All of Simon DeDeo's Comments + Replies

We've been thinking about explanations in our research (see, e.g., https://arxiv.org/abs/2205.07938) and your example of explaining the wrong answer well is lovely.

I dislike these kinds of questions, because they're usually posed at a point well before the wave equations are presented. At this point, you are largely working with verbal explanations and, as you point out, verbal explanations are much harder to pin down. 

Mathematically, if A implies B, and you are working to the best of your ability, you can't derive ~B (you may not be able to derive B,... (read more)

2AnthonyC
I agree that they're not great test questions, but they can be excellent class discussion or homework problem set questions (as long as you encourage working together on homework, which can work in college but not usually in high school). If anything, using them well puts a much higher burden of understanding on the teacher to not only know the answer but also all the ways students are likely to go wrong in trying to reason about the answer and how to steer the discussion without just giving the answer. In this case, yeah, I'm sure this question was posed at a point where the student doesn't really know what T and P mean at a fundamental level, what makes a gas "ideal," what the Maxwell-Boltzmann velocity distribution is and why, and a whole bunch of other relevant things. Given that, you should still be able to reason it out using dimensional analysis, the definition of kinetic energy, the idea that T is proportional to kinetic energy, and looking at some limiting cases and boundary conditions, but it isn't easy.
3Ben
Personally i think the verbal kinds of explanations still have an important role in more advanced physics, as something you can present after the calculation or simulation. Things like 'it kind of makes sense that we see this because...' or 'this may seem surprising but it actually makes sense if you look at it as...'.
2M. Y. Zuo
What would the same question look like when presented in mathematical form? At a quick glance I can't see a concise way to express it.

Interesting. It’s not clear that conspiracy theorists would disagree with scientists about the quality of an argument that touches on neither of their domains. It’s entirely possible that both are able to agree about good and bad arguments for (say) abortion rights, even if they have opposing positions. (E.g., they may well be able to agree that “X is a better argument than Y”, even when one disagrees with both, and the other agrees with both.)