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

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:

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

John A. Paulos — Avoiding Innumeracy (EP. 219)

Podcast Notes Playlist: Latest Episodes