Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Gandhi is famous as a pacifist who led India to independence from the United Kingdom. But since 1991, he has also gained a reputation as a warmonger leader who launches unprovoked nuclear strikes. This is because of the Civilization computer games, which have sold over 33 million copies. They pit you against several world leaders from history in a race to build the greatest civilization, one of whom is the normally peace-loving Gandhi. But ever since early versions of the game, players noticed that Gandhi was a bit of a jerk. Once he developed atomic technology, he would start dropping nuclear bombs on other nations. This was because of a mistake in the computer code. The game designers had deliberately given Gandhi the lowest non-zero aggression rating possible: a score of 1. Classic Gandhi. But later in the game, when all the civilizations were becoming more, well, civilized, every leader had their aggression rating dropped by two. For Gandhi, starting from 1, this calculation played out as 1 − 2 = 255, suddenly setting him to maximum aggression. Even though this error has since been fixed, later versions of the game have kept Gandhi as the most nuke-happy leader as a tradition. The computer was getting an answer of 255 for the same reason computers have trouble keeping track of time: digital memory is finite. The aggression ratings were stored as an 8-digit binary number. Starting at 00000001 and counting down two gave 00000000 and then 11111111 (which is 255 in normal ...