Four Ways of Thinking: Statistical, Interactive, Chaotic and Complex - David Sumpter

The speaker reflects on their career as an applied mathematician, emphasizing the secondary role of calculations in their work. They highlight their motivation to understand the world through mathematics as a toolkit. The talk promises to explore the speaker's thought process through four stages: statistical, interactive, chaotic, and complex thinking, using stories from football, science, and personal life to illustrate these concepts.

This section delves into the world of statistics, focusing on the importance of experimental design as illustrated by the historical figure Ronald Fisher. Fisher's work in combinatorics and his approach to tea-making experiments are highlighted as examples of using mathematics to solve real-world problems. The summary also touches on the limitations of statistical thinking, such as the inability to capture all aspects of a phenomenon, like a player's attitude in football.

The speaker discusses the limits of statistics in capturing the essence of success, using the example of 'grit' as a predictor of success from a TED Talk by Angela Duckworth. They point out that while grit may explain some variance in success, it is only a small percentage of the whole picture. The summary also addresses the misuse of statistical methods, such as by eugenics proponents, to defend flawed theories.

The narrative shifts to interactive thinking, introduced through the story of Alfred J. Lotka and his work on the dynamics of ecological systems like rabbits and foxes. The Lotka-Volterra equations are highlighted as a breakthrough in understanding the interactions between species and their periodic oscillations. The summary also touches on the broader applications of such models in various fields, including pandemic modeling.

This part of the talk explores the application of interactive thinking to social behaviors, such as applause in a seminar setting. The speaker describes an experiment involving students and the spread of applause through the audience, drawing parallels to epidemic curves. The summary emphasizes the importance of understanding social dynamics and the role of context in interpreting behaviors.

The speaker introduces chaos theory, sharing the story of Margaret Hamilton and her work on weather prediction models. The unpredictability of long-term weather patterns and the concept of the 'butterfly effect' are discussed. The summary reflects on the balance between control and acceptance of randomness in various aspects of life, including football and personal relationships.

In the final summary, the speaker discusses the concept of complexity, as defined by Kolmogorov, and its implications for understanding the world. They highlight the beauty of complexity in simple rules, using cellular automata models as examples. The talk concludes with an encouragement for younger researchers to embrace the complexity in their work and find inspiration in the intricate patterns that emerge from simple interactions.