Complexity A new perspective for the 21st century

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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
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ComplexityA new perspective for the 21st century
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• Welcome and Introductions
• A Short History of Science
• Order and Chaos
• Fractals
• Power Law Distributions
• Small World Networks
• Complex Adaptive Systems
• Other connections
• Discussions

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Introduction history chaos fractals power
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• 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

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ComplexityA new perspective for the 21st century
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• 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?

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A Short History of Science
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• Gallileo Gallilei Johannes Kepler Sir
  Isaac Newton

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Introduction history chaos fractals power
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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.

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A Short History of Science
Introduction history chaos fractals power
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Fma FGMm/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.
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A Short History of Science
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• Henri Poincaré and the three body problem

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A Short History of Science
Introduction history chaos fractals power
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• If we cant 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.

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A Short History of Science
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• 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.

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Chaos Theory
Introduction history chaos fractals power
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Chaos Theory
Introduction history chaos fractals power
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How do we best describe our world? Divide into
two groups and discuss.

• Random
• Chaotic
• In equilibrium
• Ordered
• Pre-determined

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Introduction history chaos fractals power
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Order and Chaos
What is the difference between random events and
chaotic events?
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Introduction history chaos fractals power
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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.
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Order and Chaos
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• 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.

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Order and Chaos
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• 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.

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Feedback Loops
Introduction history chaos fractals power
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• Complex systems often have feedback loops
• Positive Feedback Loops
• (Fold a piece of paper 50 times. How big is the
  pile?)
• Negative Feedback Loops

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The Butterfly Effect
Introduction history chaos fractals power
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Ed Lorenz, 1963
Lypanov time for chaotic systems Increased energy
for longer predictability

• dx/dt-10x10y
• dy/dt30x-y-xz
• dz/dt-3zxy

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The Butterfly Effect
Introduction history chaos fractals power
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• Sensitivity to initial conditions

Predictability Does the Flap of a Butterflys
Wing in Brazil Set off a Tornado in Texas?, 1979
What other systems might be sensitive to initial
conditions?
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The Butterfly Effect
Introduction history chaos fractals power
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Attractors
Introduction history chaos fractals power
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• Point attractor
• Cyclic attractor (limit cycle) fish in a lake

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Attractors
Introduction history chaos fractals power
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• Chaotic attractor or strange attractor
• far from equilibrium, maintains its own structure

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Strange Attractors
Introduction history chaos fractals power
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The Fitness Landscape Bifurcation Catastrophe
Theory - Renee Thom
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The Edge of Chaos
Introduction history chaos fractals power
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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
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Order and Chaos
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• 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 moments
  inattention and the system lapses into chaos.

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Order and Chaos
Introduction history chaos fractals power
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• A runner can also be at the edge of chaos.

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Emergence
Introduction history chaos fractals power
laws small world networks complex adaptive
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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.
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Order and Chaos
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• Read this short article from the website of the
  City Council of Littleton, Colorado.

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The Edge of Chaos
Introduction history chaos fractals power
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systems others discussions

• 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?

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Swarms
Introduction history chaos fractals power
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• 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

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Swarms
Introduction history chaos fractals power
laws small world networks complex adaptive
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Ant colonies Bee hives Practical
Uses Movies Trucking companies Telephone
rerouting Military robots

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Fractals
Introduction history chaos fractals power
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A scale free landscape
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Fractals
Introduction history chaos fractals power
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Fractals
Introduction history chaos fractals power
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Fractals
Introduction history chaos fractals power
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Scale free
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Fractal Coastlines
Introduction history chaos fractals power
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• 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?

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Fractal Dimensions
Introduction history chaos fractals power
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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 Cl
ouds 1.3 - 1.33 Snowflakes 1.7 Retina blood
vessels 1.7 Bacterial growth patterns 1.7 Lightn
ing 1.75 Mineral patterns 1.78
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Fractals
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

• 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?

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Fractals
Introduction history chaos fractals power
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systems others discussions
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Fractals
Introduction history chaos fractals power
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How does a tree grow to become a fractal pattern?
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Fractals
Introduction history chaos fractals power
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• Look at this fractal generated by a computer

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Examples of real world fractals
Introduction history chaos fractals power
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Turbulence
Introduction history chaos fractals power
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More Fractals
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Sierpinskis Triangle
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More Fractals
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Koch Snowflake
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The Mandelbrot Set
Introduction history chaos fractals power
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• 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 z2c

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The Mandelbrot Set
Introduction history chaos fractals power
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Zooming in on Mandelbrot Set
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Power Law Distributions
Introduction history chaos fractals power
laws small world networks complex adaptive
systems others discussions

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?
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Power Law Distributions
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Equal proportions between levels. X XX XXXX XXXXX
XXX XXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXX
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Power Law Distributions
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Power Law Distributions
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Paretos Law
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Power Law Distributions

• Introduction history chaos fractals power
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• 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, peoples
  income levels.

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Power Law Distributions

• Introduction history chaos fractals power
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• 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 wont go away? If we
  catch the worst criminals, do we just create
  opportunities for other criminals to take their
  place?

