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Authors: Hervie Haufler
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as an unsolvable mathematical problem.
The second Cambridge lecturer who most influenced Turing's thinking was Maxwell H. A. "Max" Newman, who asked if there wasn't a mechanical process that could put mathematical theorems to the test.
From this point on, Turingâin the words of his biographer Andrew Hodgesâ"dreamed of machines." In the early summer of 1935, when he was just twenty-three years old, he saw his answer. He created a theoretical "universal machine"âafterward known as the Turing machineâthat could, by using the binary system that later became the basis for digital computers, replicate logical human thought. The Turing machine could also write a verdict as to whether a specific assertion was or was not provable. This, together with his work on determining computable versus non-computable numbers, proved Hilbert wrong: there could be unsolvable problems.
The world of advanced mathematics was then centered in Princeton, New Jersey. There men such as Albert Einstein, Alonzo Church and Kurt Godel provided leadership in probing into mathematical unknowns. In 1936, Turing went to Princeton University and benefited from exchanging ideas with the older masters. While there he indulged both his theoretical and his mechanical bents in, as though by predestination, cryptology. He worked on a cryptographic system for which he needed an electrical multiplier. To build it he had to construct his own electrical relays.
Princeton Ph.D. in hand, and his multiplier in his luggage, Turing returned to Britain in July 1938 and soon afterward wound up at Bletchley Park. There, in the summer of 1939, spirits were animated by the knowledge that the Poles had broken the Enigma. Turing led BP's attack.
To him the German machine was a practical application of his theoretical machines. The Poles were right: to defeat the Enigma required counter-Enigmas. Yet the Poles were also wrong: their machines attacked the German machine through the message key indicators, and in his estimation, that was not the right way to go as indicators could be changed overnight, sending the codebreakers back to square one.
With astonishing speed Turing created an English bombe that took little from the Poles except the machine's name. Turing's bombe passed over the indicators; it sought to extract the key from the message itself.
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Turing and Welchman Team Up
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Brilliant as he was, to make his bombe effective, Turing had to have help from a colleague, Gordon Welchman. A lecturer in mathematics at Cambridge, Welchman had a frustrating time when he first came to Bletchley Park. Denniston assigned him to join Dilly Knox's small group at work in the BP building known as the Cottage. But Knox seemed to take a dislike to him and banished him to another building. There Welchman was told to study some German army messages and draw whatever information and patterns he could through an external examination. Welchman soon went beyond those parameters. On his own he realized the vulnerability of the double enciphering of the message key and independently evolved an equivalent of the Zygalski Sheets. When he reported his work to Knox, Welchman was dismayed to find that he had simply been duplicating the efforts of another BP associate and Cambridge alumnus, John Jeffreys, who had produced Bletchley's version of the Polish sheets.
Welchman's fortunes changed when he teamed up with Turing. Turing's approach to cracking the Enigma was to work with "cribs," or what Welchman called the "probable words" in a message. Since military parlance was highly standardized and repetitious, one could presume that certain words or phrases would appear in the text. The Poles had made rudimentary use of the technique by searching for messages that began with ANX. Turing meant to use his bombes to carry the method much further by finding longer passages embedded in the message itself.
The British were aided, as the Poles had been, by German overconfidence
The second Cambridge lecturer who most influenced Turing's thinking was Maxwell H. A. "Max" Newman, who asked if there wasn't a mechanical process that could put mathematical theorems to the test.
From this point on, Turingâin the words of his biographer Andrew Hodgesâ"dreamed of machines." In the early summer of 1935, when he was just twenty-three years old, he saw his answer. He created a theoretical "universal machine"âafterward known as the Turing machineâthat could, by using the binary system that later became the basis for digital computers, replicate logical human thought. The Turing machine could also write a verdict as to whether a specific assertion was or was not provable. This, together with his work on determining computable versus non-computable numbers, proved Hilbert wrong: there could be unsolvable problems.
The world of advanced mathematics was then centered in Princeton, New Jersey. There men such as Albert Einstein, Alonzo Church and Kurt Godel provided leadership in probing into mathematical unknowns. In 1936, Turing went to Princeton University and benefited from exchanging ideas with the older masters. While there he indulged both his theoretical and his mechanical bents in, as though by predestination, cryptology. He worked on a cryptographic system for which he needed an electrical multiplier. To build it he had to construct his own electrical relays.
Princeton Ph.D. in hand, and his multiplier in his luggage, Turing returned to Britain in July 1938 and soon afterward wound up at Bletchley Park. There, in the summer of 1939, spirits were animated by the knowledge that the Poles had broken the Enigma. Turing led BP's attack.
To him the German machine was a practical application of his theoretical machines. The Poles were right: to defeat the Enigma required counter-Enigmas. Yet the Poles were also wrong: their machines attacked the German machine through the message key indicators, and in his estimation, that was not the right way to go as indicators could be changed overnight, sending the codebreakers back to square one.
With astonishing speed Turing created an English bombe that took little from the Poles except the machine's name. Turing's bombe passed over the indicators; it sought to extract the key from the message itself.
Â
Â
Turing and Welchman Team Up
Â
Brilliant as he was, to make his bombe effective, Turing had to have help from a colleague, Gordon Welchman. A lecturer in mathematics at Cambridge, Welchman had a frustrating time when he first came to Bletchley Park. Denniston assigned him to join Dilly Knox's small group at work in the BP building known as the Cottage. But Knox seemed to take a dislike to him and banished him to another building. There Welchman was told to study some German army messages and draw whatever information and patterns he could through an external examination. Welchman soon went beyond those parameters. On his own he realized the vulnerability of the double enciphering of the message key and independently evolved an equivalent of the Zygalski Sheets. When he reported his work to Knox, Welchman was dismayed to find that he had simply been duplicating the efforts of another BP associate and Cambridge alumnus, John Jeffreys, who had produced Bletchley's version of the Polish sheets.
Welchman's fortunes changed when he teamed up with Turing. Turing's approach to cracking the Enigma was to work with "cribs," or what Welchman called the "probable words" in a message. Since military parlance was highly standardized and repetitious, one could presume that certain words or phrases would appear in the text. The Poles had made rudimentary use of the technique by searching for messages that began with ANX. Turing meant to use his bombes to carry the method much further by finding longer passages embedded in the message itself.
The British were aided, as the Poles had been, by German overconfidence
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