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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.

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Complexity A new perspective for the 21st century


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    1. Complexity A new perspective for the 21st century "I think the next century will be the century of complexity.” Professor Stephen Hawking

    2. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions ComplexityA 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

    3. 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

    4. Introduction: history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions ComplexityA 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?

    5. 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

    6. 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.

    7. 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.

    8. 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

    9. 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.

    10. 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.

    11. Introduction:history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Chaos Theory

    12. 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

    13. 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?

    14. 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.

    15. 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.

    16. 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.

    17. 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

    18. Introduction:history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Butterfly Effect Ed Lorenz, 1963 Lypanov time for chaotic systems Increased energy for longer predictability dx/dt=-10x+10y dy/dt=30x-y-xz dz/dt=-3z+xy

    19. 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?

    20. Introduction:history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions The Butterfly Effect

    21. 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

    22. 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

    23. Introduction:history: chaos: fractals: power laws: small world networks: complex adaptive systems: others: discussions Strange Attractors The Fitness Landscape – Bifurcation – Catastrophe Theory - Renee Thom

    24. 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

    25. 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.

    26. 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.

    27. 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.

    28. 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.

    29. 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?

    30. 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 Boids1Boids2 • Average direction of nearby agents

    31. 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

    32. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals A scale free landscape

    33. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals

    34. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals

    35. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Scale free

    36. 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?

    37. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractal Dimensions Natural PatternFractal 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

    38. 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?

    39. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals

    40. 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?

    41. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Fractals Look at this fractal generated by a computer

    42. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Examples of real world fractals

    43. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions Turbulence

    44. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions More Fractals Sierpinski’s Triangle

    45. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions More Fractals Koch Snowflake

    46. 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

    47. Introduction: history: chaos:fractals: power laws: small world networks: complex adaptive systems: others: discussions The Mandelbrot Set Zooming in on Mandelbrot Set

    48. 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?

    49. 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

    50. Introduction: history: chaos:fractals:power laws: small world networks: complex adaptive systems: others: discussions Power Law Distributions