The Student and The Barometer

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 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 hadn't 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,if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper.

"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 [gravity] 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," 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 name of the student was Niels Bohr, who later received the Nobel prize for Physics.

A Modest Essay
A Modest Essay 3A. ESSAY: IN ORDER FOR THE ADMISSIONS STAFF OF OUR COLLEGE TO GET TO KNOW YOU, THE APPLICANT, BETTER, WE ASK THAT YOU ANSWER THE FOLLOWING QUESTION: ARE THERE ANY SIGNIFICANT EXPERIENCES YOU HAVE HAD, OR ACCOMPLISHMENTS YOU HAVE REALIZED, THAT HAVE HELPED TO DEFINE YOU AS A PERSON? I am a dynamic figure, often seen scaling walls and crushing ice. I have been known to remodel train stations on my lunch breaks, making them more efficient in the area of heat retention. I translate ethnic slurs for Cuban refugees, I write award-winning operas, I manage time efficiently. Occasionally, I tread water for three days in a row. I woo women with my sensuous and godlike trombone playing, I can pilot bicycles up severe inclines with unflagging speed, and I cook Thirty-Minute Brownies in twenty minutes. I am an expert in stucco, a veteran in love, and an outlaw in Peru. Using only a hoe and a large glass of water, I once single-handedly defended a small village in the Amazon Basin from a horde of ferocious army ants. I play bluegrass cello, I was scouted by the Mets, I am the subject of numerous documentaries. When I'm bored, I build large suspension bridges in my yard. I enjoy urban hang gliding. On Wednesdays, after school, I repair electrical appliances free of charge. I am an abstract artist, a concrete analyst, and a ruthless bookie. Critics worldwide swoon over my original line of corduroy evening wear. I don't perspire. I am a private citizen, yet I receive fan mail. I have been caller number nine and have won the weekend passes. Last summer I toured New Jersey with a traveling centrifugal-force demonstration. I bat .400. My deft floral arrangements have earned me fame in international botany circles. Children trust me.I can hurl tennis rackets at small moving objects with deadly accuracy. I once read Paradise Lost, Moby Dick, and David Copperfield in one day and still had time to refurbish an entire dining room that evening. I know the exact location of every food item in the supermarket. I have performed several covert operations for the CIA. I sleep once a week; when I do sleep, I sleep in a chair. While on vacation in Canada, I successfully negotiated with a group of terrorists who had seized a small bakery. The laws of physics do not apply to me. I balance, I weave, I dodge, I frolic, and my bills are all paid. On weekends, to let off steam, I participate in full-contact origami. Years ago I discovered the meaning of life but forgot to write it down. I have made extraordinary four course meals using only a mouli and a toaster oven. I breed prizewinning clams. I have won bullfights in San Juan, cliff-diving competitions in Sri Lanka, and spelling bees at the Kremlin. I have played Hamlet, I have performed open-heart surgery, and I have spoken with Elvis. But I have not yet gone to college.