How Do We Know What We Know?

musings on scientific knowledge

Monthly Archives: May 2011

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

The fear is unfounded

The start-up had been preceded by some well-publicized hysteria on the fringes, with alarmists worrying that the L.H.C. would create a black hole that could swallow the earth. (The fear is unfounded.) There was also a cern subplot in Dan Brown’s Angels and Demons, in which Illuminati steal anti-matter from the L.H.C. in order to evaporate the Vatican. (Also not a concern—it would take an impossible amount of time and energy to produce enough anti-matter to make a bomb.) source

I have to say, it’s so nice to read a news article that actually just says when fringe opinions are fringe opinions. This gets into one of my things about the language of science, which is that we don’t like to say things are impossible: that’s like asking your next experiment to prove you wrong. We know we don’t know everything about the universe; finding the impossible stuff is the point. But that tends to give lay observers the sense that things are more probable than they are, because in other situations people round “deeply unlikely” down into “not at all possible,” and many scientists won’t.

Take the thing about the LHC destroying the universe. Before it was turned on, could we say with absolute certainty that it wouldn’t? No, because we can’t say anything with absolute certainty. But were any physicists involved with the experiment saying their last goodbyes to family members? No. (Well, perhaps jokingly.)

I like the phrase “the fear is unfounded.” It captures the right sense: not that the thing is impossible, but that it’s sufficiently unlikely that one need not worry about it.