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What’s the use of chaos? Chris Budd

What’s the use of chaos? Chris Budd. Is life predictable or unpredictable?. Can we tell what is going to happen In the next second? In the next hour? In the next year?. Does nature have an underlying order and pattern?. First answer …. YES!.

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What’s the use of chaos? Chris Budd

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  1. What’s the use of chaos? Chris Budd

  2. Is life predictable or unpredictable? • Can we tell what is going to happen • In the next second? • In the next hour? • In the next year? Does nature have an underlying order and pattern?

  3. First answer …. YES! Science is the search for order and pattern in the universe If we look we can see order and pattern all around us …..

  4. Snow crystals

  5. The animal world

  6. The motion of the planets

  7. One of the first to realise this Galileo Pisa

  8. 1600 Galileo watched a pendulum swing and realised that it was governed by predictable laws • Swing time of the pendulum was constant • Regardless of how it was pushed • Or where it was • Or when

  9. Newton

  10. 1686 In the PrincipiaNewton showed that this order and pattern could be expressed by using mathematics Pendulum equation

  11. Key idea …. • Write down the equations describing a physical system • Solve the equations • Predict the future Does this work?

  12. Newton’s law of gravitation Neptune: discovered by maths

  13. Navier-Stokes equations Weather forecasting

  14. Laplace’s prediction … If we were to know the exact position of every particle in the universe then we could predict the future with certainty No room here for free will!

  15. Lots of natural and human events seem to be very unpredictable!! Do you feel lucky?

  16. Clouds and the weather (after a week)

  17. Ocean temperature Year Climate change El Nino

  18. The stock market

  19. My dog

  20. Does this complex behaviour arise because nature is really complicated andunexplainable Or ……. does it arise naturally from Newton’s laws???

  21. The Double Pendulum Motion can be • Periodicin phase :predictable • Periodicout of phase : predictable • Chaotic :unpredictable

  22. Newton’s laws apply to the double pendulum! Angle of top part Angle of bottom part

  23. Chaos Simple rules can lead to complex and unpredictable behaviour

  24. Poincare: discoverer of chaos

  25. The problems of being a town planner

  26. Can we predict the population of a town? Population Year Population of the town in the year n Can we relate this years population: To next years population:

  27. Malthus …. Birthrate/Deathrate • a = 1 … population stays constant • a > 1 … population increases • a < 1 … population decreases

  28. Problem … population runs out of resources Improved model proposed by May Maximum population What does this predict?

  29. a = 2 Single point

  30. a = 3 Two points

  31. a = 3.55 8 points

  32. a = 3.8 Chaos

  33. So, what’s the use of chaos?

  34. Chaos: Simple rules can give complex patterns Barnsley fractal fern

  35. Computer graphics Fractal mountain Mandlebrot set

  36. New understanding of nature Turbulence: da Vinci

  37. River delta

  38. Motion of the asteroids

  39. Chaos is the science of the 21st Century!

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