Israeli Air Force instructors told Daniel Kahneman that cadets praised after an excellent landing did worse next time, while those who were scolded improved. In truth, neither blame nor praise had much to do with it: after an exceptional performance, good or bad, the next one naturally drifts back toward the average. Francis Galton had already described this phenomenon in the 19th century.
How many different structures can you build with six classic 2-by-4 Lego bricks of the same colour? The company used to quote just over 102 million. In 2005, Danish mathematician Søren Eilers recounted everything by computer: 915,103,765 combinations. The official estimate had been too low by a factor of about nine.
Fold an A4 sheet in half and you get an A5 with the same proportions. That only works for one ratio between length and width: about 1.414, the square root of 2. The A0 format measures exactly one square metre, and A4 is a sixteenth of it. With standard 80-gram-per-square-metre paper, an A4 sheet therefore weighs exactly 5 grams.