Explore the fascinating world of chaos theory and unpredictability in this captivating lecture by Professor Jens Marklof. Delve into the mathematical principles behind chaotic systems, from weather forecasts to political developments. Examine the butterfly effect and its implications for climate modeling and extreme weather prediction. Investigate the concept of determinism versus chance through experiments with coin tosses and dice. Discover how kneading dough serves as a simple model for generating randomness, and learn about exponential sensitivity in chaotic systems. Explore applications in statistical mechanics, including the Boltzmann gas and Lorentz gas models. Gain insights into the mathematics of ergodic theory and dynamical systems. Conclude with practical applications and recommendations for further study in this thought-provoking exploration of predicting the unpredictable.
Chance and Chaos - How to Predict the Unpredictable by Jens Marklof
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
WHEN: 4:00 pm to pm Sunday, 11 December 2022
Start
Introduction
Speaker Introduction
Chance and chaos: how to predict the unpredictable
KAAPI WITH KURIOSITY
The butterfly effect
Climate modelling and extreme weather prediction
The deterministic universe, chance and chaos
Unpredictability
Example: The fair coin toss
The perfect coin tosser
Let's do an experiment with dice!"
Kneading dough: a simple model for generating randomness
Step 1: Place test raisins in the dough.
Step 4: Continue repeating Steps 2 and 3.
Exponential sensitivity, and the amplification of randomness
A mathematical theorem
The grand challenge
Helpful chaos: Boltzmann's statistical mechanics
The Boltzmann gas:
The Lorentz gas
The Lorentz gas and Brownian motion
A typical Brownian path in three dimensional space.
Visibility in a forest
The Lorentz gas in a crystal
The distribution of free path lengths
Underpinning mathematics: ergodic theory and dynamical systems
Conclusions
Recommendations for further reading
Thank you
Q&A
Taught by
International Centre for Theoretical Sciences
