Simpson's Paradox
A Drug Trial Gone Wrong A hospital tests a new drug. Among patients who received it, 78% recovered. Among those who didn’t, 83% recovered. The drug appears harmful. But look a... Leaky Locks
What Counts as Information? In 1943, the telephone in Winston Churchill’s war room was a problem. Transatlantic calls to Roosevelt were encrypted by SIGSALY, fifty tons of equ... The Prophet Filter
Ten Correct Predictions You receive an email from someone you’ve never heard of. The subject line: “The market will close up tomorrow.” You ignore it. But the next day, you ch... Why Dividing Two Random Numbers Reveals π
Where More Data Doesn’t Mean More Certainty Take two random numbers and divide them. Do it again. And again. Now average the results. Does the number settle down? No matter... Edges, Vertices, and the Limits of Routing
From Roads to Routes Can you draw this figure in one continuous stroke without lifting your pen, and without retracing any line? What looks like a children’s puzzle is one of ... Global Warming and Diversity Cooling
The Same Collapse, Twice When a gas cools, its molecules slow down. They explore fewer states. The number of possible configurations drops. Entropy decreases. When an ecosyste... De Méré's Dice Paradox
When $1+1$ Is Not $2$ In 1654, a French nobleman named Antoine Gombaud—better known as the Chevalier de Méré—had a problem. Two gambling wagers that seemed identical by his rea... How Long Until the Bus?
Catch It If You Can You arrive at the stop. The sign says buses come every 10 minutes. Your watch says you should be fine. But the street is empty. Five minutes pass. Seven. A... Pushforwards and Pullbacks
The Die and the Question Roll a die. You get a 4. Now I ask: “Is it even?” Something just happened that’s easy to miss. The randomness moved. It started in a space of six fac... Frequentist Slices, Bayesian Shadows
The Same Model, Two Different Answers You fit a regression model predicting tree growth from elevation and soil moisture. You want to know: how does elevation affect growth? A...