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 valueApophenia: The phenomenon of seeing patterns where none exist as a form of cognitive bias or psychological tendencyHumans 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 cooperatedCognitive 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 competenceThe concept of “nudging” involves subtly influencing people’s decisions by altering the presentation of choices without restricting options or significantly changing incentivesIt is wise to develop a particular skepticism and wariness about the uncertainties of life Read the full notes @ podcastnotes.orgProfessor, 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