mathemachristian[he]

Manifolds such as these are actually defined by the maps used from a linear space. Two manifolds (i.e. two sets of maps) are considered the same (isomorphic) if the maps of one set can be “morphed” into the other and vice versa.

The flashlight demonstrates how the manifold’s map projects into the linear space. See stereographic projection.

That’s kind of part of a larger point actually: There is no 3d vector space in reality. It’s a made up construct used to make sense of the world around us.

So you don’t consider it a valid criticism? Then what “both” things did you think were true?

Edit: am I understanding this chain correctly that you think it’s invalid because it could be made about other nations as well??

“Dumb” and “valid” cannot be true at the same time lmfao, that’s the simple logic I am getting at.

The criticism is simultaneously both dumb and valid?