This minutephysics video on misconceptions has gotten shared with me a number of times in the past few years, and I finally decided I need to comment on it:

I enjoy a number of the minutephysics videos. Many of the explainers he's made are, frankly, the most excellent things out there. I have a lot of questions about the role of such explanations in education, but I do sometimes use them, and for what they do, they do a great job. But this particular video is not an explainer -- it is a *polemic*. The author is making an argument that high school teachers are frequently teaching the wrong material, that we should be teaching different material in a different way, and that it is our fault that students have these wrong ideas about the earth's shape, velocity addition, gravity, and so on.

My response here is also a polemic -- I think he is wrong, badly wrong, because he seems to have some misconceptions about how people learn and about what they are learning.

So let's take a look at the arguments he's making:

First, he's obviously absolutely right in all of his content claims. The earth isn't flat. Velocities don't actually add the same as regular vectors. Gravity is not due to the product of the masses of the gravitating objects.

But these are not actually misconceptions, in the sense of a "factually incorrect idea that a student has".

## These are models.

One model that explains our experience of the earth is that it is a flat surface. This model works quite well when one moves around on distance scales comparable to a city, using a grid system of streets that are mostly parallel and perpendicular to each other, with only modest hills interrupting the otherwise smooth surface. When this model is applied to the task of making a paper (or screen) visualization of the earth, the flatness of the model is convenient in construction, but deeply misleading if the map is to show features at scales greater than a few hundred miles. Consider the shape of Greenland on most flat maps. Consider the crazy zigzags on maps of counties and properties in the northwest corners of some US states. And the model gives deeply wrong predictions when considering the motions of the planets and the stars. A deeper, more correct model says that the earth is a sphere. A deeper model than that says it is an oblate spheroid. A deeper model than that gives a map of the mass distribution of the planet in excruciating detail. Which of these is the "correct" model?

They all are, depending on your purpose. minutephysics argues that the belief that the Earth is flat is a paradigm example of a misconception about the world that all teachers should seek to correct, and I argue that it is a paradigm example of a model of the natural world that has a specific domain of applicability. The flat earth is a good model for small distances and for making maps of cities. The other models are better for other, specific purposes. The nice thing about the spherical model of the Earth is that it is one that a kindergartner can understand by giving them a globe, so they really never have to be "stuck" with the flat model -- starting in kindergarten one can talk about the how the planet seems flat if you don't walk very far, but it is really a very big sphere. Starting in middle school or high school or college, students can talk about the limitations of the spherical model and how it really does a good enough job for pretty much every question they are likely to face.

On the question of the shape of the earth, I think the video is mostly right that we should be teaching the spherical model -- because (1) It is simple enough to be understood by a 6 year old, and (2) It does not make it more difficult for the student to navigate (hah) the world they actually live in, which seems mostly flat and which has flat map representations on the walls, (3) as long as teaching is careful to talk about the limitations of the model at appropriate times in the child's development. In any case, the video is using the flat earth as an example of something we *don't teach* because it is obviously ridiculous (I mostly agree), so that we can agree with him that it is equally ridiculous that we teach:

- That gravity obeys Newton's law of universal gravitation \(\mathbf{F} = -G \frac{m_1 m_2}{r^2}\hat{r}\)
- And that relative velocities follow the "Galilean" transformation of simple vector addition

I completely disagree with the second, partially with the first.

## Vector addition model

Let's start with the second one. Vector addition of velocities is a model that helps us understand how relative velocity works. If I am driving 20 miles per hour and I hit from behind a car that is travelling in the same direction at 17 miles per hour, the thing I want to know to know how bad the accident is going to be is that the velocity *difference* is 3 miles per hour. If we flip that around so the collision is head on, I want to know that the relative speed in that crash is 37 miles per hour. I immediately understand that the second situation is much, much worse, and understand why there are concrete dividers between the two directions on a freeway.

- This is a model that
*works*for just about every conceivable situation an ordinary person is likely to face as they navigate around a city, the country, in cars, on trains, while walking, while throwing baseballs, while getting on and off space ships, and so on and so on. The domain of applicability of this model is*enormous*. - This is a model that requires practice to use effectively. My 12th grade students understand the basic idea and find it basically intuitive, but using it to make predictions does require some thought and practice, particularly if the velocities being added are not colinear.
- This model has some subtle but important consequences that are both correct and not obvious. If you throw objects around inside of a vehicle, they behave exactly the same (from the point of view of someone in the vehicle) no matter how fast the vehicle is moving (as long as it doesn't accelerate). If you don't practice using the model by making predictions about situations like this, you will have dramatically wrong ideas about the rest of physics. (Like the independence of vector components and the implications of momentum conservation)

For those three reasons, this model is *worth spending time on* at the high school level. My students would be wrong about a lot of mechanics if they didn't have this model down.

So what does the "more correct" model of velocity addition that comes from special relativity give us?

It corrects the velocities obtained in the "naive" way in the example in the video by a factor in the 17th freaking decimal place!!!!!!!!!!!!!

Yes, this is absolutely more correct. But is minutephysics seriously saying that I should teach the relativistic velocity transformation *instead of* simple vector addition? How could a student even begin to understand the relativistic transformation if they didn't *first* have a solid understanding of vector addition? Spending time on one model means spending less time on some other model -- we have scarcity in education and scarcity in brain resources. If I teach both of these models at the same time, students will not be able to use either one in the future. And supposing that I do somehow help them to the point that they have the "correct" model down, have I then cheated them of a better understanding of the kinds of situations they will actually experience every single day of their lives?

Incidentally, I am saying this as a high school physics teacher who *does* teach special relativity, so I agree that it is worth learning at some point. But not first. And if I had to choose between Lorentz and simple vector addition due to time constraints, you can bet I'm choosing vector addition.

## Inverse square law model

So what about the gravity issue? This one is a little less problematic, because there are fewer people who truly have an everyday experience of Newton's inverse square law, thus it is less of a problem if they don't understand the simple model as well. There is basically less cost in helping them develop the more "correct" model from general relativity instead of the simple model from Newton. In that case, if the objective of the class is to have some correct ideas about how the world works, without needing necessarily to be able to calculate or predict with it -- then Einstein's gravity is a better choice than Newton's.

But if my students have any expectation of using physics to do anything, I am doing Newton's gravity first, and I am content not to get to Einstein if there isn't time. Because Newton's gravity can get you to the moon. The model

- works for a wide domain,
- it requires practice to use effectively, and
- it has a lot of subtle but important consequences that are both correct and not obvious.

Exploring the inverse square law is really rich, it makes connections to other areas of physics, to calculus, to the history of the subject. It's awesome stuff, and it is worth spending time on it, at the high school level, as long as there is some discussion of the domain of applicability, as there should be with *every* model.

## What are we doing this for?

I think I would summarize my position like this: Good physics teaching & learning is about learning how to understand, use, create, and refine models of the physical world, and to understand the domains in which they are applicable and useful. The process of developing those models is as important (more important) than developing the "correct" models, because students who won't become physicists will take away from my class the mindset, and students who will become physicists will find that their job is to create new models when they discover the old ones have limitations -- what better way to prepare than to work with models that work, but which have limitations that they can discover? I am not cheating my students of the truth if I don't teach them relativistic velocity addition or the stress-energy-momentum tensor. I am helping them develop the tools to understand the world they experience, and the mindset to question those tools as they continue to develop. We would all be better off if those whose goal is simply to explain science (rather than help students learn to *do* science) would remember that their goals are not my goals, and their advice is likely to be the product of, shall we say, *a limited model* of the role of the teacher.