Which way is up?

Today, I was showing the Calculus class how to analyze graphs using something known as a side chart, which is a number line with random-looking scribbling on it. I was setting this up and somebody gently asked, "Is it okay if I put -2 to the left of 0 and 2 to the right of 0?" So I looked and saw that I was doing my number line backwards, counting down instead of up as I moved from left to right. There is nothing intrinsically wrong with this. The number 2 is not to the left of 0 any more than North on a map is actually up.

There is no correct way to make a number line, no matter what the math teacher and book says. When you are doing one "correctly," what you are doing is what the convention is and what the authority figure told you to do, nothing more. In fact, any Algebra book is filled with number lines that don't go from left to right. Every graph has one that goes up and down as well, and a 3D graph would have one sticking straight out from the page, if lines were actual things. Any convention that is dependent on the orientation of your paper is just silly (what I did would be perfect if you were looking at it upside-down) and violates the beauty of working with something that is entirely conceptual. Math certainly has plenty of absolute rules, but none of them say anything about left, right, up and down.

Maps, on the other hand, are a completely different thing. North and South are just ways of going around in a circle, and there's nothing up or down about that. And making a map means taking the surface of a sphere (or spheroid, anyway) and translating onto a 2-dimensional representation. There are few things less 2-dimensional than a sphere, so the whole idea is a travesty and a sham. It's done for people's convenience with no regard to accuracy. It's a mess and I just hope nobody ever tries to do it to me.