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Power Law Distributions

• Introduction history chaos fractals power
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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 didnt
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.
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Power Law Distributions

• Introduction history chaos fractals power
  laws small world networks complex adaptive
  systems others discussions

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
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• Introduction history chaos fractals power
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Power Law Distributions

• Zipfs 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.
  PnP1/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.

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Power Law Distributions
Introduction history chaos fractals power
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Fat tail graph

• Why are we so surprised by large scale
  catastrophes?

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• Introduction history chaos fractals power
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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.

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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?

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Power Law Distributions

• Introduction history chaos fractals power
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• 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.

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Power Law Distributions

• Introduction history chaos fractals power
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Rivers catch water from a widely distributed area
of land and take it efficiently to one river
mouth.
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Complexity Theory

• Introduction history chaos fractals power
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Small World Networks

• Introduction history chaos fractals power
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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
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Small World Networks

• Introduction history chaos fractals power
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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
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Small World Networks

• Introduction history chaos fractals power
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How might a network be most effectively linked?

• Random
• Hierarchical
• Sparse links
• Heavily linked

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Small World Networks

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Social Network Analysis
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Small World Networks

• Introduction history chaos fractals power
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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.
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Small World Networks

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Small World Networks

• Introduction history chaos fractals power
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• 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

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Small World Networks

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Small World Networks

• Introduction history chaos fractals power
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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 dont
know as well in other clusters, that can be very
useful.
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Small World Networks

• Introduction history chaos fractals power
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What are the strengths and weaknesses of a small
world network? The importance of strong and weak
links.
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Small World Networks

• Introduction history chaos fractals power
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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.
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Small World Networks

• Introduction history chaos fractals power
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There is no brain cell or part of the brain that
is in charge. The intense interactions between
brain cells allows the brains activity to
self-organise, enabling the emergence of thoughts
and feelings, a sense of self and other qualities
of our mind.
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Small World Networks

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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.
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• Introduction history chaos fractals power
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Small World Networks

How do international airline network works? It is
not efficient to have direct flights from Dunedin
NZ to Dunedin, Florida.
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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.
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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.
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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.

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Six Degrees of Separation

The Bacon Game Following from Stanley Milgrams
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.
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Six Degrees of Separation

Erdos Number Paul Erdos was a Hungarian
Mathematician who did important pioneering work
on small world networks. Scientists calculate
their Erdos number
By the number of links through collaborated
research papers to get back to Paul Erdos. Benoit
Mandelbrot is a 2 Stephen Hawking is a 3
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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.
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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.
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Tipping Points

• What factors would make a new dynamic more likely
  (or less likely) to spread through a network?

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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?

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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.
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Tipping Points

Coronation Street Harry Potter Bill Gates and
Microsoft
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Tipping Points

Fax machines could not reach a tipping point
until, enough people owned a fax machine.
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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.
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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.
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The Tipping Point

• Malcolm Gladwell
• Mavens trend setters
• Connectors know lots of people
• Sales people Sells ideas

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Complex Adaptive SystemsWolfram ClassesClass
1 Point AttractorClass 2 Cyclic AttractorClass
3 Strange Attractor
(Chaotic attractor)Class 4 Complex Adaptive
SystemAll living systems are complex adaptive
systems.
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Complex Adaptive SystemsSanta Fe
Instituteestablished in the 1980s Chris
Langton Stuart Kaufmann
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Introduction history chaos
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• Complex Adaptive Systems
• So, What is Life.?

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Entropy
Introduction history chaos fractals power
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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.
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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
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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.

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Introduction history chaos
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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.
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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.)

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• 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.

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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?
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• 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

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• 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.

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• 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)

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• 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.

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• 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.

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• Complex Adaptive Systems
• Autopoiesis
• Humberto Maturana and Francisco Varela
• Mind - body - environment
• Structural Coupling
• The observer affects the system.

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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.

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Fuzzy Logic Aristotles 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.
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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.

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Fuzzy Logic We can create a continuum of
birdness.

0
Brick
Horse
Dog
0.25
Ostrich
Kiwi
0.5
Finch
Seagull
0.75
Eagle
1.00
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• Fuzzy Logic
• Human beings naturally work with fuzzy logic.
• Language is Fuzzy
• We use words like
• quite
• a lot
• not much
• rather
• sort of

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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.
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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
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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.
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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.

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Game Theory
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Game Theory
Try playing a few games. What strategies might be
effective?
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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. Sometime
s 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.
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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.
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Synchrony

• Complex Systems can self-organise towards
  synchorinising their rhythm.
• Circadian rhythms
• Fireflys
• heartbeats
• Steven Strogatz

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Cellular Automata

• John Van Neumann
  Stephen Wolfram
• One dimensional Cellular Automata
• Edge of Chaos Cellular Automata

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Cellular Automata
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Agent Based Modelling
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Complexity Theory Applications

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• 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?

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• 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

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• 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

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• 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.

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Final round, feedback and evaluation.
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The End