Answer to mirror problem, I think...
1. As you look into a mirror, you see the top of your head at the top of the reflection, bottom of face at the bottom of the image, right side of face to the right of the image, and left to the left. The process of reflection is the same in all directions.
2. In order to compare the reflection with the original reflected object (your face in this case), the object or the image must be flipped through 180 degrees. This is how the inversion happens.
3. You choose the axis of flip. The vertical axis is strongly preferred, but you could equally correctly decide that the image is upside-down.
Perhaps it's Descartes' fault for trivialising the difference between up and down, and left to right. It's common to think the mirror problem is about having two eyes, but actually, like storks and babies, there is a common cause: gravity. The real vertical axis is fundamentally different from the horizontals.
I wonder how mirror writing seems in Chinese?