Re:Swirling Forces, Crushing Pressures Measured in the Proton
by bmacho on Thursday March 14, 2024 @02:44PM
(#39707503)
> (You can build a globally consistent map on a torus.)
No, you can not, there is no global map on the torus.
Re:Swirling Forces, Crushing Pressures Measured in the Proton
by itishappy on Thursday March 14, 2024 @04:24PM
(#39708544)
My language may be imprecise.
What I mean is that you can assign a direction to each point of the torus, and have it be consistent with it's neighbors (free of discontinuities) throughout the entire surface. This is in contrast to a sphere, which will always have tufts (poles) at at least one point.
Note that this only applies within the surface itself, not to it's embedding in 3d space (the donut shape we're all familiar with). If north points up on the outside edge, it'll point down to us on the inside edge, but an ant on the surface would experience no contradictions.
https://en.wikipedia.org/wiki/Torus#/media/File:Torus_cycles...
Another way to think about it is assigning cardinal directions to the Earth. Which way is north from the north pole? There's no possible way to create a map that has defined directions at every point.
The pictures in the Wikipedia article give a great intuitive understanding, particularly if you can figure out why a sphere and torus behave differently. (You can build a globally consistent map on a torus.)