..."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.*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.

## Comments

don't write about Geodesics or metrics they deal with symmetric surfaces like Sphere or Earth or Symmetric curvatures. I'm asking about Ocean's surface.

I think you got my point.