Friday, October 08, 2004

WORTH READING 8 Oct 2004

'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.


The physics examination question read, "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 and
measure 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 because he had
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.


As an arbiter, I suggested that the student have another try. I gave the
student six minutes to answer the question with the warning that the answer
must demonstrate some knowledge of physics. Five minutes past, but he had
not written anything. I asked if he wished to give up, but he said he had
many answers to this problem and 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, lean over the edge of the roof, and then 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 determining 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 using simple proportion,
determine the height of the building."


"Fine," I said, "and other answers?" "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, mark
off the length of the barometer along the wall. Then count the number of
marks, which equals the height of the building in barometer units."


"That's 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 method 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 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 know the
answer, but was fed up with high school and college instructors trying to
teach him how to think.'


The student was "Neils Bohr" (quantum theory, physics, mechanics, hydrogen
atom guru etc.) and the arbiter, "Rutherford."


THINK DIFFERENT!

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