Right after I submitted my last post, this showed up in my email:
It might not be entirely accurate or perhaps just a legend, but it's a
great story about learning how to think differently.
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Some time ago I received a
call from a colleague. He was about to give
a student a zero for his answer to a physics question, while the
student claimed a perfect score. The instructor and the student agreed
to an impartial arbiter, and I was selected.I 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."
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 and to certify competence in physics, but
the answer did not confirm this. I suggested that the student have
another try. 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 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=0.5*a*t^^2,
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. While 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 tact, 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," he said, "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 Nobel
prize winning physicists Neils Bohr.