# Think differently

I came across a story that was simply too good to not repost. Titled learning to think differently, I first saw it in Slashdot comments, though it seems that Snopes has found it to be an urban legend, with roots going as far back as 1958. The Barometer Problem is a story of education, physics, and inspirational ingenuity.

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 to 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 had not 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, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of simple proportion, determine the height of the building.” “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 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 tact, 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.

Absolutely brilliant! There are a lot of valid solutions to solving the given problem. Many indeed demonstrate knowledge of physics.

I could probably add another one to the list. A barometer has fine precision marks along its circumference. Those could be used to count off the angle between the base, you, and the top of the building. Measure the distance from yourself to the building, and then it’s a matter of simple trig. Height = distance from building * Tan(angle).

I would like to take all of this an in inspirational message in favour of creativity, in favour of thinking differently. Oftentimes, the solutions that we don’t expect are the most interesting ones.

Uhh... nothing else appears to be relevant enough.

## Discussion

1. Posted by Adam McKerlie | October 9, 2007, 8:26 am

I personally I would have used the “Letting it fall” method mainly because I enjoy watching things break.

This has a lot of relevance in the CS field as well. Profs are always telling you to solve problems this way or that way when there are probably a million different ways to solve the problem.

It all comes down to marking. If a professor accepted every single “right” answer they would have to carefully go through every question of every student to make sure that its right. If they only allow the “most right” answer they can scan through the submitted answers and look for key words or equations.

Thanks for posting this, I hadn’t seen it before.

2. Posted by Tony | October 9, 2007, 8:30 am

Adam – I also like the “drop the barometer” approach the best, but it’s not about breaking things (after all, you can later trade the barometer in for some additional information from the superintendent). Though this does reflect well on programming in a number of ways:

• It’s good to run programs through sets of test cases and mark on the correctness of the output. To such extend, I’d like to see a course where I get to pick a new (freely available) programming language, best suitable for each assignment.
• It’s a bad idea where a problem set requires one to write a, very specific, missing line of code. When one is told exactly how to think, you no longer have to think at all – blunt memorization will do.

Of course, not every correct output is achieved in a correct way.

3. Posted by Olga | October 9, 2007, 1:54 pm

lol
This reminds me of that ‘Hell Explained By A Chemistry Student’ story Nic sent us a while back.

4. Posted by Geoff | October 9, 2007, 2:46 pm

The moral of the story is very true, but I’d rather see it from an example more related to modern physics. All the solutions to this problem could have been solved in the time of Newton (or even Galileo?). This makes it more accessible to the layman, but then you have to ask if there’s really that much freedom of thought in modern physics. The answer is yes, there is still freedom of thought (I can’t quantify how much, though), but it’s still nice to see examples of it.

5. Posted by Tony | October 9, 2007, 3:53 pm

For anyone who’s interested, the Hell Explained By A Chemistry Student references a “proof” that Hell is exothermic, and also proves the existence of a divine being, all while getting laid. Science has never been so much fun!

Geoff – the story would probably not have gotten as much popularity if students could not relate to the simpler approaches.

I think quantum computation would be a fine example of different thought in modern Physics, especially as it relates to Computer Science. Students are taught to think linearly, in 1s and 0s. Though here’s a new world that requires a completely different mindset – concurrent computation with states that are sometimes both 1 and 0! It could be mind boggling.

6. Posted by Geoff | October 9, 2007, 4:33 pm

Well, in that realm, what is the problem? We’re looking for situations where we have a well-defined problem and have multiple solutions. Of course there are plenty of examples of this in Quantum Computing. Many are engineering type problems though: how do you build a qubit? Superconductors? Lasers? Ions in a lattice? Perhaps there are more ways to do it that we haven’t yet conceived. Or, how do you measure the state of a qubit? But these aren’t very well defined questions. I’m looking more for questions that are things like “prove this” or “calculate that”. I vaguely remember one example from String Theory. Something about if you look at the string over time it forms an encompassing surface that can shield the universe from otherwise potentially disastrous events.

7. Posted by Abhijit Nadgouda | October 10, 2007, 2:31 am

I think this is a classic case study for software development. A problem can have various solutions, which one to choose will depend on the constraints. A prerequisite to be able to pick out the best solution is that you have to think of multiple solutions first. Good one!

8. Posted by maximina ballada | October 10, 2007, 8:35 am

My head was a little bit shaken with all those mathematical formula you presented. But I admire your superb analysis on the problem solution you even impress me on the way you dig an analogy of the student’s premise to common situation in a classroom. I could somehow relate that to all my bookies professor during my college days who were just lazy to teach and just let students memorize the pages of the books.

9. Posted by cbright | October 10, 2007, 10:54 pm

Ok, he’s creative, but this also makes him a smartass.

10. Posted by Tony | October 11, 2007, 3:24 am

The story is meant to inspire and bring across a message about the state of education. If it takes a “smartass” character to do so – so be it.