Infinite Loops

Key Takeaways * “Uncertainty is the only certainty.” – John Paulos * People use terms like millions, billions, and trillions as if they are the same thing; when in reality, these are vastly different amounts! * “We live in a probabilistic world, and yet we remain deterministic thinkers.” – Jim O’Shaughnessy * The Law of Large Numbers is a fundamental principle in probability and statistics that states that as the size of a sample increases, the average of the sample becomes closer to the expected value * Apophenia: The phenomenon of seeing patterns where none exist as a form of cognitive bias or psychological tendency * Humans are excellent pattern-recognition machines; but sometimes, we wrongly attribute patterns to random data that can lead us astray * The human operating system is more driven by the emotional centers of the brain than the rational centers of the brain * There is a tension between objective likelihood (probability) and subjective belief or reasonableness (plausibility) * The Prisoner’s Dilemma is a scenario in game theory where two individuals acting in their self-interest end up with a worse outcome than if they had cooperated * Cognitive foibles such as confirmation bias, the anchoring effect, and negativity bias should be taught in mathematical courses * Dunning-Kruger Effect: The phenomenon where people with low ability at a task overestimate their ability, while those with high ability underestimate their competence * The concept of “nudging” involves subtly influencing people’s decisions by altering the presentation of choices without restricting options or significantly changing incentives * It is wise to develop a particular skepticism and wariness about the uncertainties of life

Read the full notes @ podcastnotes.org


Professor, Mathematician and Writer John A. Paulos joins the show to discuss math education, the power of puzzles, cognitive biases, and MUCH more!

Important Links:

  • John’s Website
  • John’s Twitter

Show Notes:

  • Why Do People Hate Math?
  • The Power of Posing Problems with Counterintuitive or Shocking Results
  • Using Everyday Examples to Understand Math Concepts
  • Systems Designed to Take Advantage of Innumeracy
  • People’s Ignorance of Randomness and Random Samples
  • The Strange Power of Anchoring Bias
  • Tradeoffs between Probability and Plausibility
  • The Prisoner’s Dilemma & Math Anxiety
  • Improving the Monty Hall Problem
  • Designing an Ideal Intro Math Course
  • The Big Brother Aspect of Nudging
  • John as Emperor of the World
  • MORE!

Books Mentioned:

  • Innumeracy - Mathematical Illiteracy and Its Consequences; by J.A. Paulos
  • A Mathematician Plays the Stock Market; by J.A. Paulos
  • A Mathematician Reads the Newspaper; by J.A. Paulos
  • Statistics; by D.A. Freedman, R. Pisani, and R.A. Purves
  • Thinking Fast and Slow; by Daniel Kahneman