Thinking Out of the Box - A True Story
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| Thinking out of the box! |
Thinking Out of the Box - A True Story
There are
two kinds of imagination: first is the idealistic or utopian imagination;
second is the practical imagination. Here are some examples of this second kind
of imagination.
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:
Question: Show
how is it 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 the
rope 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.”
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| What to think and what not to think.....! |
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 Neils Bohr and the arbiter was Ernest Rutherford.
“Truly
Amazing Story!!!”
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