4 ms·

Consider the surface of a sphere. It is finite but has no centre.

krisgee 11y ago
To make it clear we're on the surface of the sphere, not inside it. I misunderstood this analogy for a long time.
TeMPOraL 11y ago
Oh, I forgot about those cases. Thanks! But are those types of models the only finite universe models currently considered? What about just bog standard "surface of a circle", aka. space in a sphere? After all, Olbers' paradox gets resolved by the speed of light and the expansion of the universe.
- pdonis 11y ago
  > are those types of models the only finite universe models currently considered? Yes. > What about just bog standard "surface of a circle", aka. space in a sphere? Such a model would not be spatially homogeneous or isotropic; the "radial" direction (toward or away from the center of the sphere) would be different from the tangential directions. But all of our observations indicate that our universe is spatially homogeneous and isotropic.
- TheOtherHobbes 11y ago
  The "sphere" has more than the usual three dimensions, so the "surface" is really our four dimensional space/time. From the point of view of any observer in our universe, space/time accelerates away equally in all directions - just like a grid on a ball that's inflating spreads out over time. But the grid has more than two dimensions. You may be wondering what's "inside" the "sphere." Whatever is there can't be reached from the universe, no matter which direction you travel in. It's literally in a different dimension. But that's almost completely meaningless as a statement. No one has any idea how the "sphere" really works. In our universe we can take it for granted that space/time defines a system for measuring shapes and distances. Outside of the "surface" of the universe, there's no way to know how shapes or distances work, or whether there even needs to be something on the "inside" - it's possible the "sphere" only exists as a mathematical template, because it's the only way space/time can hang together, and it's some kind of weird emergent thing that has to happen. (Insert further idle speculation here.) This is all really, really hard to imagine. Brains evolved for swinging through trees can't visualise it without math. Brains with math are still very much struggling with it.

To make it clear we're on the surface of the sphere, not inside it. I misunderstood this analogy for a long time.

Oh, I forgot about those cases. Thanks! But are those types of models the only finite universe models currently considered? What about just bog standard "surface of a circle", aka. space in a sphere? After all, Olbers' paradox gets resolved by the speed of light and the expansion of the universe.

pdonis 11y ago
> are those types of models the only finite universe models currently considered? Yes. > What about just bog standard "surface of a circle", aka. space in a sphere? Such a model would not be spatially homogeneous or isotropic; the "radial" direction (toward or away from the center of the sphere) would be different from the tangential directions. But all of our observations indicate that our universe is spatially homogeneous and isotropic.
TheOtherHobbes 11y ago
The "sphere" has more than the usual three dimensions, so the "surface" is really our four dimensional space/time. From the point of view of any observer in our universe, space/time accelerates away equally in all directions - just like a grid on a ball that's inflating spreads out over time. But the grid has more than two dimensions. You may be wondering what's "inside" the "sphere." Whatever is there can't be reached from the universe, no matter which direction you travel in. It's literally in a different dimension. But that's almost completely meaningless as a statement. No one has any idea how the "sphere" really works. In our universe we can take it for granted that space/time defines a system for measuring shapes and distances. Outside of the "surface" of the universe, there's no way to know how shapes or distances work, or whether there even needs to be something on the "inside" - it's possible the "sphere" only exists as a mathematical template, because it's the only way space/time can hang together, and it's some kind of weird emergent thing that has to happen. (Insert further idle speculation here.) This is all really, really hard to imagine. Brains evolved for swinging through trees can't visualise it without math. Brains with math are still very much struggling with it.