Ramani K. Raman

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Angels on a Pin

By Alexander Calandra

Saturday Review, Dec 21, 1968.

Note: The following story is often circulated around the internet and attributed to the great Danish Physicist Neils Bohr. This attribution however is entirely false. The story is entirely fictional, a satire on the regrettable manner in which Physics is taught in schools across the globe.

Some time ago I received a call from a colleague who asked if I would agree to be the referee on the grading of an examination question. He had given a student a zero for his answer to a physics question, which was contested by the student. The student claimed that he should instead receive a perfect score. Hence my colleague and his student agreed to submit this to an impartial arbiter, for which I was selected.

I went to my colleague's office and read the examination question which was straightforward enough: "How would you 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 the barometer 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 answered the question completely and correctly. On the other hand, if full credit was given, it would end up making a mockery of the course. A high grade is supposed to certify competence in physics, but the answer did not confirm to this. I suggested that the best way out would be to let the student have another try at answering the question.

I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. The student sat motionless on the chair for five minutes without saying a word. At the end of five minutes, I asked if he wished to give up. On the contrary, he replied that he had many answers to this problem; but was not sure which would be the best one to present. I asked him to present any one of the solutions he had - never mind if its not the best one.

He replied: "Take the barometer to the top of the building and lean over the edge of the roof. Drop that barometer, timing its fall with a stopwatch. Then using the formula S = ½at², one could easily calculate the height of the building.

At this point I asked my colleague if we should give up. He conceded, and I gave the student almost full credit.

However, curious, I asked the student to list the other solutions he had thought of. "Oh yes," said the student. "There are a great many ways of getting the height of a tall building with a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer and the length of its shadow. Then determine the length of the shadow of the building, and by the use of a simple proportion, determine the height of the building."

"Fine," I asked. "And the others?"

"Yes," said the student. "There is a very basic measurement method that 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 of the two values of `g' the height of the building can be calculated."

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 janitors door. When he answers, you tell him: "I have a fine barometer which will be yours if you tell me the height of this building".

At this point I asked the student if he really did know the conventional answer to this question. He admitted that he did, said that he was fed up with high school and college instructors trying to teach him how to think, using the "scientific method," and to explore the deep inner logic of the subject in a pedantic way, as is often done in the new mathematics, rather than teaching him the structure of the subject.