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.

And God Created ... Pets
A newly discovered chapter in the Book of Genesis has
provided the answer to, "Where do pets come from?"

Adam said, "Lord, when I was in the garden, you walked with
me everyday. Now I don't see you anymore. I'm lonesome here
and it's difficult for me to remember how much you love me."

And God said, "No problem! I will create a companion for you
that will be with you forever and who will be a reflection of
my love for you, so that you will love me even when you
cannot see me. Regardless of how selfish or childish or
unlovable you may be, this new companion will accept you as
you are and will love you as I do, in spite of yourself."

And God created a new animal to be a companion for Adam. And
it was a good animal. And God was pleased. And the new animal
was pleased to be with Adam and he wagged his tail. And Adam
said, "Lord, I have already named all the animals in the
Kingdom and I cannot think of a name for this new animal."

And God said, "No problem, because I have created this new
animal to be a reflection of my love for you. His name will
be a reflection of my own name, and you will call him
'Dog.'"

And Dog lived with Adam and was a companion to him and loved
him.

And Adam was comforted.

And God was pleased.

And Dog was content and wagged his tail.

After a while, it came to pass that Adam's guardian angel
came to the Lord and said, "Lord, Adam has become filled with
pride. He struts and preens like a peacock and he believes he
is worthy of adoration. Dog has indeed taught him that he is
loved, but perhaps too well."

And the Lord said, "No problem! I will create for him a
companion who will be with him forever and who will see him
as he is. The companion will remind him of his limitations,
so he will know that he is not always worthy of adoration."

And God created CAT to be a companion to Adam. And Cat would
not obey Adam.

And when Adam gazed into Cat's eyes, he was reminded that he
was not the Supreme Being. And Adam learned humility.

And God was pleased.

And Adam was pleased.

And the Dog was pleased.

And the Cat didn't care one way or the other.