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Chaos and Complexity

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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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