Alan Turing · Mathematics
Turing’s war - how he led the codebreaking effort against the German Enigma cipher at Bletchley Park, designed the Bombe machine that cracked it, and helped change the course of the Second World War.
When the Second World War broke out in 1939, Alan Turing - by then known among mathematicians for his work on computability - was recruited into Britain’s secret codebreaking establishment at Bletchley Park, a country house north of London where a remarkable assembly of mathematicians, linguists, chess champions, and crossword experts laboured in total secrecy to break the ciphers of Nazi Germany. The stakes could scarcely have been higher. Germany’s armed forces encrypted their radio communications - orders to U-boat wolfpacks hunting the Atlantic convoys, army and air-force movements, naval deployments - using cipher machines the Germans believed were unbreakable. If the Allies could read these messages, they would gain an almost unimaginable advantage; if they could not, Britain might be starved into surrender by the U-boat blockade. Turing was assigned to the hardest and most important target: the naval Enigma, the cipher protecting the very U-boat communications on which the Battle of the Atlantic turned. Over the next years, his mathematical genius, applied to this brutally practical problem of war, would help turn the tide. It is one of history’s most dramatic demonstrations that abstract mathematics, pursued for its own sake, can prove decisive in the most concrete of human affairs - and that a man who had been thinking about the foundations of computation could, when his country needed it, break the codes that helped win a war.
To appreciate Turing’s achievement, one must understand the Enigma machine itself. It looked like a typewriter in a wooden box. When an operator pressed a key, an electrical current passed through a series of rotating wheels - the rotors - each of which scrambled the signal by rewiring the alphabet in a complex way, then through a reflector that sent the current back through the rotors again, finally lighting up a lamp showing the enciphered letter. Crucially, after each keypress the rotors turned, so that the wiring changed for every single letter: press ‘A’ twice in a row and you would usually get two different enciphered letters, defeating the simple frequency analysis that breaks ordinary ciphers. The total scrambling depended on which rotors were chosen and in what order, their starting positions, the wiring of a plugboard that swapped pairs of letters, and the ring settings - and the Germans changed these settings every day, according to secret monthly key-sheets. The number of possible configurations was so vast, and changed so frequently, that the Germans were confident Enigma was unbreakable: even if the enemy captured a machine and knew exactly how it worked (which they did), they would still have to find the daily settings from among the astronomical number of possibilities, afresh, every single day, before the messages became useless. The security of Enigma rested not on secrecy of design but on the impossibility, as the Germans saw it, of searching so enormous a space in time to matter. Turing’s task was to make the impossible possible - and to do it anew each day.
Turing’s great practical creation at Bletchley was the Bombe - an electromechanical machine, refining an earlier Polish device (the bomba) built by the brilliant Polish cryptanalysts who had first broken Enigma before the war and shared their methods with Britain and France. Turing’s redesigned Bombe was a method made into a mechanism. Given a crib - a guessed plaintext-ciphertext correspondence - Turing’s analysis produced a logical chain of deductions about the rotor wirings, in which certain settings would lead, if assumed, to a logical contradiction, and could therefore be eliminated. The Bombe was built to test settings at high speed, racing through the rotor positions and, for each, electrically checking whether the crib’s chain of letter-relationships was logically consistent or led to a contradiction. When it found a setting that did not produce a contradiction, it stopped: this was a candidate for the day’s true setting, to be checked by hand. By mechanising this process of elimination, the Bombe could reduce the astronomical space of settings to a tiny handful of candidates in hours rather than the millennia a blind search would require. Banks of Bombes, operated around the clock largely by women of the Women’s Royal Naval Service, broke Enigma keys daily for much of the war. The Bombe was not a general-purpose computer - it did one specialised job - but it embodied the principle that would define computing: the mechanisation of a complex logical process, the automation of reasoning itself. In designing a machine to defeat a machine, Turing took another step from the abstract universal machine of 1936 toward the physical computers that the war effort, partly at Bletchley, was beginning to build.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned how Turing led the attack on the Enigma cipher at Bletchley Park, designing the Bombe machine to break it. Explain how Enigma worked, how Turing’s method defeated it, and why this mattered for the war and for computing.
Leads to Blaise Pascal.
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