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Why the most common word is twice as common as the next: Zipf's law
Sort every word in a book from most to least common and a pattern appears: the top word is about twice as common as the second, three times as common as the…
Why sand on a vibrating plate draws pictures: Chladni figures
Sprinkle sand on a thin metal plate, draw a violin bow along its edge, and the sand leaps into sharp, symmetrical lines. Change the pitch and the picture…
How a computer finds one flipped bit and fixes it: Hamming's code
A bit can flip in memory, on a disk or in a radio signal, and nothing tells you which one went wrong. In 1950 Richard Hamming published a code that finds the…
Why you can't hold 12 digits but can hold 3 years: working memory chunks
Try to hold 149217891945 in your head and it slips away. Read it as 1492, 1789, 1945 and it sticks. The digits are the same; the number of things to hold is…
Why a squeezed ruler bows sideways: Euler's buckling and the hollow tube
Squeeze a ruler between your palms and it doesn't crush: it bows sideways and gives way. That's buckling, and it decides how slender a column can be. Euler…
Why rival ice-cream carts end up side by side: Hotelling's beach
Put two ice-cream carts on a long beach and each one is tempted to creep toward the other, because standing next to a rival steals customers without losing…
Why popcorn pops: a pea-sized pressure cooker that gives way at 180 °C
A popcorn kernel is a pressure cooker the size of a pea. Its tough hull seals in about 14% water, so as the pan heats, the water cannot boil away and the…
Why a dried coffee drop leaves a ring: the edge is stuck and the rim dries first
Spill coffee, let it dry, and you get a dark ring with a pale middle, not an even stain. The pigment started out spread through the whole drop. The drop's edge…
Why fishing less gave the Adriatic more sharks: foxes, rabbits and a loop
When fishing slowed during the First World War, the Adriatic catch held a bigger share of sharks and rays, not a smaller one. Mathematician Vito Volterra…
Why washing hands saved mothers in 1847: Semmelweis and the two wards
In 1846, mothers in one Vienna maternity ward died at four times the rate of mothers in the ward next door. The doctors' ward was losing 11.4% of its patients…
Why 1 leads far more often than 9: Benford's law of first digits
Look only at the first digit of any long list of real-world numbers, such as river areas, populations or the figures in a company's accounts. You'd expect each…
Why the Moon always shows us the same face: tidal locking
The Moon does spin. It turns exactly once for every trip around the Earth, so the same face always points our way. Walk around a chair while always facing it…