How Do We Know What We Know?

musings on scientific knowledge

The Evils of SI Units

The post title is kind of a misnomer: I actually think SI units are a net positive. No reason to spend a lot of time doing complex unit conversions. That being said…

I think the introduction of SI units in classes–and the lazy way lots of teachers, myself included, do examples–hurts the way students learn science. In particular, it tends to make people think that units don’t matter.

Now, the particular unit you choose for one dimension–such as choosing feet or meters for length–doesn’t matter a great deal. I am the same height if you say I am 5.50 feet tall or 1.67 m tall. But that dimension is really important: it’s nonsensical to say I am 1.67, without reference to a system for measuring lengths, or to use an inappropriate unit (I am not 100 Watts tall). The problem is that you can usually get the right answer in SI without keeping track of your units step to step, and so beginning students often think the dimension as well as the unit is unimportant. This problem is particularly noticeable in astronomy because we use so many idiosyncratic units (a problem in itself, but anyway…).

In some sense, if you’re using SI units, the units really aren’t that important and, if we were more sensible, nobody should need the kind of facility most astronomers have with unit conversions1. As long as you know what dimensions you need to have, keeping track step to step is one of those things like simple algebraic manipulations that–given practice–you can usually do in your head, going back only if you can tell at the end that you’ve screwed up. But on the other hand, sometimes it’s the units themselves that tell you you’ve screwed up! In some classes I’ve taught, students get tangled up with G, the gravitational constant, and g, the acceleration due to gravity on the surface of the Earth. They have different units, so you’d be able to tell if you had the wrong result if you were careful doing the calculation–the units are important not just because they’re part of reality, but because they help you understand the problem you’re doing.

How do we solve this problem? I think a bit of dimensional analysis is one option, especially in physics classes. It helps illustrate that you can sometimes figure out how do to a problem just by the dimensions involved. Also, instructors need to be really careful in introductory classes not to drop the units in intermediate steps. It’s a pain, but it’s really important for understanding.

And we keep the SI units. What can I say, powers of ten make me happy.

1: No unit is going to have easily comparable values when we deal with scales from optical wavelengths (~10-6 m) to the distance between galaxies (~1022 m). Why do we insist on sticking with the centimeter when everybody else is using the meter? Are we really that perverse??2 back

2: Yes. Also, I think we’re stuck with arcseconds.back

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