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.
Seems to me like it’s demonstrating the projection of a complex three dimensional shape which produces a simple pattern on a two dimensional plane.
It’s worse. It’s the projection of a 3d shape onto a 2d shape, which is then captured on a different 2d shape to be displayed to us.
It also has a brief 4d dimension, sliced at the second the picture was taken.
Rolling shutter, my beloathed…
thatsthejoke.jpg
But what’s the time equivalent flashlight?!
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.
deleted by creator
Hiu