1. Making sense of a complex world
Chris Budd

2. Many natural (and human
Many natural (and human!) systems appear complex and hard to understand
National Electricity Grid

3. Atmosphere and climate
Clouds
El Nino

4. Turbulence
Flocking
Geology

5. Complex designs
Aircraft undercarriage

6. Human behaviour
Crowds

7. What makes a system complex ?
Many components with individual behavior
Coupling between components
Many different scales in space and time

8. Can scientists, mathematicians and engineers make any sense of complexity?
And can we use this knowledge to our advantage?

9. Traditional view
Things are complicated because there are lots of independent things all going on at once

10. A complicated example: The tides
Bombay tides 1872
h(t) t

11. Kelvin decomposed h(t) into 37 independent components
He found these out using past data and added them up using an analogue computer

12. Kelvin’s Tidal predictor
US Tidal predictor

13. 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!

14. 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

15. 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

16. Aircraft undercarriage can be very similar

17. 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

18. 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

19. Coherent Patterns

20. Emergent Patterns often arise because of the way that things interact and communicate with each other
Flocking
Slime mould
All described using mathematical equations

21. Patterns in rocks

22. Crowds at a scramble crossing

23. Scaling laws

24. Microstructure of a ceramic. Al2O3-TiO2

25. Frequency
Conductivity

26. The ac conductivity of 255 2D squae networks randomly
filled with 512 components 60% 1 k resistors
& 40% 1 nF capacitors
Frequency
PERCOLATION
DETERMINED DC
CONDUCTIVITY
POWER LAW
EMERGENT
PROPERTY
Random
Conductivity
Emergent scaling law

27. We see examples of scaling laws in many other complex systems:
Homogeneous system
The Internet
Epidemics
Mechanical systems
Rocks and water

28. 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

29. Bringing this all together … forecasting the weather
The atmosphere/ocean is a very complex system with many length and time scales

30. 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!

31. 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!!

32. 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!!!

33. Eg. The digestive system
Stomach
Intestine
Intestinal wall:
Villi and Microvilli