Mei arrives a little after Lan Wangji. She is also excited at the prospect of Combat Math. She perhaps did not read the course description very carefully.

Wei Wuxian is sitting half out of his chair and spinning his sliderule. "Everyone ready to punch math?"

Masozi followed Wei Wuxian from their previous class together, which was pretty interesting. 

He's SO excited about more math! Though he's a bit stressed about it all being in Mandarin. He makes sure to sit right next to Wei Wuxian, as soon as he's finished checking the entire room very carefully for mals. 

On every one of their desks is a piece of paper which says:

1. Wetting your feet
1.1 Estimate how many liters are in a barrel of oil and how many barrels of oil China imports every year.
1.2 The mass of the sun is 2 · 1030 kg. Estimate the mass of earth and the ratio mass of sun / mass of earth.

This isn't about combat at all.

This is the best math class ever.

This is the worst math class ever.

Masozi puzzles over the Mandarin characters for a bit, and even recognizes a few, but eventually has to admit defeat on understanding the question and ask Wei Wuxian to translate. 

….Those questions are SO UNFAIR how is he supposed to know literally anything that could help him out here???

“Wei Wuxian?” he whispers. “Is the sun bigger or smaller than the earth - am I supposed to know the answer to that already…?”

Wei Wuxian immediately begins singing:

The sun is a mass of incandescent gas
A gigantic nuclear furnace
Where hydrogen is built into helium
At a temperature of millions of degrees

The sun is hot

It is so hot that everything on it is a gas
Iron, copper, aluminum, and many others

The sun is large

If the sun were hollow, a million Earths could fit inside
And yet, the sun is only a middle-sized star

The sun is far away

About ninety-three million miles away!
And that's why it looks so small

And even when it's out of sight, the sun shines night and day!

"Except," he says at the end, "it's actually not gas, it's plasma, which is what happens when you heat things up so much that they stop being gas."

"Do you guys think we're allowed to say the mass of the earth is one earth mass? That's a real unit of measure they use it for planets." 

"I think it's worth a try to see if the school will accept it."

"- So if a million earths fit inside then it's a millionth of - no wait sometimes things take up the same space but are heavier. I......would the sun sink or float on water?"

This class is extremely weird! Not in a bad way but Masozi feels like he's mostly going to end up learning things totally unrelated to math. 

"I think the sun is denser than water?"

"The sun is way less dense than water. But it's still a lot bigger than the earth in mass, you can tell because the earth revolves around it but I don't actually remember how much one earth-mass is in kilograms so I don't know how much bigger?" 

"Well, a million earths could fit inside, so probably it's a million times larger?"

"That's volume, though, and the sun is less dense than water so it has to be less dense than rock..."

He trails off. Confidently disagreeing with people is hard.

"Oh, that's a good point. How much less dense is water than rock?" He starts scribbling on a piece of paper.

"Yeah, rocks definitely sink–" Masozi stops. "Oh! I know how many miles it is from Malawi to Johannesburg. If you know how big that would be on a map of the whole world, then we can guess how many miles around the whole earth is! And then we could figure out its volume from there and then its weight - does anyone have a rock and a scale so we could actually check how dense rock -" 

He doesn't understand this class but it involves a lot of Wei Wuxian smiling so he's not very upset by it. 

"It depends on the kind of rock I think?" 

While they were distracted a second paper appeared on their desks:

Simple Methods for Order-of-Magnitude Approximation:

Divide and conquer: Split a complicated problem into manageable chunks, especially when you must deal with tiny or huge numbers, or when a formula naturally factors into parts.

Guess: Make a guess before solving a problem. The guess may suggest a method of attack. For example, if the guess results in a tiny or huge number, consider using divide and conquer. The guess may provide a rough estimate; then you can remember the final estimate as a correction to the guess. Furthermore, guessing—and checking and modifying your guess—improves your intuition and guesses for future problems.

Talk to your gut: When you make a guess, ask your gut how it feels. Is it too high? Too low? If the guess is both, then it’s probably reliable.

Lie skillfully: Simplify a complicated situation by assuming what you need to know to solve it. For example, when you do not know what shape an object has, assume that it is a sphere or a cube.

Cross-check: Solve a problem in more than one way, to check whether your answers correspond.

Use guerrilla warfare: Dredge up related facts to help you make an estimate.

Punt: If you’re worried about a physical effect, do not worry about it in your first attempt at a solution. The productive strategy is to start estimating, to explore the problem, and then to handle the exceptions once you understand the domain.

Be an optimist: This method is related to punt. If an assumption allows a solution, make it, and worry about the damage afterward.

Lower your standards: If you cannot solve the entire problem as asked, solve those parts of it that you can, because the subproblem might still be interesting. Solving the subproblem also clarifies what you need to know to solve the original problem.

Use symbols: Even if you do not know a certain value—for example, the energy density stored in muscle—define a symbol for it. It may cancel later. If it does not, and the problem is still too complex, then lower your standards.

Masozi is pretty sure that contains MANY Mandarin characters he's never seen before! He goes through it and circles everything that he does recognize and spends a bit of time breaking down bits that he thinks are 'radicals' like Lan Xichen explained. 

And then turns to Wei Wuxian. "It says - small, here? And this says something about parts and something about - cutting? I think I might be remembering that wrong though. And this says something about being tall? ....Sorry I can't actually figure out what this paper says can you help please." 

Wei Wuxian reads it out loud to him in English.

Why is this math class about trusting your gut! The whole point of math is that there are numbers and you do things with the numbers and you know what the rules are and at absolutely no point do you have to trust your gut! 

Masozi thinks this math class is great! It's - actually kind of the way he does math all the time in his head anyway? The main problem is that it expects him to know things like 'the sun is bigger than the Earth.' 

"Wei Wuxian?" he asks. "Why does the sun being bigger mean that the earth goes around it?"