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“[Von Neumann's childhood home's] library’s centrepiece [was] the Allgemeine Geschichte, a massive history of the world edited by the German historian Wilhelm Oncken, which began in Ancient Egypt and concluded with a biography of Wilhelm I, the first German emperor, commissioned by the Kaiser himself. When von Neumann became embroiled in American politics after he emigrated, he would sometimes avoid arguments that were threatening to become too heated by citing (sometimes word for word) the outcome of some obscurely related affair in antiquity that he had read about in Oncken as a child.”
― The Man from the Future: The Visionary Ideas of John von Neumann
― The Man from the Future: The Visionary Ideas of John von Neumann
“Von Neumann enjoyed driving very much but had never passed a test. At Mariette’s suggestion, he bribed a driving examiner. This did nothing to improve his driving. He sped along crowded roads as if they were many-body problems to be negotiated by calculating the best route through on the fly. He often failed, and an intersection in Princeton was soon christened ‘von Neumann corner’ on account of the many accidents he had there. Bored on open roads, he slowed down. When conversation faltered, he would sing; swaying and rocking the steering wheel from side to side with him. The couple would buy a new car every year, usually because von Neumann had totalled the previous one. His vehicle of choice was a Cadillac, ‘because’, he explained whenever anyone asked, ‘no one would sell me a tank’. Miraculously, he escaped largely unscathed from these smash-ups, often returning with the unlikeliest of explanations. ‘I was proceeding down the road,’ begins one fabulous excuse. ‘The trees on the right were passing me in orderly fashion at 60 miles an hour. Suddenly one of them stepped in my path. Boom!”
― The Man from the Future: The Visionary Ideas of John von Neumann
― The Man from the Future: The Visionary Ideas of John von Neumann
“Philosophy is a dangerous thing for any dogmatic religion; it makes people think.”
― Glimpses of World History by Jawaharlal Nehru: Sneak peek into World History and Independent India Before and After Biography Book by Jawaharlal Nehru Penguin Books
― Glimpses of World History by Jawaharlal Nehru: Sneak peek into World History and Independent India Before and After Biography Book by Jawaharlal Nehru Penguin Books
“Von Neumann’s remarkable foresight is evident in letters he wrote to Ortvay between 1928 and 1939. ‘There will be a war in Europe in the next decade,’ he told the Hungarian physicist in 1935, further predicting that America would enter the war ‘if England is in trouble’. He feared that during that war, European Jews would suffer a genocide as the Armenians had under the Ottoman Empire. In 1940, he predicted that Britain would be able to hold a German invasion at bay (far from obvious at the time), and that America would join the war the following year (as it did after the bombing of Pearl Harbor).”
― The Man from the Future: The Visionary Ideas of John von Neumann
― The Man from the Future: The Visionary Ideas of John von Neumann
“Russell’s paradox threatened to deal a far more serious blow to set theory than earlier ideological objections. The problem was this: consider a set of objects – all possible types of cheesecake, say. This set may include any number of different cheesecakes (New York cheesecake, German Käsekuchen, lemon ricotta, etc.) but, because a set is not literally a cheesecake, the set of all cheesecakes is not a member of itself. The set of all things that are not cheesecakes, on the other hand, is a member of itself.
But what, Russell wondered, about the set of all sets that are not members of themselves. If this is not a member of itself, then, by definition, it should be (because its members do not include itself). Conversely, if it is a member of itself, then it should not be (because it does). This was Russell’s paradox in a nutshell. His analysis of the paradox revealed it to be similar in form to several others, including the liar’s paradox (‘this statement is a lie’). ‘It seemed unworthy of a grown man to spend time on such trivialities,’ he complained, desperate for a solution, ‘but what was I to do?”
― The Man from the Future: The Visionary Ideas of John von Neumann
But what, Russell wondered, about the set of all sets that are not members of themselves. If this is not a member of itself, then, by definition, it should be (because its members do not include itself). Conversely, if it is a member of itself, then it should not be (because it does). This was Russell’s paradox in a nutshell. His analysis of the paradox revealed it to be similar in form to several others, including the liar’s paradox (‘this statement is a lie’). ‘It seemed unworthy of a grown man to spend time on such trivialities,’ he complained, desperate for a solution, ‘but what was I to do?”
― The Man from the Future: The Visionary Ideas of John von Neumann
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