How to Think

A physics professor at Queen's University was asked to be the arbitrator in a dispute over a grade. One of his colleagues was grading the exams and had decided to give the student 0. The student felt he should receive full marks. Both parties agreed to let an impartial arbiter make the final decision.

The 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 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".

The arbiter 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 were given, it could well contribute to a high grade for the student and a high grade should certify a certain competency in Physics, which the student had not proven. The student was therefore asked to have another try at the question and that his response should show some knowledge of the principles of physics.

The student noted that there were a number of options but finally said "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 S is equal to BD at 2, calculate the height of the building." At this point, everyone gave up and the student was given full credit.

When asked about his other options he replied: "There are many ways to do this. 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 the simple proportion, determine the height of the building."

"There's also a very basic measurement method. In this method, take the barometer and begin to walk up the stairs. As you climb, 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".

"Of course, if you want a more sophisticated method, you can tie the barometer to the end of a string, swing it like 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 can, in principle, be calculated."

"Probably the best method, however", he concluded, "is to take the barometer to the basement and knock on the superintendent's door. When he answers, you speak to him as follows: 'Mr. Superintendent, here I have a fine barometer. If you will tell me the height of this building, I will give you this barometer....'"

The student acknowledged that he did not use the conventional answer to the question but that he was fed up with people trying to teach him what to think instead of how to think.