannot be red and not red. Lotfi Zadeh developed the idea of fuzzy logic, saying real life is often not as clear cut. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic What is a bird? A sea gull or an eagle is more likely to come to mind when we think of a bird than a kiwi or an ostrich. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic We can create a continuum of birdness. 0 Brick Horse Dog 0.25 Ostrich Kiwi 0.5 Finch 0.75 Seagull Eagle 1.00 Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic Human beings naturally work with fuzzy logic. Language is Fuzzy We use words like: • quite • a lot • not much • rather • sort of Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic Fuzzy logic is used as a control system., e.g. in heating a room. A thermostat turns the heat on when the temperature reaches a certain level and turns off again when the temperature reduces to a certain level. Fuzzy control system has a series of controls, so if it is very cold, it will instruct the heater to heat more quickly than if it is a little cool. This Makes it much more efficient than on ordinary control system. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic Fuzzy logic is used for: Washing machines - measures dirt content and washes clothes for as long as they need, not just a set time Digital cameras - self focussing Cars / Trains - smoother more accurate travel Traffic lights - reduces waiting time Automatic concrete mixing - getting quantities right Vacuum cleaners - clean til floor is clean. Elevators - smoother travel Video games - more life like Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Fuzzy Logic Fuzziness is infinite When you look closely at something that is fuzzy to make it clearer, we only find more fuzziness. How many times have you wondered about a problem of life? You try to understanding it only to find it creates more questions. The more you look, the fuzzines remains. It is like a fractal. No matter how closely you look at it, the is always another level to be understood. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Game Theory Robert Axelrod •The prisoners dilemma is a game where two prisoners gets a choice of confessing to their crime or not with differing outcomes depending on what they both choose. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Game Theory A A Not confess confess B 5 years A 10yrs confess each B 3 yrs B Not A 3yrs Both confess B 10yrs free Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Game Theory A A Not confess confess B 5 years A 10yrs confess each B 3 yrs B Not A 3yrs Both confess B 10yrs free Try playing a few games. What strategies might be effective? Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Genetic Algorithms In natural selection many organisms are born, most of which will not survive. Those that do survive will tend to be more fit for their environment. Over the generations the organism becomes extremely effective at surviving. Sometimes creating mathematical equations to describe a system is very difficult. It can be more productive to generate many many possible equations and they are left to naturally select. Over generations of algorithms they can become very accurate. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Genetic Algorithms With genetic algorithms we do not need to know why the system is behaving as it is, we just find an effective solution. Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Synchrony Complex Systems can self-organise towards synchorinising their rhythm. • Circadian rhythms • Fireflys • heartbeats Steven Strogatz Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Cellular Automata John Van Neumann Stephen Wolfram • One dimensional Cellular Automata • Edge of Chaos Cellular Automata Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Cellular Automata Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Agent Based Modelling Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Complexity Theory Applications •Medical •Organisational dynamics •Psychology and •Military social •Combating terrorism •Urban planning •Group dynamics •Computer simulation •Ecology •Control systems •Weather prediction •Economics •Business •Technology development Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Towards a Philosophy of Complexity Recap - What are the assumptions behind reductionist science and what is the philosophy of reductionist science? What are concepts within Complexity Theory that might inform a philosophy of complexity? Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Towards a Philosophy of Complexity • Life is ultimately unpredictable. Catastrophes happen. There is luck. • Emergence happens - there is mystery and magic in life • Life tends towards greater complexity (but not necessarily towards a predetermined end point) • Life is co-creation - there is no external observer • Survival of the fittest Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Towards a Philosophy of Complexity • There will always be inequality • Life requires tension between elements • Loss at fundamental levels collapses all levels above (death is the end) • We neither have total control over our lives nor have no control • Competition and Co-operation are equally important Introduction: history: chaos: fractals: small world networks: complex adaptive systems: others: discussions Towards a Philosophy of Complexity • We cannot make emergence happen, but we can create an environment where it is more likely to occur. • Goodness might be defined by how well something makes self organisation and emergence more likely. • In nested systems, some levels are more complex and “advanced” than others, but all levels are vital. Chaos and Complexity Final round, feedback and evaluation. Chaos and Complexity The End

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