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Monday, August 3, 2009

Niels Bohr and the barometer

I was recently reminded of a classic urban legend:

The following concerns a question in a physics degree exam at the
University of Copenhagen:

"Describe how to determine the height of a skyscraper with a barometer."

One student replied:

"You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building."

This highly original answer so incensed the examiner that the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case.

The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer that showed at least a minimal familiarity with the basic principles of physics.

For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use. On being advised to hurry up the student replied as follows:

"Firstly, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from the formula H = 0.5g x t squared. But bad luck on the barometer."

"Or 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."

"But if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked
out by the difference in the gravitational restoring force T =2 pi sqr root (l /g)."

"Or if the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up."

"If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and convert the difference in millibars into feet to give the height of the building."

"But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'."

The student was Niels Bohr, the only Dane to win the Nobel Prize for physics.

(text collected by snopes.com in '99)

There are lots of 'points' to this story, but what stands out to me is the challenge to educators here. Are our 'open' assessement questions really open, or are they multiple choice without the options being clearly presented to our students? How ready are we to accept pupils thinking way 'outside the box', particularly in formal assessment? How ready are we to accept that some of our pupils may be smarter than we are?

The story is also a good one because of the deliberately provacative attitude of the student. He must have understood from the beginning the answer the examiners wanted, yet some combination of self-importance, humour and lack of respect for formal education makes him risk his exam by giving an alternate answer. Even under the second chance he is given, he is deliberately provocative, clearly making a point of his disdain for the exam. I know many educators who would have trouble standing for this kind of disrespect coupled with 'the wrong answer'. How do we react when the next Niels Bohr appears in our classroom?

The choice of physics for this story is also telling - 'doing physics' requires questioning basic assumptions about the nature of reality, but teaching phyics easily falls into a pattern that unfortunately does not nurture the kind of thinking physicists need.

As an educator hearing this story, I am reminded that humility is one of a teacher's most important qualities.

Oh, and the story? Probably not completely true. May have happened, but no-one can prove it was Bohr. The part about him being the only Dane to win the Nobel prize for physics is also not true, but it was when this story first surfaced in the '50's.

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