----Russell and Hardy The great logician Bertrand Russell (or was it A.N. Whitehead?) once claimed that he could prove anything if given that 1+1=1. So one day, some smarty-pants asked him, "Ok. Prove that you're the Pope." He thought for a while and proclaimed, "I am one. The Pope is one. Therefore, the Pope and I are one." [NOTE: The following is from merritt@Gendev.slc.paramax.com (Merritt). The story about 1+1=1 causing ridiculous consequences was, I believe, originally the product of a conversation at the Trinity High Table. It is recorded in Sir Harold Jeffreys' "Scientific Inference", in a note to chapter one. Jeffreys remarks that the fact that everything followed from a single contradiction had been noticed by Aristotle (I doubt this way of putting it is quite correct, but that is beside the point). He goes on to say that McTaggart denied the consequence: "if 2+2=5, how can you prove that I am the pope?" Hardy is supposed to have replied: "if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and the pope are two; therefore McTaggart and the pope are one." When I consider this story, I am astonished at how much more brilliant some people are than I (quite independent of the fallacies in the argument). _______________Von Neumann The following problem can be solved either the easy way or the hard way. Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown? The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it. When this problem was posed to John von Neumann, he immediately replied, "150 miles." "It is very strange," said the poser, "but nearly everyone tries to sum the infinite series." "What do you mean, strange?" asked Von Neumann. "That's how I did it!" _____________Von Neumann From: thommark@access5.digex.net (Mark A. Thomas) How about the apocryphal story about the MIT student who cornered the famous John von Neumann in the hallway: Student: "Er, excuse me, Professor von Neumann, could you please help me with a calculus problem?" John: "Okay, sonny, if it's real quick -- I'm a busy man." Student: "I'm having trouble with this integral." John: "Let's have a look." (insert brief pause here) "Alright, sonny, the answer's two-pi over 5." Student: "I know that, sir, the answer's in the back -- I'm having trouble deriving it, though." John: "Okay, let me see it again." (another pause) "The answer's two-pi over 5." Student (frustrated): "Uh, sir, I _know_ the answer, I just don't see how to derive it." John: "Whaddya want, sonny, I worked the problem in two different ways!" _____________Isaac Newton From: mstueben@tjhsst.vak12ed.edu (Michael A. Stueben) The English mathematician John Wallis (1616-1703) was a friend of . According to his diary, Newton once bragged to Wallis about his little dog Diamond. "My dog Diamond knows some mathematics. Today he proved two theorems before lunch." "Your dog must be a genius," said Wallis. "Oh I wouldn't go that far," replied Newton. "The first theorem had an error and the second had a pathological exception." _________________ Von Neumann and Norbert Weiner Von Neumann and Norbert Weiner were both the subject of many dotty professor stories. Von Neumann supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes". Weiner was in fact very absent minded. The following story is told about him: When they moved from Cambridge to Newton his wife, knowing that he would be absolutely useless on the move, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him. Naturally, in the course of the day, an insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away. At the end of the day he went home (to the old address in Cambridge, of course). When he got there he realized that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck. There was a young girl on the street and he conceived the idea of asking her where he had moved to, saying, "Excuse me, perhaps you know me. I'm Norbert Weiner and we've just moved. Would you know where we've moved to?" To which the young girl replied, "Yes daddy, mommy thought you would forget." The capper to the story is that I asked his daughter (the girl in the story) about the truth of the story, many years later. She said that it wasn't quite true -- that he never forgot who his children were! The rest of it, however, was pretty close to what actually happened... ---------------------- Found on the "Annals of Improbable Research" Web site http://www.improb.com/.

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