School Daze - Intuition & Memory
Date: Thu, 20 Oct 94 14:45:20 PDT
Subject: School Daze - Intuition & Memory
Forwarded-by: email@example.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