Four Ways of Thinking

Introduction

• Science and mathematics are, in large part, about finding better ways of reasoning. This book describes four ways of getting nearer to the truth.
• Stephen Wolfram hypothesized that every process, biological or physical, personal or social, natural or artificial, lies in one of only four classes of behavior:
  • Stable systems - Are those that reach and stay at an equilibrium, like a ball rolling to rest.
  • Periodic systems - Are those that exhibit repeating patterns, like walking or cycle or our daily routines
  • Chaos - Is unpredictable, life the weather or the roll of a dice or the flip of a coin
  • Complexity - Is like the rise and fall of civilizations, the structure of governments or multinationals
• Sumpter suggests there are only two types of worthwhile arguments:
  • Class 1, which reach a stable resolution and class 4, where important ideas are discussed but may never be resolved.
  • Class 2, recurrent bickering over the same point and class 3, chaotic back and forths, should be avoided
• Classes 1-3 are about solving everyday problems. Class 4, complex thinking is more focused on introspection and self-reflection.

Statistical Thinking

• American researchers after the war invented the methods for handling, processing and understanding information, and now we are using our skills to feed entropy to the masses.
• While the mean is the average of a set of values, the median is the middle value in the set.
• Statistical thinking about our health works.
• There is just one correct way of making measurements and treating data, hidden within infinitely many incorrect ways.
• We cannot know, from cross-country comparison data alone, which factors cause happiness or merely happen to correlate with it. We don't know if better healthcare or better social support causes an increase in happiness, or if nations in which people have developed a more positive outlook on life build better healthcare and social support. What we do know is that people in more stable, more prosperous countries with greater social support tend to describe themselves as happier.
• Statistical significance is a measure of the probability that results of a study would have arisen by chance. Small differences can be explained by chance.
• Effect size is the impact of the identified difference. If I buy this am I significantly happier? If not, then the effect size is small.
• All three aspects - causality, statistical significance, and effect size must hold, for a study to have value.
• In any good scientific research group or community, a balance is needed between the contrarians and the less individualistic majority who push for consensus. We want our hypotheses to be challenged, but we don't want to be paralyzed by uncertainty; We want to get as close as possible to the truth, given the limited time and resources we have to collect data and conduct experiments.
• Many of the inspirational ideas which permeate our collective consciousness have only very limited application to you as an individual. Positive psychology interventions - like asking participants to write down all the good things that happened to them during a day - can be helpful for some, but they explain only around 1% of the variance between people.
• Numbers are essential to understanding humanity, but they are not enough if we want to know about ourselves and those around us as individuals.
• The way to find connections is to change our point of view. Instead of seeing the world from above, as if we were all-powerful and all-knowing, we should see it from below. We should realize there is more than one way of thinking about the world.