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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

ComplexityA new perspective for the 21st century

Introduction history chaos fractals power

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- 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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- 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

ComplexityA new perspective for the 21st century

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- 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?

A Short History of Science

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- Gallileo Gallilei Johannes Kepler Sir

Isaac Newton

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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.

A Short History of Science

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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.

A Short History of Science

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- Henri Poincaré and the three body problem

A Short History of Science

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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.

A Short History of Science

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- 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.

Chaos Theory

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Chaos Theory

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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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Order and Chaos

What is the difference between random events and

chaotic events?

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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.

Order and Chaos

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- 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.

Order and Chaos

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- 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.

Feedback Loops

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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

The Butterfly Effect

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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

The Butterfly Effect

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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?

The Butterfly Effect

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Attractors

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- Point attractor
- Cyclic attractor (limit cycle) fish in a lake

Attractors

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- Chaotic attractor or strange attractor
- far from equilibrium, maintains its own structure

Strange Attractors

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The Fitness Landscape Bifurcation Catastrophe

Theory - Renee Thom

The Edge of Chaos

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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

Order and Chaos

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- 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.

Order and Chaos

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- A runner can also be at the edge of chaos.

Emergence

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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.

Order and Chaos

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- Read this short article from the website of the

City Council of Littleton, Colorado.

The Edge of Chaos

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- 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?

Swarms

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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

Swarms

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Ant colonies Bee hives Practical

Uses Movies Trucking companies Telephone

rerouting Military robots

Fractals

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A scale free landscape

Fractals

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Fractals

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Fractals

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Scale free

Fractal Coastlines

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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?

Fractal Dimensions

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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

Fractals

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- 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?

Fractals

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Fractals

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How does a tree grow to become a fractal pattern?

Fractals

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- Look at this fractal generated by a computer

Examples of real world fractals

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Turbulence

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More Fractals

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Sierpinskis Triangle

More Fractals

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Koch Snowflake

The Mandelbrot Set

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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

The Mandelbrot Set

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Zooming in on Mandelbrot Set

Power Law Distributions

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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?

Power Law Distributions

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Equal proportions between levels. X XX XXXX XXXXX

XXX XXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX

XXX

Power Law Distributions

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Power Law Distributions

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Paretos Law

Power Law Distributions

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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.

Power Law Distributions

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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?

Power Law Distributions

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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.

Power Law Distributions

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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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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.

Power Law Distributions

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Fat tail graph

- Why are we so surprised by large scale

catastrophes?

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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?

Power Law Distributions

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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.

Power Law Distributions

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Rivers catch water from a widely distributed area

of land and take it efficiently to one river

mouth.

Complexity Theory

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Small World Networks

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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

Small World Networks

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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

Small World Networks

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How might a network be most effectively linked?

- Random
- Hierarchical
- Sparse links
- Heavily linked

Small World Networks

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Social Network Analysis

Small World Networks

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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.

Small World Networks

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Small World Networks

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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

Small World Networks

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Small World Networks

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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.

Small World Networks

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What are the strengths and weaknesses of a small

world network? The importance of strong and weak

links.

Small World Networks

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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.

Small World Networks

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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.

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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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

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.?

Entropy

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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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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)

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

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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.

Introduction history chaos

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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.

Introduction history chaos

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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.

Introduction history chaos

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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.

Introduction history chaos

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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

Introduction history chaos

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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.

Introduction history chaos

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Game Theory

Introduction history chaos

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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.

Introduction history chaos

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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

Introduction history chaos

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Cellular Automata

Introduction history chaos

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Agent Based Modelling

Introduction history chaos

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Complexity Theory Applications

Introduction history chaos

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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?

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

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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

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