I can't even sharpen a chain-saw properly, so I'm not much of an asset in the forest. All that book-l'arning ain't worth squat out there. But when it comes to measuring the height of a single tree in a manicured park, then I can contribute. I've had a lot of help in this task over the last half decade from several batches of Transition Year (TY) interns who came to The University (where I "worked" before I started working at The Institute in January) for a week's work experience. Transition Year occurs in some Irish schools immediately after the national mid-teen examinations (Junior Certificate) and before the poor creatures launch themselves at the two-year Leaving Certificate course to graduate from secondary school. The interns came for some experience working in a science laboratory. But my boss decided that they would get all wan and pasty if they were indoors all week and that they should also get out to explore the beautiful and inspiring University campus.
treasure hunts. The TY TH consisted of a map and a dozen or more find-me questions illustrated with pictures. One of these questions was "What is the height of this fine plane tree next to the Civil Engineering Building?"
An integral part of the TH each year was the post-mortem discussion and de-briefing when each of the several teams of interns got a chance to tell us their considered answer and reflect on the, often wildly different, estimates of the other people.
We got some strange and creative ideas over the years but hardly anyone ever applied the "mathematics" that they had just sweated blood from their eyeballs over during their Junior Certificate.
This discussion sometimes gave me a chance to share one of the great urban legends of creativity in science which is usually attached to precociously sassy student Nils Bohr long before he won his Nobel Prize:
He was set to fail his Physics Exams because he hadn't deigned to answer the question "How would you use a barometer to calculate the height of such-and-such tall building". But two of his professors asked him to a viva voce examination to redeem himself because he showed promise. Still refusing to give the "physics" answer involving the relationship between atmospheric pressure and height, Bohr rattled off a dozen solutions to the problem as stated. These have been gathered together in a famous essay by Alexander Calandra and include
- go to the top of the building with barometer and stop-watch and time the former's descent under gravity (g = 9.8 m/s2 = 32 ft/s2) with the latter
- lower the barometer on a string to almost touch the ground and time its period as a pendulum (Galileo's method)
- find the building custodian in the cellar and offer him a fine barometer if he will show you the plans of the building
Answers in the comments please. Precociously sassy answers def'ny allowed. I'll show you mine after you show me yours. Ladies and gentlemen, commit!
Note added 13Jun13: you can get a few different solutions to methods that work.