Re:Galois Theory
by fredilo on Thursday August 15, 2024 @02:11PM
(#41258836)
The sentence you quote actually gives you the answer to your question but it is not completely obvious why. :)
The complex numbers are essentially the theory of 2D-space. You are asking about 3D-space. The statement that you quoted tells you that you cannot distinguish between up and down in theory.
Now, 2D-space is part of every 3D-space. There are multiple ways to see this. The easiest is to just drop the z-coordinate.
Suppose you could distinguish left-handed and right-handed in 3D-space. In this case, you would have a way to distinguish up and down in the embedded 2D-space. However, you cannot do this distinction in 2D-space and therefore you cannot distinguish left-handed and right-handed in 3D-space.
The complex numbers are essentially the theory of 2D-space. You are asking about 3D-space. The statement that you quoted tells you that you cannot distinguish between up and down in theory.
Now, 2D-space is part of every 3D-space. There are multiple ways to see this. The easiest is to just drop the z-coordinate.
Suppose you could distinguish left-handed and right-handed in 3D-space. In this case, you would have a way to distinguish up and down in the embedded 2D-space. However, you cannot do this distinction in 2D-space and therefore you cannot distinguish left-handed and right-handed in 3D-space.