Last time, I told part of a story about you being an elementary school teacher of a particularly accomplished class grade six class. I set the story with the children at that age because it was then that my father encouraged my best friend at the time to measure the diagonal path in the roughly squarish park between our homes. He assigned the tape measure he had — 50 feet long — and helped us get started. I don’t remember the result, but nothing crossed my mind that suggested this was any different (except by length and flexibility) than the rulers I had used in class at school and at home.
I received no feedback on my little story, so I will continue the tale twice: first as an instrumentalist, then as a realist.
“No, my pupils, you have not done the same thing at all. Some of you used rulers, and some laser beams, and some a wheel.”
“But isn’t the park the way it is and not the way we say it is?“ Karen asks. “My cousins played in the park when they were younger than I am now, and since they are five or six years older, that was a while ago!” You encourage Karen to continue. “And so I think it was the same then. I mean it doesn’t change much. The slide is new, but it is the same size, right?”
“But did your cousins measure the park the way you did?”
“No, of course not. They didn’t have a teacher like you.”
“So, because length is what you get when you measure with a ruler, then it really was different. This sounds weird, but you have always held an instrumentalist view of measurement.”
“That is weird!” one of the more boisterous kids says when called upon next.
“But what about the units? We spent all that time a week ago learning about the metric system. Why are the units the same if they are not measuring the same thing?”
The class looks fairly confused at this point, and you consider your answer. “That’s just a simplification. In some contexts the outcome would be different.”
“George, Henri, did you ever fly your drone when it was cloudy?”
“Yes,” they answer.
“Did you try the laser then?”
“Yes, I remember,” Henri says. “It was hard to use.”
Considering your words carefully, you speak to the class about how the world contains relationships between things, or more correctly, between their properties. Some of the students know already that a smooth track makes for easier movement of toy cars than a rough one; others remember hearing the difference between a low note and a high note on their favorite instrument.
Measurements are a way to learn these properties by exploiting these indicators. The ear even performs a measurement of sorts, as your students learn with astonishment. But it is also true that we build instruments like rulers and measuring wheels because sometimes we need more accuracy than our own senses can produce.
You talk next about units. Using a ruler is too coarse to determine how far apart the gratings in the window grill are, but it was suitable to measure the park, with a bit of error. You discuss that next and how the cloudy day may interfere with the range laser on the drone but not the wheel. On the other hand, the wheel will be difficult to use for very long distances.
The class ends with Dora asking, “I heard someone at the planetarium say that the sun is 150 million kilometers away. I don’t think even the drone laser would help you figuring that out, right?”
“That’s right. How do you think they do it?”
Thinking that the class is really into this, you tell the students that they have two pieces of homework. One is to find out how people measure distances to things like the Sun. The other is to start the unit on ecology, by again going to the park and counting beetles.
“Is that a measurement?” you are asked.
End, For Now
I have tried to explain the instrumentalist view as reliably as possible. Let me know if I have been unfair. Years ago I was fortunate enough to ask the late Vic Stenger — who waffled between realism and instrumentalism — about some of the puzzles that these sorts of stories bring out in literary form. I found invariably that this pushed him towards realism, though something would always eventually bring him back to instrumentalism.
I have discussed physics examples because they are the easiest to get started with. To complicate your view, consider the question that you-the-teacher were asked in the last sentence of the realist ending. Also think about measurements of properties our senses do not seem to register: e.g., electric field strength, polarization of light, concentration of arbitrary ions in aqueous solution, even the wavelength of light.
Please let us know in the comments if you have a conundrum for Keith to investigate!