Day 854: Training Your Barometer To Be A Really Long Ruler

originally published May 3, 2014

One day a young student at the University of Copenhagen was asked if he knew how to measure the height of a building using only a barometer. The correct answer involves measuring the atmospheric pressure on the building’s roof and again on the street below, then calculating the height through the difference between the two results. The student came up with a number of alternative answers instead, forcing the professor to re-think the very nature of how he asked questions of his students. That young man was none other than Niels Bohr, future winner of the Nobel Prize for Physics.

Don’t believe me? What if I told you that student was future Vice-President of the United States Spiro Agnew? No? How about a savvy teenage Marc Price, who played Skippy on Family Ties? Are you getting the sense that I have no idea what I’m talking about? 854 days and finally the truth is revealed.

The barometer question is one of the most pristine examples of a true urban legend. We can trace its publication origin perfectly, yet not even the super-sleuths at snopes.com can confirm whether or not such a dastardly comedic display of youthful insouciance ever actually occurred in a college classroom.

Dr. Alexander Calandra, a test designer with a face that practically dares you to challenge his charming and home-spun anecdotes, included this story in his 1961 blockbuster, The Teaching of Elementary Science of Mathematics. The legend’s origins can be traced to a Reader’s Digest story three years earlier. Dr. Calandra claims the incident actually happened to his colleague during the Sputnik Crisis, when American scientific minds were in a panic to avoid being the second superpower nation to conquer outer space.

The story was reprinted in other published works by Calandra, including an issue of Current Science in 1964, the Saturday Review in 1968 and as part of an unusually science-based letter to Penthouse Forum in the late 70’s. Academics swarmed on the tale because it provides an interesting ethical dilemma: if we are teaching students to arrive at an answer, yet they arrive at that same correct answer through an inventively roundabout route, is it right to deduct marks for it?

And how many ways are there to measure the height of a building with a barometer?

One option is to tie a string to the barometer and lower it from the roof, measuring the length of the string after it touches the ground. Another is to drop the barometer off the roof and time how long it takes to fall. We know the rate of acceleration due to gravity, so calculating the height of the building this way would be simple – though you’ll be sacrificing your precious barometer. If it’s sunny out you can measure the length of the barometer’s shadow and measure the length of the building’s shadow and calculate the difference.

There are so many ways of doing this that have nothing to do with taking actual barometric pressure readings. You can build a small pendulum for the barometer to swing on, both on the ground and again up top, and calculate the height via the gravitational resisting force (I have no idea what I’m talking about here, but apparently this works). You could walk up the building’s staircase, notching lengths of the barometer as you go; if you know how tall your barometer is, just use it as a measuring tool.

The deeper you sink your mental spoon into this thought-pudding the weirder and lumpier it gets.

The most straightforward answer would be to find the building’s owner or superintendent and offer to trade your shiny new barometer for the answer to your question. If he or she doesn’t want to do the trade, you could use the barometer to beat the answer of them. If the building is well-known enough to have a Wikipedia page (and if not, you can probably find it on emporis.com), you could break off the barometer’s needle and use that to type the building’s name into the search field. You’ll feel a little weird doing that, but at least you’ll have used the barometer.

According to Dr. Calandra’s initial account, this actually happened to a colleague of his. After the student’s chain of creative answers (which did include the bribery option but not the savage beating scenario), Calandra and his colleague were faced with a moral dilemma. Does the student get full marks for technically providing a correct answer even though he displayed absolutely no knowledge of the material he was supposed to learn for the course? Was the student being a clever smart-ass or just a prick?

Exam shortcuts or loopholes are the stuff of dreams to a sharp kid with a penchant for taking the quickest route to a task’s completion. This is why writing the questions for an exam requires an unflappable attention to detail. Another great exam legend involves the instruction “Choose one of the exercises below” for a lengthy English test, with each exercise consisting of a piece of writing followed by a series of questions. The smart kid (and probably future lawyer) writes, “I choose number two” and closes his exam book. Hey, technically he followed the instructions.

That’s why exams should say “Choose and complete one of the exercises below” instead, right? But if the student opts to write a bunch of nonsense to fill in the lines of the exam paper, technically he or she is ‘completing’ the exercise. Now we’re deep down a semantic rabbit-hole in which we might get lost. Do exam writers really need to specify that we should answer the questions correctly?

And is there any student both ballsy and idiotic enough to risk a failing grade by trying to squeeze through on a technicality like this?

The barometer question raises the issue of how we should be teaching our kids to think. Education is at its best when it branches away from fact-regurgitation and elbows our kids’ skull-goop into some critical concluding. Pushing someone’s brain into devising new ways to achieve a result is a more powerful mental exercise, and not giving full marks simply because the answer you get back was excavated through fresh cerebral soil is simply ridiculous.

Besides, as a teacher would you really want some smart-ass Val-Kilmer-type showing you up in front of the rest of the class? You flunk a kid like that and you’re liable to get thwacked in the head by a rogue barometer.

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