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Various. "Undecidability" is the correct technical term for this.
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[[Image:Ture.jpg|right|thumb]]
 
[[Image:Ture.jpg|right|thumb]]
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'''Alan Turing''' (23 June 1912 – 7 June 1954) was a British mathematician who is generally recognized as the father of computer science.<ref>[http://books.google.de/books?id=r5kOgS1IB-8C&pg=PA35&hl=de#v=onepage&q&f=false Steven Homer, Alan L. Selman: ''Computability and Complexity Theory''], p. 35</ref>  He also made contributions to [[cryptography]],<ref>[http://www.turing.org.uk/bio The Biography of Alan Turing], ''turing.org''</ref> and [[artificial intelligence]].
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'''Alan Mathison Turing''' (23 June 1912 – 7 June 1954) was a British mathematician who is generally recognized as the father of computer science.<ref>[http://books.google.de/books?id=r5kOgS1IB-8C&pg=PA35&hl=de#v=onepage&q&f=false Steven Homer, Alan L. Selman: ''Computability and Complexity Theory''], p. 35</ref>  He also made contributions to [[cryptography]],<ref>[http://www.turing.org.uk/bio The Biography of Alan Turing], ''turing.org''</ref> and [[artificial intelligence]].
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Inventing computer science is not the same as inventing the computer.  The invention of the computer&mdash;that is, a device that can automatically process data algorithmically, goes back to the the non-electronic "analytical engine" devised (but never actually built) by [[Charles Babbage]] and [[Ada Lovelace]].  Actual electronic computers were invented by John Atanasoff in the 1930s and J. Presper Eckert and John Mauchly in the 1940s, among others.  Alan Turing was associated with one of the early engineering efforts in the 1940's to make practical computers, the "ACE" (Automatic Computing Engine) project at the UK's National Physical Laboratory, but it was bested by the EDSAC and EDVAC projects elsewhere in the UK.
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Inventing computer science is not the same as inventing the computer.  The invention of the computer&mdash;that is, a device that can automatically process data algorithmically, goes back to the the non-electronic "analytical engine" devised (but never actually built) by [[Charles Babbage]] and [[Ada Lovelace]].  Actual electronic computers were invented by John Atanasoff in the 1930s and J. Presper Eckert and John Mauchly in the 1940s, among others.  Alan Turing was associated with one of the early engineering efforts in the 1940's to make practical computers, the "ACE" (Automatic Computing Engine) project at the UK's National Physical Laboratory, but it was bested by the ENIAC, EDSAC, and EDVAC projects elsewhere.
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Alan Turing's claim to fame came from the invention of the field of [[Computer science]].  He took the concepts of mathematical logic and recursive function theory, from such people and Alonzo Church and [[Kurt Gödel ]], and showed that a certain type of automatic computing device, called a [[Turing machine]], was deeply connected to those concepts.  His major paper on the subject was the 1937 paper ''On Computable Numbers, with an Application to the Entscheidungsproblem'', in the Proceedings of the London Mathematical Society.  The concepts of [[Undecidable|Decidability]], the [[Halting problem]], and the [[Turing machine]], all staples of college-level computer science, originated with him.
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Alan Turing's claim to fame came from the invention of the field of [[Computer science]].  He took the concepts of mathematical logic and recursive function theory, from such people and Alonzo Church and [[Kurt Gödel ]], and showed that a certain type of automatic computing device, called a [[Turing machine]], was deeply connected to those concepts.  His major paper on the subject was the 1937 paper ''On Computable Numbers, with an Application to the Entscheidungsproblem'', in the Proceedings of the London Mathematical Society. ("Entscheidungsproblem" is a german word for "decision problem", a term that logicians were using.) The concepts of [[Undecidable|Decidability]], the [[Halting problem]], and the [[Turing machine]], all staples of college-level computer science, originated with him.
    
Turing is also known for his contributions to the Allied war effort in [[World War II]] with the work of breaking the Nazi [[Enigma]] codes.  He formuated the "[[Turing Test]]" as a criterion for determining whether a computer can actually exhibit humanlike intelligence.
 
Turing is also known for his contributions to the Allied war effort in [[World War II]] with the work of breaking the Nazi [[Enigma]] codes.  He formuated the "[[Turing Test]]" as a criterion for determining whether a computer can actually exhibit humanlike intelligence.
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There is a prestigious annual "Turing Award", considered the computer science equivalent of the [[Nobel Prize]] named after him, and a separate annual invited "Turing Lecture" in the UK.  There are buildings named after him, and statues of him at Bletchley Park, where the wartime cryptography work was done, and in Manchester.
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There is a prestigious annual "Turing Award", considered the computer science equivalent of the [[Nobel Prize]], named after him, and a separate annual invited "Turing Lecture" in the UK.  There are buildings named after him, and statues of him at Bletchley Park, where the wartime cryptography work was done, and in Manchester.
    
