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> if I understand the whole comment right, a curved universe is guaranteed to have an edge, but with a non-curved one it's a toss-up because no one knows what i

by sounds 4y ago

> if I understand the whole comment right, a curved universe is guaranteed to have an edge, but with a non-curved one it's a toss-up because no one knows what it would look like. A curved universe doesn't "have an edge," I'm referring to Euclidean and non-Euclidean geometry [1]. As in, if the curvature is truly and perfectly zero, then the space-time we live in goes on forever. If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean. If it is truly and perfectly zero, then all I'm trying to say is that it goes on forever like an "ideal" 2D plane or 3D space. [1] https://en.wikipedia.org/wiki/Plane_(geometry) https://en.wikipedia.org/wiki/Plane_(geometry)

aasasd 4y ago
> A curved universe doesn't "have an edge" Ah, indeed, quite a brain fart moment from me there, since you explained the structure right in the previous comment. Pondering cosmology while sleep-deprived is suboptimal, I guess. Though now I'm curious about this: > If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean Would it be possible in theory that the three dimensions are curved like a helix—so they have constant curvature but don't intersect themselves? This way the universe would still stretch infinitely in most directions, but would be non-Euclidean, and you'd need to know where the ‘axis’ is to be able to see in a direction that shortcuts to another one.
- sounds 4y ago
  Just hypothetical 3D curved spaces here, not saying this has any physical reality - If the X axis curves into Y (i.e. wraps around the Z axis) and also has a slight negative Z component (i.e. to move in a helical fashioin) each of those curvatures would mean a line segment eventually intersected itself. It's the nature of the curvature: the space is not sheared (like a rhombus), it is curved (like latitude and longitude), which is why the line segment eventually intersects itself.

by sounds 4y ago

aasasd 4y ago

> A curved universe doesn't "have an edge" Ah, indeed, quite a brain fart moment from me there, since you explained the structure right in the previous comment. Pondering cosmology while sleep-deprived is suboptimal, I guess. Though now I'm curious about this: > If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean Would it be possible in theory that the three dimensions are curved like a helix—so they have constant curvature but don't intersect themselves? This way the universe would still stretch infinitely in most directions, but would be non-Euclidean, and you'd need to know where the ‘axis’ is to be able to see in a direction that shortcuts to another one.

sounds 4y ago
Just hypothetical 3D curved spaces here, not saying this has any physical reality - If the X axis curves into Y (i.e. wraps around the Z axis) and also has a slight negative Z component (i.e. to move in a helical fashioin) each of those curvatures would mean a line segment eventually intersected itself. It's the nature of the curvature: the space is not sheared (like a rhombus), it is curved (like latitude and longitude), which is why the line segment eventually intersects itself.