Is the space unending, i.e it has no boundaries? If yes, how can a thing exist which is non-ending? Its impossible for me to imagine something like that. Secondly, if its not and has boundaries then it must be inside some other thing which is either non-ending or itself contained in another thing. Yet, again same problem. If it is also inside some other thing, and the other thing is also inside other thing, then this series will never end. Imagining about this scenario makes me insane.

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    $\begingroup$ The surface of the Earth has no boundaries, yet it is finite. Infinite and unbounded are different concepts. $\endgroup$ Jul 2 '12 at 7:15
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    $\begingroup$ possible duplicate of Is the universe finite or infinite? $\endgroup$ Jul 2 '12 at 7:17
  • $\begingroup$ @Raskolnikov: I think not compact fits better than unbounded in the second sentece. The first sentence is a good example due to Heine–Borel, but in a metric space, the concept "infinite" is pretty much given by the property of unboundness, isn't it? $\endgroup$
    – Nikolaj-K
    Jul 2 '12 at 10:15
  • $\begingroup$ @NickKidman: The mathematical concept of compactness is in these cases saying that an infinite sequence of points accumulates somewhere, but the details are to define a notion of "finite" for spaces which do not has a distance structure and which are infinite down-below, with no ultraviolet regulator. We know we have an ultraviolet regulator of some sort, so it isn't clear a compactness notion is the best way to go about defining a physical notion of finite volume. Maybe finite maximum entropy is more correct for physics. $\endgroup$
    – Ron Maimon
    Jul 2 '12 at 17:45
  • $\begingroup$ Ashwin, there is one other option and that is the "closed universe" where if you go in one direction you eventually return to where you started, but from the other direction. This is impossible according to the intuitive "Euclidean" idea of space, but it is a logically self-consistent alternative idea. However, if you have to choose between the two insanities of "it goes on forever" and "it ends with a wall and there's nothing on the other side", I would advise you to choose "it goes on forever". "Space ends at a wall" is a logically well-defined possibility but it is not well-motivated. $\endgroup$ Aug 2 '12 at 8:36

If, by unending, you genuinely mean "no boundaries", then you can in fact easily imagine a thing with no boundaries; imagine a sphere and, well, you've done it.

Now, if, by unending, you mean "without end", then you're correct, it's difficult and perhaps impossible to imagine a thing that is unending.

But, is it impossible to imagine that space is without end? No, not if you recognize that space isn't a thing.

Now, we stray from physics to metaphysics.

If Space is a thing, an entity, then it follows that it must have identity and, to have identity, it must be finite.

But, if entities are in space, then to say that space is unending is simply to say that two entities may be arbitrarily far apart. But, and this is crucial, regardless of how large their separation, it is always, always finite.

It is the case that entities can be out of causal contact but that is in the realm of epistemology (what we can know), not metaphysics (what is).

  • $\begingroup$ In regard to the sphere example we may never meet an end in the two dimensions but what if we went up? $\endgroup$ Nov 27 '12 at 8:13
  • $\begingroup$ It is possible to describe a sphere intrinsically, without thinking of it as embedded in three dimensional space. Perhaps a better example would be the torus: The game world of some arcade video games like snake has that shape: If you leave the screen on one side, you reappear on the other side. This gives the example of a finite but unbounded two dimensional space. $\endgroup$
    – orbifold
    Mar 29 '13 at 17:32
  • $\begingroup$ @legrojan, you're evidently confusing a sphere with a ball. A sphere is the boundary of a ball and has no edge (boundary). For a 3D ball, the boundary is a 2D sphere - there is no r coordinate on said sphere, only the angular coordinates, e.g., latitude and longitude. $\endgroup$ Mar 11 '14 at 12:11

The most commonly accepted model of the universe is that it is finite yet unbounded

  • 1d analogy: you can walk forever around the circumference of a circle
  • 2d analogy: you can fly forever around the equator of the earth

In any of these cases, you will never reach any kind of barrier or edge.

In each case the space is curved in a higher dimension.

See http://www.bartleby.com/173/31.html


Cosmology can model space as infinite. But we are not sure how to model the very early universe as quantum gravity is needed once the density gets high enough. So there is some limit to what we can observationally infer about the size as we can't model effects beyond what light speed information could have travelled from the quantum gravity epoch.


It is not unending--- there is a big black wall 13.7 billion light years away (in what I consider the right definition of distance to the wall), which marks the end of what you should call space. This big black wall is the cosmological horizon, and it's like a black hole horizon, except surrounding us. We can't see past this wall, so it is consistent to say space stops there. In fact, it is probably necessary to say space stops there in quantum gravity, except we don't know how to do quantum gravity for this kind of horizon yet.

If you go there, the boundary just moves away from you to surround you in another way, so it is not paradoxical. By the time you reach the wall, the wall moves away, or if you wait long enough so that the horizon stops moving (due to the cosmological constant), when you go there, you can't come back to Earth anymore. So the limitless thing is gone, space is finite. It isn't necessary to say it is contained in something bigger, because we know what the natural boundary to a finite space can be--- one possibility is that it's a horizon. Another possibility is just a space that closes in on itself, like a sphere (but this was another answer).

This argument you give appears almost verbatim in the beginning of Aristotle's physics, and it, like everything else Aristotle writes, is both trite and wrong.

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    $\begingroup$ you've read "everything" Aristotle has written and it's all both trite and wrong? $\endgroup$ Aug 2 '12 at 3:26
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    $\begingroup$ @Richardbernstein: I have read enough to be certain--- it's like public opinion polling, you don't have to ask everybody, just a representative sample. I've read enough to know that he is not worth reading. The one thing in his writing which is not totally idiotic is the notion of "final cause" "efficient cause", etc, which is somewhat useful, but I doubt it's original to him, considering the awfulness of the other ideas. $\endgroup$
    – Ron Maimon
    Aug 2 '12 at 7:23
  • $\begingroup$ The true holographic boundary is future infinity, Ron. Galaxies don't stop existing when they cross our horizon! :-) $\endgroup$ Aug 2 '12 at 8:38
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    $\begingroup$ @MitchellPorter: No it isn't, this doesn't work, and yes they stop "existing" (whatever that means), the holographic boundary you imagine is inconsistent in quantum gravity, see the Nariai limit of deSitter for a simple example. In this case, a black hole horizon can swap roles with a cosmological horizon! This means that a singularity inside the black hole vanishes, and the future infinity of the infinite deSitter part turns into the future infinity of the black hole. The "existence" of the outside part is contingent on crossing the horizon to observe it, and this is a statistical thing. $\endgroup$
    – Ron Maimon
    Aug 2 '12 at 15:59
  • $\begingroup$ Can we perhaps consider the "big black wall" to be the fields of space-time moving outwards at the speed of light into the void? $\endgroup$
    – Michael
    Dec 18 '14 at 15:07

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