# Is the universe "curved?" **URL:** \ **Category:** Factual Questions\ **Created:** [September 28, 2012, 11:42am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127 "2012-09-28T11:42:07Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [September 28, 2012, 11:42am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/1 "2012-09-28T11:42:07Z")
Inspired by [my previous question re: the universe.](http://boards.straightdope.com/sdmb/showthread.php?t=666887) One often hears that space is “curved”, and that if you continue traveling straight in one direction, you will end up back where you started. The common analogy is that of the surface of the earth; to a casual observer it looks superficially like an infinite flat plane, but it is in fact curved, and if you travel in one direction long enough (~25K miles), you do indeed end up back where you started. Question: Is the curvature of the universe some kind of supposition, or is it a robust theory that is well-supported by observable facts? If the latter, what are those supporting facts/observations? ---
**Author:** ![Ken001](https://avatars.discourse-cdn.com/v4/letter/k/43a26b/32.png) [@Ken001](https://boards.straightdope.com/u/Ken001)\ **Post date:** [September 28, 2012, 11:56am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/2 "2012-09-28T11:56:52Z")
The Universe is saddle shaped but most of us (well, me) struggle with that. An hyperbolic paraboloid where parallel lines meet. The balloon analogy is easier to imagine but the saddle is more correct. I’ll leave it to others far more clever than I to explain further. ---
**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\ **Post date:** [September 28, 2012, 12:34pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/3 "2012-09-28T12:34:46Z")
> [@Ken001](#): > > The Universe is saddle shaped … I’m pretty sure the jury is still out but that all evidence points to a flat universe. ---
**Author:** ![Darth\_Panda](https://avatars.discourse-cdn.com/v4/letter/d/ee7513/32.png) [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)\ **Post date:** [September 28, 2012, 1:00pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/4 "2012-09-28T13:00:29Z")
Would a saddle shaped universe imply that God is a cowboy? ---
**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\ **Post date:** [September 28, 2012, 1:45pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/5 "2012-09-28T13:45:17Z")
Some experts think it’s shaped like a burrito. Early work on this hypothesis may be found [here](http://www.tumblr.com/tagged/shaped-like-a-burrito). A more serious review of the topic made my head hurt. [shape of the universe](http://en.wikipedia.org/wiki/Shape_of_the_Universe). ---
**Author:** ![si\_blakely](https://avatars.discourse-cdn.com/v4/letter/s/d9b06d/32.png) [@si\_blakely](https://boards.straightdope.com/u/si_blakely)\ **Post date:** [September 28, 2012, 1:50pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/6 "2012-09-28T13:50:19Z")
It should also be noted that not all “curved” universes allow return. It has to also be closed. In a toroidal universe (which is both closed and curved) you can travel in a straight line all you like, but will never return to your initial point (or so I was informed). Si ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [September 28, 2012, 2:23pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/7 "2012-09-28T14:23:24Z")
> [@si\_blakely](#): > > In a toroidal universe (which is both closed and curved) > > Si Can’t a toroid be flat? Like a game of Pac-man? ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [September 28, 2012, 2:30pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/8 "2012-09-28T14:30:10Z")
My personal theory (which I came up with when I was about seven) is that the universe is shaped like a ring, only in a demension we can’t perceive - so yeah, you end up back where you started. ---
**Author:** ![President\_Johnny\_Gentle](https://avatars.discourse-cdn.com/v4/letter/p/5f9b8f/32.png) [@President\_Johnny\_Gentle](https://boards.straightdope.com/u/President_Johnny_Gentle)\ **Post date:** [September 28, 2012, 2:40pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/9 "2012-09-28T14:40:47Z")
> [@hibernicus](#): > > Can’t a toroid be flat? Like a game of Pac-man? Pac-man is not necessarily toroidal (but not inconsistent with it either) because it can be played on a cylinder. The game Asteroids, on the other hand, is toroidal. The difference is the difference between two-dimensional space and three-dimensional space. You can think of a two-dimensional torus by [connecting opposite sides of a square](http://upload.wikimedia.org/wikipedia/commons/6/60/Torus_from_rectangle.gif). The three-dimensional torus is obtained in a similar way, except by identifying opposite sides of a cube. I couldn’t find any good animation of this in a quick search though. To answer your question, yes, a torus can be flat. In fact, if you don’t bother with the folding, but just accept that a spaceship can move off one side then appear on the other (as in Asteroids or Pac-man), that is flat. > [@si\_blakely](#): > > It should also be noted that not all “curved” universes allow return. It has to also be closed. In a toroidal universe (which is both closed and curved) you can travel in a straight line all you like, but will never return to your initial point (or so I was informed). It is possible to do so in a toroidal universe, but there are some straight lines that will return. In the two dimensional torus, a straight line which doesn’t return will get arbitrarily close to your starting point, however, so although it doesn’t exactly return, for all intents and purposes, it does. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 29, 2012, 1:13am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/10 "2012-09-29T01:13:35Z")
