Keith’s Conundrums: Measurements

Keith Douglas

Last time I posed what I called “puzzles from childhood”. Alex graciously answered a good many of them; thanks! I will give a one liner answer to each one by name; read the original article to see the details  

1. Grade 10 physics lesson. Rays of light may be able to travel in all directions, but you do not have eyes all over your body and in particular, you are not a point, either.
2. Elementary school age macroeconomics. This one I have no idea about, still.
3. Wildfires. My father suggested that a single spark (never mind a lightning strike) would be enough to get the oxygen remaining to ignite all the carbon-hydrogen (he said “organic”, actually, which to an organic chemist is basically equivalent) based molecules on Earth. Note well: we are made of such (modulo a few things like water and the mineral part of bones).
4. Gambling. I knew at the time that a casino run with no overhead and no cheaters long term cannot lose. I do wonder in retrospect if the problem came from what one can presume was the religion of my classmate’s parents. (The name was a typical one associated with a religion that is often regarded as banning gambling.)
5. Muffins. I said the second classmate thought our first classmate was crazy to try to do this. I agree – work out how long it would take to do.
6. Folded paper. Usually people guess around 30 or 40 and are surprised to find that even 10 is very hard.
7. TV. Still don’t know this one.
8. TV inspiration. I have no idea how realistic it is – I’m more of a physicist (which is not saying much) than an automotive engineer, so I do not know if the calculations based on high school physics (which a precocious 10-12 year old as depicted on the show might know) would meet appropriate levels of un-idealizations.
9. Numbers. My answer now is that they are identical because we agree to the fiction that they are.

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Measurements

You are a teacher in an elementary school classroom – roughly grade 6. You assign your students the following task: determine how big the park near the school is. You recommend that the students start by measuring various dimensions of the park. Since many of the students love to bike along a diagonal path and hardly ever see some of the corners, 6 of the pairs of them start with that. They pair off and report back with the following: Abigail and Bob report that the diagonal is 18.3 meters long. Chen and Dora report that the diagonal is 18 meters long. Emily and Faisal report 19 meters. George and Henri report 1837 centimeters, Irene and Jo report 2 decameters, and Karen and Lundy report 60 feet.

You are pleased that your students got what appears to be good data and their presentations go well – for such young folks. One of the other students, who has yet to present his work on the perimeter of the park, asks a question. “Teacher, why did they all do so well? They did not do the same thing!” You think about the question, and say, “They reported in different units, and with different degrees of precision and accuracy, which we will talk about when the groups are finished, after the rest of you have had your turn.” The student is satisfied for a while, and then just as the first of the “perimeter groups” is ready to speak, he raises his hand insistently again, and asks: “I read the reports again, they didn’t do the same thing.” “He’s right!” speaks up a normally quiet girl in the class. “What do you mean? And please raise your hand next time.”, you ask.

“Well …” she begins. Her classmate speaks again, “I think we both saw that Abigail and Bob used a measuring tape. Chen and Dora used the blade of Dora’s hockey stick as being 30 centimeters long. Sort of like a ruler, I guess. And …” Enthusiastically, the second student finishes, “Emily and Faisal used an actual ruler. Georgie …” “GEORGE.” “Sorry, George, anyway you and Henri found a laser ranging system in your drone kit. Irene and Jo got a ball of string and stretched that out, finding it easier to measure hand over hand later with another kind of ruler and Karen and Lundy used a surveying wheel they got somewhere.” “My dad’s an architect and my mother is a carpenter, we’ve got lots of that sort of stuff”, Karen said proudly. The class murmurs with excitement. Seeing that the class is getting really into this discussion, you agree to return to this topic after the remaining presentations from the remaining 8 groups. By that time it is time for lunch, and the class files into the lunch area enthusiastically debating whether or not some group “did the right thing” or not.

The first part of our story ends here. 

(I had promised David to discuss realism vs. instrumentalism this time, but I think I have to leave the ending of the story to next time. Think about the debate I alluded to last time and the time before, and sketch out in your head how the story could continue. There’s another topic or two that are connected that might also come to mind when doing this exploration; feel free to post about those as well.)