Mastering Chaos with Pen and Paper  

The world in which we live is densely packed with randomness and disorder. From the stampede of pedestrians navigating a major intersection and meshing together at the zebra crossing, to a flock of blackbirds hovering above like a shapeless dark cloud. All seems random and without any sense of pattern. However, at a very fundamental level, all of these processes can be described by logic and equations; as once remarked by Galileo, “the order of the natural world is written in the language of mathematics”. 

 

Through the tireless efforts of natural scientists from across the world, over millennia we have developed a remarkable understanding of the nature of the physical world. At the atomic scale of quantum physics right up to the largest astronomical objects in our universe, physics can both describe the present and decisively predict the future and past of a system. This is all with a pinch of salt, of course, as we run into some serious issues where probability and uncertainty takes over at the quantum level (best saved for another feature article), however, by and large we are capable of determining how a rocket will launch into space and where it will land on dry land, thanks to this deterministic tool. 

 

This may seem like the end of the story, however, Mother Nature will not dispel all her secrets at once. In the past century, scientists studying random behaviour, such as how clouds move and disperse or how the small fluctuations in the stock market can be tracked, have been at a loss applying deterministic methods (i.e. methods where we can determine or predict the outcome from a few fixed starting conditions) to these systems. There seemed to be no way to accurately predict the evolution of the system through time. This began with the likes of Poincare fruitlessly predicting the future movement of the planets in our solar system at the request of a monarch, and later Lorenz with his breakthrough and accidental discovery of the mathematical field of chaos itself. 

 

“Chaos Theory” is the study of complex nonlinear dynamic systems. In other words, a reckoning with systems that display persistent randomness and a perceived lack of total predictability. There is a nuance to this, however, as a system can simultaneously appear ordered, yet harbour chaotic behaviour within (as Lorenz discovered). Alternatively the systems may seem entirely chaotic however it obeys certain patterns when looked at closely (such as the aforementioned flocking birds).

 

Among all the far reaching applications of Chaos Theory in describing the natural and human-made world, the most recent development has also been deemed worthy of the Nobel Prize. On Tuesday 5th October of this year, three leading scientists in their respective fields were awarded the title of the Nobel Prize, including a share in a $1.53 AUD million reward, by the Royal Swedish Academy of the Sciences. The Nobel recipients are Syukuro Manabe of Princeton University, Klaus Hasselmann of the Max Planck Institute for Meteorology, and Giorgio Parisi of Sapienza University of Rome. The prize itself was awarded “for groundbreaking contributions to our understanding of complex physical systems”, including “the physical modelling of Earth’s climate… and reliably predicting global warming”. This is the first occasion a Nobel Prize in Physics has been attributed to the field of environmental science and studying the future of the world’s changing climate, and initiates an interesting chapter in the interplay between research in physics, mathematics, and the global climate in decades to come. 

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Receiving one half of the total prize money, Professor Parisi was awarded for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales. Having been at the cutting edge of complex systems research since the 1980’s, Parisi observed hidden patterns in disordered complex materials. His discoveries in understanding and describing the behaviour of these seemingly random materials and phenomena has far reaching contributions into biology, neuroscience and machine learning. Parisi’s work provides a mathematical framework for studying the evolution of the global climate as an example of a complex system. 

 

The Earth’s climate is a complex system of vital importance to humankind. Professors Manabe and Hasselmann, two senior climate scientists, shared in the other half of the prize for their contributions in modelling the Earth’s climate system to reliably predict global warming and climate change. In the 1960’s, Professor Manabe led the development of physical modelling of the Earth’s climate, uniting previously separate models of the ocean and atmosphere to demonstrate how increased levels of carbon dioxide impact on temperature on the Earth’s surface. This has effectively laid the foundations of modern climate models used today. 

 

Professor Hasselmann followed this up with research of his own a decade later, finding a link between local weather and climate. Hasselmann and his colleagues produced a model which described why climate models can be reliable despite weather being changeable and chaotic, and his work has been used to prove that the increased temperature in the atmosphere is due to human emissions of carbon dioxide. 

 

The decades-long work of all three Nobel Laureates fundamentally shaped our understanding and ability to predict how the chaotic and interwoven behavior of the atmosphere, oceans and land will change over time, and strengthen our understanding of the changing climate on our planet. As put by the Nobel Committee for Physics, their discoveries demonstrate that our knowledge about the climate rests on a “solid scientific foundation”, one which can only grow with future generations of climate scientists, physicists and inquirers of the world under a scientific lens. 

 

The world in which we live is a random and chaotic one. Despite this sea of unpredictability, a deeper understanding of its mathematical nature can reveal patterns which have far reaching ramifications to our society and even our existence on planet Earth. The Nobel Prize in Physics is one significant step toward greater understanding of real-world complex systems which impact us, and a deeper recognition of the impact we have upon the Earth’s climate. Our ability to understand complex systems is one of a myriad of stepping stones into the great unknowns of science. To those turning away from studies in mathematics and physics for their seemingly abstract and complex nature, the future of our society is written in these laws and it is up to us to master them with pen and paper.