20 Oct

School Daze - Intuition & Memory

Date: Thu, 20 Oct 94 14:45:20 PDT To: Fun_People Subject: School Daze - Intuition & Memory Forwarded-by: cate3@netcom.com (Henry Cate) My electromagnetics professor, Dr. Andrew Dienes, defines "trivial" as "Any problem that can be solved by a Nobel Laureate in less than 24 hours." You can imagine that I was relieved to hear that my final would be trivial. ---------------------------------------------------- Just to throw in my two cents worth in to the Intuitively Obvious bucket, when I was a math student at Towson State University we were given a final exam that involved proving that two N dimesional matrices were related in a given way. I started with the first matrix and used every theorem that I could remember trying to reach the second, but I got stuck halfway through. Working feverishly on a piece of scrap paper, I started on the second matrix, but couldn't work it back to the first. In a flash of inspiration, I set the two intermediate results equal to each other and copied the second set of equations backwards onto the tail of the first. When I got the paper back, there was a C which was crossed out and replaced by an A, the midpoint of my equations was underlined, with a note saying - At first I doubted that this step was intuitively obvious, but after thinking about it for several hours, I decided that it was. ---------------------------------------------------- Von Neumann and Nobert 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... ---------------------------------------------------- A (possibly apocryphal) story related to me by a graduate student who had come from a large midwest (Wisconsin?) univ. Seems that one of his classes was taught by the department emeritus prof who was very old (in his 80's) and sometimes a bit vague, but at other times incredibly sharp. One day in lecture he was explaining something abstruse and paused to look at the board for a moment. Thereupon he wrote down a result and said, eyes twinking, "And this is intuitively obvious...". Whereupon he smiled, looked out over the class, saw the rows of blank stares, and turned back to the board to contemplate the statement written there. This went on for about a minute, at the end of which time he started to wander, rather deeply in thought, across the stage. This went on for a minute or two, after which the prof. drifted out into the hall and was heard walking back and forth. People started to, well, look at each other and smile. A scout was sent out who reported the old boy was pacing around and muttering to himself. The class, incredibly, remained reasonably calm. About five minutes after the scout had returned, there was a happy shout from the hallway, and the again bright-eyed prof. scuttled back in, pointed to the intuitively obvious result written on the blackboard, turned to the class and said, all aglow, "Yes, yes, it IS intuitively obvious".

© 1994 Peter Langston