4 ms·

> These things aren't ordered, and in fact you can't really distinguish between the three familiar spatial dimensions: imagine trying to point along dimension o

by bmitc 3y ago

> These things aren't ordered, and in fact you can't really distinguish between the three familiar spatial dimensions: imagine trying to point along dimension one, whatever that means. I actually don't know what this means. You can certainly distinguish between the three spatial dimensions. Pointing along dimension one is irrelevant. Once you point in a direction, you can define the others given an orientation, and there are only two unique orientations on a three dimensional manifold.

lupire 3y ago
What they are saying is that you can't make a non-arbitrary identification of each dimension. You can call them 1,2,3, and I can call them 2,3,1, and that changes nothing except your arbitrary labels. A third party has no way to know whose choice of "1" is better for any reason related to the space itself, only by reference to some preferred object in the space, like the direction my pencil is pointing right now. Space itself has no such preferred object or direction.
- bmitc 3y ago
  > What they are saying is that you can't make a non-arbitrary identification of each dimension. You can call them 1,2,3, and I can call them 2,3,1, and that changes nothing except your arbitrary labels. I don't understand the point. What is the supposed consequence of that? As far as I can tell, it's an empty statement. And as I said, there are only two orientations in three dimensions. For an orientation, which is an equivalence class of ordered bases, the order actually does matter. You can call them whatever you want, but once you've called them something, their order matters, which was my original retort.
  - lupire 3y ago
    > You can call them whatever you want, but once you've called them something, their order matters, which was my original retort. Right and different "local cultures" in Flatland call them different things, so the order matters. Orientation is a red herring. The same issue appears in 2-D manifolds inhabited by 1-D sub manifolds that one day "discover" the "other" dimension.

by bmitc 3y ago

lupire 3y ago

What they are saying is that you can't make a non-arbitrary identification of each dimension. You can call them 1,2,3, and I can call them 2,3,1, and that changes nothing except your arbitrary labels. A third party has no way to know whose choice of "1" is better for any reason related to the space itself, only by reference to some preferred object in the space, like the direction my pencil is pointing right now. Space itself has no such preferred object or direction.

bmitc 3y ago
> What they are saying is that you can't make a non-arbitrary identification of each dimension. You can call them 1,2,3, and I can call them 2,3,1, and that changes nothing except your arbitrary labels. I don't understand the point. What is the supposed consequence of that? As far as I can tell, it's an empty statement. And as I said, there are only two orientations in three dimensions. For an orientation, which is an equivalence class of ordered bases, the order actually does matter. You can call them whatever you want, but once you've called them something, their order matters, which was my original retort.
- lupire 3y ago
  > You can call them whatever you want, but once you've called them something, their order matters, which was my original retort. Right and different "local cultures" in Flatland call them different things, so the order matters. Orientation is a red herring. The same issue appears in 2-D manifolds inhabited by 1-D sub manifolds that one day "discover" the "other" dimension.