Think Your Own Way

I confess that I can't pinpoint where I found this, but it's well worth reading. This anecdote dates from a long time ago, but its message is even more relevant now: Think your own way.


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 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.


Look him up if the name means nothing to you. His birthday is October 7th, so think of this as My way of celebrating your own way of thinking.

(The "correct" method is to measure barometric pressure at street level and rooftop level and convert the difference into height based on their relative pressures. Three other methods I could suggest: (1) Measure the barometer, then measure the apparent height of the barometer from a known distance. Measure the apparent height of the building from the same distance. Simple math will give the approximate height of the building. (2) Throw or fire the barometer, tied with string, to the rooftop. Measure the string. Variation: Tie the barometer to a helium balloon that floats to the rooftop. (3) Find the final building plans; use the barometer to make sure the plans don't roll up as you write down the answer.)


The Jenius Has Spoken.