Making sense of a complex world

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Making sense of a complex world Chris Budd
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Many natural (and human!) systems appear complex
and hard to understand
National Electricity Grid
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Atmosphere and climate
Clouds
El Nino
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Turbulence
Flocking
Geology
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Complex designs
Aircraft undercarriage
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Human behaviour
Crowds
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What makes a system complex ?
Many components with individual behavior Coupling
between components Many different scales in space
and time
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Can scientists, mathematicians and engineers make
any sense of complexity? And can we use this
knowledge to our advantage?
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Traditional view
Things are complicated because there are lots of
independent things all going on at once
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A complicated example The tides
Bombay tides 1872
h(t)
t
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Kelvin decomposed h(t) into 37 independent
components
He found these out using past data and added them
up using an analogue computer
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US Tidal predictor
Kelvins Tidal predictor
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In the tides we see complicated behaviour due to
a large number of independent uncoupled systems
combining their effects The tides are a
resultant property of this combination
But many examples of complexity in nature are not
like this!
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The Double Pendulum .. An example of complex
behaviour in a simple coupled system
Motion can be

• Periodic in phase predictable
• Periodic out of phase predictable
• Chaotic unpredictable

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Each part of the system is relatively simple,
with easy to understand behavior
It is the coupling which leads to new complex
emergent behavior which we understand by using
maths
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Aircraft undercarriage can be very similar
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Emergence .. A property of a complex system which
is more than the sum of its parts
Emergence arises from the way that the components
interact with each other and not just from their
individual properties
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Emergent properties of complex systems can allow
us to make predictions and even to new designs.
They include

• Coherent Patterns ..
• Much of science and maths involves the search
  for, and study of, these patterns
• Scaling laws

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Coherent Patterns
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Emergent Patterns often arise because of the way
that things interact and communicate with each
other
Flocking
Slime mould
All described using mathematical equations
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Patterns in rocks
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Crowds at a scramble crossing
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Scaling laws
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Frequency
Conductivity
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Frequency
Random
Conductivity
Emergent scaling law
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We see examples of scaling laws in many other
complex systems

• The Internet
• Epidemics
• Mechanical systems
• Rocks and water

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A very complex example .. The H Bomb
r Radius of fireball E Energy of the bomb t
Time after the explosion
Scaling law
G I Taylor
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Bringing this all together forecasting the
weather
The atmosphere/ocean is a very complex system
with many length and time scales
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Need to make predictions but

• System has far more degrees of freedom than data
• Small scale behavior is very can be chaotic
• Small and large scales interact
• Lots of random events

Turbulence

• Computations are hard!

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Make use of all of the previous ideas to improve
predictability
Scaling laws show how energy is transferred from
small to large scales and from small heights to
large heights and greatly speed up computations
Fit coherent patterns of weather eg. depressions
to the sparse data to start and monitor computer
weather forecasts (data assimilation)
1987!!
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Complexity .. May apply to many many other
problems Where many things interact with each
other

• Spread of disease
• Customer behavior
• Transport networks
• The national grid
• Chemical reactions

Much still to be discovered!!!
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Eg. The digestive system
Stomach
Intestine
Intestinal wall Villi and Microvilli