Chance and Chaos: How to Predict the Unpredictable by Jens Marklof
KAAPI WITH KURIOSITY
CHANCE AND CHAOS: HOW TO PREDICT THE UNPREDICTABLE
SPEAKER : Jens Marklof (University of Bristol, UK)
WHEN: 4:00 pm to 5:30 pm Sunday, 11 December 2022
WHERE : Jawaharlal Nehru Planetarium, Bengaluru
Abstract:
We live in a chaotic world: from weather forecasts and natural disasters to political developments, it seems often impossible to even make the most basic predictions. In this lecture I will discuss one of the most fundamental mathematical principles behind such unpredictability: the inherent instability of systems with chaotic behaviour that leads to extreme amplification of the smallest errors in the data. In particular, I will explore with you the legendary question “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” (Lorenz 1972) and explain how chaos theory has established the best way of kneading bread dough! By the end of this lecture, I hope to have convinced you of the power of mathematical tools in the analysis of chaotic systems. But will these tools allow you to win the jackpot in the lottery? Come to my lecture and find out!
About the Speaker:
Professor Jens Marklof FRS is an international expert on the mathematical modelling of chaotic systems. His research has answered long-standing questions in quantum chaos, number theory and statistical physics. He graduated from the Universities of Hamburg and Ulm, and held research fellowships at Princeton University, Hewlett-Packard, the Isaac Newton Institute in Cambridge, the Institut des Hautes Etudes Scientifique and the Laboratoire de Physique Theorique et Modeles Statistiques near Paris. Jens Marklof is Professor of Mathematical Physics and Dean of the Faculty of Science at the University of Bristol, and a Fellow of the Royal Society. During the current academic year, he is visiting India as a Royal Society Yusuf Hamied Visiting Professor.
Table of Contents (powered by https://videoken.com)
0:00:00 Start
0:00:16 Introduction
0:04:53 Speaker Introduction
0:06:12 Chance and chaos: how to predict the unpredictable
0:06:39 KAAPI WITH KURIOSITY
0:07:57 The butterfly effect
0:09:14 Climate modelling and extreme weather prediction
0:10:22 The deterministic universe, chance and chaos
0:12:38 Unpredictability
0:14:19 Example: The fair coin toss
0:15:12 The perfect coin tosser
0:18:13 Let's do an experiment with dice!"
0:27:13 Kneading dough: a simple model for generating randomness
0:27:41 Step 1: Place test raisins in the dough.
0:28:49 Step 4: Continue repeating Steps 2 and 3.
0:29:21 Exponential sensitivity, and the amplification of randomness
0:31:58 A mathematical theorem
0:35:56 The grand challenge
0:37:07 Helpful chaos: Boltzmann's statistical mechanics
0:37:58 The Boltzmann gas:
0:40:55 The Lorentz gas
0:41:40 The Lorentz gas and Brownian motion
0:41:55 A typical Brownian path in three dimensional space.
0:42:33 Visibility in a forest
0:43:21 The Lorentz gas in a crystal
0:46:31 The distribution of free path lengths
0:47:19 Underpinning mathematics: ergodic theory and dynamical systems
0:47:45 Conclusions
0:51:17 Recommendations for further reading
0:51:46 Thank you
0:52:02 Q&A
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