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

Key Takeaways from the Talk:

On the Philosophy of Applied Mathematics:

• The speaker believes that although calculations are important, they are not the primary motivator for his interest in mathematics. Instead, it's the desire to understand the world using mathematics as a toolkit.

Four Stages of Thinking:

1. Statistical Thinking:

   • Ronald Fisher's work on experimental design exemplifies statistical thinking.
   • Fisher was interested in the practical application of mathematical ideas to real-world problems, such as determining whether Dr. Muriel Bristol could discern the difference between tea poured before or after milk.
   • Statistical analysis can measure aspects like a football player's performance after their team concedes a goal.

2. Interactive Thinking:

   • Alfred J Lotka is noted for his contributions, conceptualizing interactions in terms of unbalanced reactions, like interacting populations of predators and prey.
   • Applied to modern contexts, interactive thinking helps understand phenomena such as fish behavior and football player movements.

3. Chaotic Thinking:

   • Margaret Hamilton, who worked with Edward Lorenz, discovered that tiny variations in input data could lead to vastly different outcomes in weather prediction models.
   • This sensitivity to initial conditions is known as chaos theory and has implications for situations we cannot control, like the inherent randomness in a football match.

4. Complex Thinking:

   • The speaker hints at the concept of complexity, mentioning the creations of Michael Hansen's cellular automata and Twitter-based graphics designed within 240-character limits.
   • Complexity is related to the length of the shortest description that can reproduce a pattern, as described by Andrey Kolmogorov.

Other Notable Points:

• The speaker emphasizes that while statistics and exact measurements are powerful tools, they can also have limitations. Context and qualitative aspects of problems matter.
• Fisher's and Lotka's ambitious, sometimes error-prone pursuits reveal that rigorous statistical and interactive models don't always lead to perfect predictions or comprehensive theories.
• The principles of chaos theory are expressed through an experiment with audience participation, demonstrating divergence from a simple mathematical process.
• The talk underscores the importance of balance between order and chaos in both science and personal life, using various analogies and personal stories.

The speaker concludes by emphasizing the importance of seeking succinct yet comprehensive descriptions to capture the complexity of the world.