Jordan Ellenberg's How Not to Be Wrong opened doors. These essays walk through them — exploring Kelly betting, ergodicity, Arrow's impossibility, Berkson's paradox, and more with working simulations, calculators, and games.
Part I: The Bets You Make
Mathematics of risk, ruin, and the irrational mind.
The Kelly Criterion
Why knowing how much to bet matters more than knowing what to bet on. The formula that keeps you from going broke even when you're right.
Ergodicity
The difference between the average and the actual. Why GDP per capita lies about your life, and what Ole Peters proved to the economists.
Gambler's Ruin
The mathematical certainty that the house wins. Not luck — the asymmetry of absorbing barriers.
Prospect Theory
Why cab drivers quit early on good days and work late on bad ones. Kahneman and Tversky's demolition of homo economicus.
Part II: When to Decide
The mathematics of optimal stopping, belief updating, and impossible voting systems.
Bayes' Theorem
The theorem that reads your mind and catches your cancer. Why a 99% accurate test doesn't mean 99% probability.
Optimal Stopping
When to stop looking and start choosing. The 37% rule for hiring, dating, and apartment hunting.
Arrow's Impossibility Theorem
Democracy is mathematically doomed — but vote anyway. Why no voting system satisfies three reasonable conditions.
Part III: Hidden Structure
Patterns that emerge from numbers, from Benford's Law to the birthday problem.
Benford's Law
The law that catches liars. How the first digit of a number reveals fraud, from Enron to election audits.
Power Laws
When the average doesn't exist. Why one earthquake can release more energy than all others combined.
The Birthday Problem
The coincidence that isn't. Why 23 people have a 50% chance of a shared birthday — and why this breaks encryption.
Regression to the Mean
The most important statistical concept you've never heard of. Why the Sports Illustrated cover jinx isn't a jinx.
Part IV: The Data Lies
When aggregation reverses trends, selection creates phantom correlations, and the dead don't talk.
Simpson's Paradox
When the data tells two opposite stories. Berkeley's 1973 admissions scandal and when to aggregate vs. disaggregate.
Survivorship Bias
The dead don't talk. Abraham Wald's armor problem, mutual fund illusions, and why you don't hear about failed dropouts.
Berkson's Paradox
The phantom correlation. Why attractive people seem to have terrible personalities and restaurants are food OR ambiance.
The Inspection Paradox
Why the bus is always late, your friends have more friends than you, and class sizes are larger than advertised.
Part V: Systems That Eat Themselves
When measures become targets, and the old outlast the new.
These essays extend Jordan Ellenberg's How Not to Be Wrong: The Power of Mathematical Thinking (2014). Each covers a concept Ellenberg might have written — with original research, working simulations, and hand-crafted illustrations. Built with math, not magic.