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Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.

John D. Barrow
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At the laboratory, Turing designed the first relatively complete electronic stored-program digital computer for code breaking in 1945. Darwin deemed it too ambitious, however, and after several years Turing left in disgust. When the laboratory finally built his design in 1950, it was the fastest computer in the world and, astonishingly, had the memory capacity of an early Macintosh built three decades later.

Sharon Bertsch McGrayne, The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy
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Like Alan Turing, Zuse was educated in a system that focused on a child's emotional and philosophical life as well as his intellectual life, and at the end of school, like Turing, Zuse found himself to be something of an outsider—to the disappointment of his very conventional parents, he no longer believed in God or religion.(Jane Smiley (2010). The Man Who Invented the Computer)

Konrad Zuse
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So this is where all the vapid talk about the 'soul' of the universe is actually headed. Once the hard-won principles of reason and science have been discredited, the world will not pass into the hands of credulous herbivores who keep crystals by their sides and swoon over the poems of Khalil Gibran. The 'vacuum' will be invaded instead by determined fundamentalists of every stripe who already know the truth by means of revelation and who actually seek real and serious power in the here and now. One thinks of the painstaking, cloud-dispelling labor of British scientists from Isaac Newton to Joseph Priestley to Charles Darwin to Ernest Rutherford to Alan Turing and Francis Crick, much of it built upon the shoulders of Galileo and Copernicus, only to see it casually slandered by a moral and intellectual weakling from the usurping House of Hanover. An awful embarrassment awaits the British if they do not declare for a republic based on verifiable laws and principles, both political and scientific.

Christopher Hitchens
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I want a permanent relationship, and I might feel inclined to reject anything which of its nature could not be permanent.

Alan Turing
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Science is a differential equation. Religion is a boundary condition.

Alan Turing
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The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer.

Alan Turing
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I have had a dream indicating rather clearly that I am on the way to being hetero, though I don't accept it with much enthusiasm either awake or in the dreams.

Alan Turing
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The isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first twenty years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques must be regarded as carried out by the human community as a whole, rather than by individuals.

Alan Turing
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What a familiarity with the construction of Turing test bots had begun to show me was that we fail - again and again- to actually be human with other humans, so maddeningly much of the time.

Brian Christian, The Most Human Human: What Artificial Intelligence Teaches Us About Being Alive
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