RE: No perfect circles in space...
July 22, 2018 at 12:56 pm
(This post was last modified: July 22, 2018 at 12:57 pm by Jehanne.)
(July 22, 2018 at 12:38 pm)polymath257 Wrote:(July 22, 2018 at 7:49 am)Jehanne Wrote: A dimple is fine in 2D; but, how do we imagine such in 3D?
Through practice, mostly. Start by trying to imagine a sphere in 4 dimensions: it provides an example of a curved *three* dimensional manifold.
I might recommend the book 'The Shape of Space' as an introduction:
https://www.amazon.com/Shape-Space-Chapm...e+of+space
Like seeing "dead people" (from the movie)? I can't imagine that 4th dimension, although, the math (tensors) is completely reasonable and valid.