Peter Saunders, Co-Director of The Institute of Science in Society, London, and Emeritus professor of Applied Mathematics, King’s College London, provides a thorough and interesting overview of catastrophe theory and its many real and relevant applications.
Saunders holds a BA in Applied Mathematics from the University of Toronto as well as a PhD in Theoretical Astrophysics from the University of London. He is a sought-after lecturer and keynote speaker and has presented his findings and theories for many groups and events, notably at Queen Elizabeth College and then at King’s College.
Saunders discusses the etymology of the word, ‘catastrophe,’ and discusses the background of catastrophe theory. Saunders explains that catastrophe theory is a theory that allows us to deal mathematically with things that change suddenly. And as he states, things that change suddenly are often the most interesting. He details catastrophe theory, explaining that if you have a system that is displaying certain jumps of one kind or another that these jumps will occur in a pattern. Saunders outlines the five basic properties that tend to go together: sudden jumps, hysteresis, divergence, inaccessibility, and bimodality. As Saunders explains, when you observe one, you begin looking for the other four. He talks about the many applications of the theory and how it enables researchers to come to conclusions within their research.
Saunders explains that when a researcher is considering what has been observed, he or she makes a statement, and what is most desired is a theory that enables one to take that statement, that is based on observable actions, and do something with it. He discusses the relevance to applied mathematicians, and elaborates on how they seek to utilize what they do know, and little else, so their applications are based on truth. Saunders discusses the many possible applications for catastrophe theory, and he specifically talks about utilizing the theory to study important issues such as climate change. He provides interesting examples, regarding extreme fluctuations and how they can be indicators of increasing instability in regard to climate changes. As he explains catastrophe theory doesn’t provide absolute proof, but in fact it only provides signs and indicators. Saunders states that if you want absolute proof, the only way to get that is to sit back and let something happen, but by then it will be too late to prevent that ‘something’ from happening.
Saunders’ groundbreaking book on the subject, An Introduction to Catastrophe Theory, breaks down catastrophe theory for everyone, even those who may have only a basic understanding of mathematics. The book explains the basic tenets of the theory and discusses practical applications, often citing biological science examples due to their particular ability to demonstrate catastrophe theory’s distinctive nature. The celebrated book is a good read for theoretical biologists, scientists in general, and anyone who has an inquisitive mind and seeks to learn more about the theory and its applications.