==Early life==
 
==Early life==
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==The Turing Machine==
 
==The Turing Machine==
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At Princeton, Turing proposed the concept of a "[[Turing machine|Universal Machine]]". Turing had first proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive [[Recursion|recursive functions]]) that could, in principle, be followed by a machine: the "Turing Machine". Once fully formalized, the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine. The looped logic allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the insolubility of the [[halting problem]]. After gaining his PhD in June 1938, he returned to Cambridge University.
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At Princeton, Turing proposed the concept of a "[[Turing machine|Universal Machine]]". Turing had first proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive [[Recursion|recursive functions]]) that could, in principle, be followed by a machine: the "Turing Machine". Once fully formalized, the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine. The looped logic allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the undecidability of the [[halting problem]]. After gaining his PhD in June 1938, he returned to Cambridge University.
    
==Code breaking==
 
==Code breaking==
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In the later part of WW2, because of the capture of the Enigma machine, the Nazis shifted from using the Enigma code to using a far more complicated one. They called it the Lorenz cipher and the Bletchley control nicknamed it Tunny, or the Fish. While the Enigma code machine had only three wheels, the Tunny machine had twelve, and had other random tricks built into it to make decoding so difficult that even a mathematician could hardly calculate all the possible combinations. The code changed with every letter of the same message. In the later part of the war, from 1943 onwards, Tunny, not Enigma, was the code that the Germans depended on for their top-most secrets and attack plans. Tutte and Flowers worked on breaking the Tunny code.
 
In the later part of WW2, because of the capture of the Enigma machine, the Nazis shifted from using the Enigma code to using a far more complicated one. They called it the Lorenz cipher and the Bletchley control nicknamed it Tunny, or the Fish. While the Enigma code machine had only three wheels, the Tunny machine had twelve, and had other random tricks built into it to make decoding so difficult that even a mathematician could hardly calculate all the possible combinations. The code changed with every letter of the same message. In the later part of the war, from 1943 onwards, Tunny, not Enigma, was the code that the Germans depended on for their top-most secrets and attack plans. Tutte and Flowers worked on breaking the Tunny code.
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[[Bill Tutte]], the principal mathematician who undertook the work on Tunny, came from a humble background, being the son of a gardener and a cook, and he went to a grammar school - unlike Turing who had been to an elite private school. From there Tutte won a scholarship to university where he studied chemistry. He was aged only 24 when he arrived at Bletchley. His feats of deduction and analysis were extraordinary and have been described as a "miracle". Because the sheer quantity of data to be processed was overwhelming, Professor [[Max Newman]] suggested that they try to build a calculating machine along the lines suggested by Turing. Turing took no other part in the Tunny project. Turing's first machine did not work very well and the successful machine, "Colossus" was built by [[Tommy Flowers]]. He was a Post Office telephone engineer from a working-class background. He used electric circuits and valves. Because all this work was top secret, even after the war ended, neither of them could talk about what they had done or get credit for it.<ref>http://www.computerweekly.com/video/Unsung-heroes-of-IT-The-story-of-Bill-Tutte-and-Tommy-Flowers
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[[Bill Tutte]], the principal mathematician who undertook the work on Tunny, came from a humble background, being the son of a gardener and a cook, and he went to a grammar school - unlike Turing who had been to an elite private school. From there Tutte won a scholarship to university where he studied chemistry. He was aged only 24 when he arrived at Bletchley. His feats of deduction and analysis were extraordinary and have been described as a "miracle". Because the sheer quantity of data to be processed was overwhelming, Professor [[Max Newman]] suggested that they try to build a calculating machine along the lines suggested by Turing. Turing took no other part in the Tunny project. Turing's first machine did not work very well and the successful machine, "Colossus" was built by [[Tommy Flowers]]. He was a Post Office telephone engineer from a working-class background. He used electric circuits and vacuum tubes (called "valves" at the time). Because all this work was top secret, even after the war ended, neither of them could talk about what they had done or get credit for it.<ref>http://www.computerweekly.com/video/Unsung-heroes-of-IT-The-story-of-Bill-Tutte-and-Tommy-Flowers
 
http://www.telegraph.co.uk/news/obituaries/1393587/Professor-Bill-Tutte.html
 
http://www.telegraph.co.uk/news/obituaries/1393587/Professor-Bill-Tutte.html
 
http://www.stephenkettle.co.uk/turing.html</ref>
 
http://www.stephenkettle.co.uk/turing.html</ref>
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