At 01:21 pm 07/05/2006 -0400, you wrote:
>...producing up to a hundred particles in each collision...
>
>By sheer coincidence, that's how many angels can dance on the head of a pin...
>
>P.
Doing a little research on angels and pins I came across
this rather amusing tale which younger Vorts might not
have seen before.
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Angels on the Head of a Pin
A Modern Parable
by Alexander Calandra
Saturday Review, 21 Dec 1968
Some time ago I received a call from a colleague
who asked if I would be the referee on the grading
of an examination question. He was about to give
a student a zero for his answer to a physics question,
while the student claimed he should receive a perfect
score and would if the system were not set up against
the student: The instructor and the student agreed
to submit this to an impartial arbiter, and I was
selected.
I went to my colleague's office and 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 a 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."
I 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 was given, it could well contribute to a high
grade for the student in his physics course. A high
grade is supposed to certify competence in physics,
but the answer did not confirm this. I suggested that
the student have another try at answering the question
I was not surprised that my colleague agreed, but I
was surprised that the student did.
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 no. 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 that barometer,
timing its fall with a stopwatch. Then using the formula
S = ½ a t2,
calculate the height of the building.
At this point I asked my colleague if he would give up.
He conceded, and I gave the student almost full credit.
In leaving my colleague's office, I recalled that the
student had said he had many other answers to the problem,
so I asked him what they were. "Oh yes," said the student.
"There are a great many ways of getting the height of a
tall building with a barometer. For example, you could
take the barometer out on a sunny day and measure the
height of the barometer and the length of its shadow,
and the length of the shadow of the building and by the
use of a simple proportion, determine the height of the
building."
"Fine," I asked. "And the others?"
"Yes," said the student. "There is a very basic
measurement method that 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 of the two values of `g', the height of the
building can be calculated."
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 I have a fine barometer. If you tell me the height
of this building, I will give you this barometer."
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Mind you - quite what the parable has to do with angels or
pins rather escapes me. 8-)
Frank
