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Why fair coin flips end with one person owning almost everything: the yard-sale model of wealth
Give 60 people 100 coins each and let them trade by fair coin flips, with the stake a fixed share of the poorer person's wealth. Nobody has any skill or…
Why a microwave leaves cold spots: a standing wave 12.2 cm long, and a chocolate bar that measures the speed of light
Microwave ovens fill a metal box with radio waves 12.2 cm long. The waves bounce off the walls and add up into a standing wave, a frozen pattern of hot spots…
Why a skater spins faster when she pulls her arms in: angular momentum and r squared
A skater starts a slow spin with her arms wide, pulls them in, and blurs into a fast spin with no push from anything. The trick is a quantity that cannot…
Why an elephant doesn't eat 200,000 times more than a mouse: Kleiber's three-quarter law
A mouse is 200,000 times lighter than an elephant, yet the elephant burns only about 9,000 times more energy. In 1932 Max Kleiber found that resting metabolic…
Why Egyptians poured water on sand: the wet-sand trick for dragging giant stones
A wall painting in an Egyptian tomb shows 172 men hauling a colossal statue on a sledge, while one man pours water onto the sand in front of it. In 2014…
Why no walk can cross all seven bridges of Königsberg once: Euler's odd-places rule
Seven bridges, two islands, two river banks: in 1700s Königsberg nobody could find a walk crossing each bridge exactly once. Euler didn't search harder, he…
How astronomers find planets by their shadow: the dip in starlight
Most planets around other stars are far too faint to see directly, so astronomers watch the star instead. When a planet crosses its face, a tiny dark disc…
How babies find words in a stream of sound: transitional probabilities
Babies hear speech as one unbroken smear, with no gaps between words, yet somehow they start picking out words long before they can say one. One clue sits in…
Why dragging a bow makes a steady note: stick-slip and Helmholtz's travelling kink
A bow moves at a steady speed, yet the string under it vibrates in an exact rhythm hundreds of times a second. The secret is stick-slip: rosin grips the…
How your phone finds the quickest route: Dijkstra's shortest-path algorithm
Your phone finds the fastest route across millions of roads without trying them all. The trick is a rule Edsger Dijkstra devised in 1956: always finish the…
Why real coin flips look fake: streaks and the way we imagine randomness
Ask people to write down 100 random coin flips and they almost never include a streak of six, yet a real coin makes one about four times in five. Our gut…
Why a falling pole can be held up: feedback, and the PID controller
A pole on a cart wants to fall, and a controller that watches the lean and shoves the cart can hold it up. But how hard it pushes matters: too weak and it…