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