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.

Billy Gates writes to Santa
Dear Santa,

How are you doing? I hope you've had a successful year and have come up with a lot of interesting toys. It's really neat how you're able to do that year after year. I guess that's how you stay number one in the Christmas presents business business.

Actually, I admire the way you run Christmas. You really have a handle on it. You find out what people want (with letters like this and having kids tell you in person), and then you make the presents and control how they are delivered. It's an impressive operation.

I also like how you've got it to where when somebody says "Christmas presents," people automatically think Santa Claus. What a marketing advantage. Best of all, even though you're a huge success, people still don't know much about your private life. It's just rumors. That's so neat.

I think being at the North Pole helps. That was a good move. For example, when you're designing toys, only your elves know what you're doing, and you're way up there where nobody can spy on you and steal your ideas. And even if they do, you can always just let it out that you're making the same stuff to bring to people for free, so why would they buy the other guy's stuff?

Also, other people who make Christmas presents can't deliver them like you can. Yours is the only sleigh on the distribution highway. You must get some great discounts from them, because if they don't play ball you can just refuse to give out their presents. Very Sharp.

What I don't get is why you give away stuff. That's the dumbest idea I've ever heard. I admit, it's why you're number one - who could compete with a deal like that? But it must make it hard to stay in business, especially when you have to visit every kid in the world. You have to keep growing or fail.

Here's an idea on how you can help finance your operation: Give everybody at least one present at Christmas, then you could make batteries and sell them the rest of the year. It would create a demand: You give people something and then sell them what they need to make it work.

Another thing, about you coming down the chimney. That's so slow and inefficient. And what about all the people who don't have chimneys? Santa. I have one word for you--windows. Everybody has windows.

That's about all I have to say. You're probably wondering if I was good or bad this year, but I don't really like to talk about my personal life, if that's O.K. (Just out of curiosity: When you were a boy, did any of the other kids call you a nerd?) Anyway, I don't really have anything to ask for. Mostly I think up something to play with and then build it myself. I guess I'm sort of like you--I make my own toys.

Best of luck,
Billy Gates