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Whats the use of chaos? Chris Budd

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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?

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

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Snow crystals

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The animal world

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The motion of the planets

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Galileo Pisa One of the first to realise this

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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

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Newton

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1686 In the Principia Newton showed that this order and pattern could be expressed by using mathematics Pendulum equation

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

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Neptune: discovered by maths Newtons law of gravitation

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Weather forecasting Navier-Stokes equations

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Laplaces 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!

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

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Clouds and the weather (after a week)

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El Nino Ocean temperature Year Climate change

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The stock market

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My dog

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Does this complex behaviour arise because nature is really complicated and unexplainable does it arise naturally from Newtons laws??? Or …….

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The Double Pendulum Motion can be Periodic in phase : predictable Periodic out of phase : predictable Chaotic : unpredictable

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Newtons laws apply to the double pendulum! Angle of top part Angle of bottom part

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Chaos Simple rules can lead to complex and unpredictable behaviour

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Poincare: discoverer of chaos

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The problems of being a town planner

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

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

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

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a = 2 Single point

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a = 3 Two points

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a = 3.55 8 points

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a = 3.8 Chaos

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So, whats the use of chaos?

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Chaos: Simple rules can give complex patterns Barnsley fractal fern

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Mandlebrot set Fractal mountain Computer graphics

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Turbulence: da Vinci New understanding of nature

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River delta

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Motion of the asteroids

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Chaos is the science of the 21 st Century!

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