A three-rotor Enigma machine on display at the National Cryptologic Museum of the American security agency. At the top, the rotors; in the middle, the lamps; below, the keyboard; at the front, the plugboard.National Security Agency · Wikimedia Commons · public domain The Enigma looked like a typewriter inside a wooden box. The operator pressed a letter on the keyboard and another letter lit up on a panel of lamps. A second operator wrote down the letters that lit up, and that sequence was sent by radio, in Morse code. At the other end, an operator with an identical machine, set up the same way, typed in the enciphered message and read the original text on the lamps.
The bombe was fast, but not fast enough to test every rotor order of the naval Enigma. In 1940 Turing invented a pencil-and-paper method to rule out most of them before switching on the machines. Because the sheets used in the method were printed in the town of Banbury, his colleagues named it Banburismus. The method is statistical. And to devise it, Turing reinvented one of the central ideas of modern statistics.