From: gardar@hugvit.is
Date: Mon Nov 22 1999 - 06:42:18 MST
The following story may or may not be authentic (I don't know where it comes
from) but it's very amusing and interesting.
=================================================================
Some time ago I received a call from a colleague, who asked if I would be
the referee on the grading of an examination question. He was about to
give a student a zero for his answer to a physics question, while the
student claimed he should receive a perfect score and would if the system
were not set up against the student. The instructor and the student
agreed to an impartial arbiter, and I was selected.
I went to my colleague's office and read the examination question: "Show
how it is possible to determine the height of a tall building with the
aid of a barometer." The student had answered: "Take the barometer to the
top of the building, attach a long rope to it, lower it to the street,
and then bring it up, measuring the length of the rope. The length of the
rope is the height of the building."
I pointed out that the student really had a strong case for full credit
since he had really answered the question completely and correctly. On
the other hand, if full credit were given, it could well contribute to a
high grade in his physics course. A high grade is supposed to certify
competence in physics, but the answer did not confirm this. I suggested
that the student have another try at answering the question. I was not
surprised that my colleague agreed, but I was surprised when the student
did.
I gave the student six minutes to answer the question with the warning
that the answer should show some knowledge of physics. At the end of five
minutes, he had not written anything. I asked if he wished to give up,
but he said no. He had many answers to this problem; he was just thinking
of the best one. I excused myself for interrupting him and asked him to
please go on. In the next minute, he dashed off his answer which read:
"Take the barometer to the top of the building and lean over the edge of
the roof. Drop the barometer, timing its fall with a stopwatch. Then,
using the formula x =3D0.5 * a * t2, calculate the height of the building."
At this point, I asked my colleague if he would give up. He conceded, and
gave the student almost full credit.
In leaving my colleague's office, I recalled that the student had said
that he had other answers to the problem, so I asked him what they were.
"Well," said the student. "there are many ways of getting the height of a
tall building with the aid of a barometer. For example , you could take
the barometer out on a sunny day and measure the height of the barometer,
the length of its shadow, and the length of the shadow of the building,
and by the use of simple proportion, determine the height of the building."
"Fine," I said, "and others?"
"Yes," said the student. "There is a very basic measurement method you
will like. In this method, you take the barometer and begin to walk up
the stairs. As you climb the stairs, you mark off the length of the
barometer along the wall. You then count the number of marks, and this
will give you the height of the building in barometer units."
"A very direct method."
"Of course, if you want a more sophisticated method, you can tie the
barometer to the end of a string, swing it as a pendulum, and determine
the value of g at the street level and at the top of the building. From
the difference between the two values of g, the height of the building,
in principle, can be calculated. On this same tack, you could take the
barometer to the top of the building, attach a long rope to it, lower it
to just above the street, and then swing it as a pendulum. You could then
calculate the height of the building by the period of the precession".
"Finally," he concluded, "there are many other ways of solving the
problem. Probably the best is to take the barometer to the basement and
knock on the superintendent's door. When the superintendent answers, you
speak to him as follows: 'Mr. Superintendent, here is a fine barometer.
If you will tell me the height of the building, I will give you this
barometer.'"
At this point, I asked the student if he really did not know the
conventional answer to this question. He admitted that he did, but said
that he was fed up with high school and college instructors trying to
teach him how to think.
The student was Neils Bohr and the arbiter Rutherford...
________________________________________________________________
The five levels of ignorance:
1) You know the answer -- so you are not ignorant
2) You don't know the answer, but at least you know the right question
3) You don't know that you don't know the answer
4) You don't know how to find out how much you don't know
5) You don't even know about the five orders of ignorance
Regards,
Gardar Gardarsson
gardar@hugvit.is
http://www.brainsense.com
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