Locally, space is certainly curved, positively in some places and negatively in others. This is what causes gravity. Globally, space appears, to the best of our ability to measure, to be flat, though it’s possible that it’s just curved on a scale too large for us to notice (positively or negatively, we can’t say). If it’s positively curved (analogous to a sphere, in higher dimensions), then it certainly closes in on itself, and you can go “around the Universe” to get back to where you started. If it’s flat or negatively curved and has trivial topology, then it does not close in on itself. If it’s flat or negatively curved and has some other topology, then it might still close in on itself. A toroidal universe would be one example of a universe that is flat (i.e., uncurved) but still closes in on itself; there are also other possible topologies with similar effects. ---
**Author:** ![Jamicat](https://avatars.discourse-cdn.com/v4/letter/j/c67d28/32.png) [@Jamicat](https://boards.straightdope.com/u/Jamicat)\ **Post date:** [September 29, 2012, 2:19am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/11 "2012-09-29T02:19:12Z")
Yes it is, but what we call curved is just a facsimile of what the shape really is, because, we can neither see nor think _it_ in proper perspective with out primitive brains. ---
**Author:** ![aldiboronti](https://avatars.discourse-cdn.com/v4/letter/a/9fc348/32.png) [@aldiboronti](https://boards.straightdope.com/u/aldiboronti)\ **Post date:** [September 29, 2012, 2:33am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/12 "2012-09-29T02:33:29Z")
> [@Really\_Not\_All\_That\_Bright](#): > > My personal theory (which I came up with when I was about seven) is that the universe is shaped like a ring, only in a demension we can’t perceive - so yeah, you end up back where you started. The 17th century poet Henry Vaughan had the same idea. > [@](#): > > I saw Eternity the other night, > Like a great ring of pure and endless light, > All calm, as it was bright; > And round beneath it, Time in hours, days, years, > Driv’n by the spheres > Like a vast shadow mov’d; in which the world > And all her train were hurl’d. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [September 29, 2012, 4:46am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/13 "2012-09-29T04:46:52Z")
> [@Chronos](#): > > A toroidal universe would be one example of a universe that is flat (i.e., uncurved) but still closes in on itself; there are also other possible topologies with similar effects. Need some ignorance fighting here. Am I misunderstanding what “toroidal” means? Doesn’t that mean donut-shaped (or whatever is sort of equivalent to that in higher dimensions)? If so, how is that not curved? Does toroidal mean something else? What’s stopping a universe from having any of various other shapes? Why not hyberboloid or cylindrical or something even weirder? Whatever the overall shape of the Big U, is there some necessary reason for it, or does it just so happen? ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [September 29, 2012, 8:58am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/14 "2012-09-29T08:58:19Z")
> [@Senegoid](#): > > Need some ignorance fighting here. Am I misunderstanding what “toroidal” means? Doesn’t that mean donut-shaped (or whatever is sort of equivalent to that in higher dimensions)? If so, how is that not curved? Does toroidal mean something else? Toroidal does mean donut-shaped, and it’s not curved in the same sense that a cylinder is not curved: you can cut it open, and flatten it out; you can’t do that with a sphere, for instance – it possesses intrinsic curvature. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [September 29, 2012, 11:45am UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/15 "2012-09-29T11:45:53Z")
Let me try to correct some misinformation in some of the above posts. First, parallel lines do not meet in a hyperbolic (saddle-shaped) space. Instead a line (that is, geodesic or shortest distance) can have many parallels through the same point not on it. Infinitely many, in fact. Second, while a torus in any dimension does have a flat geometry, it also has lots of non-flat geometries. It all depends how you measure distance on it. As observed, you can cut it open and flatten it out to get a flat geometry and you cannot do that with a sphere. But an ordinary inner tube is certainly curved and flattening it changes the distance function on it. Although it does not change which lines are straight. If you travel straight on a torus you could come back to your starting point, but must come arbitrarily close to it, as noted above. This would mean, if the 4-dimensional universe were toroidal, that you would come arbitrarily close to the same time as well as place. This doesn’t seem plausible. In any case this is all speculative. AFAIK, the only thing that can affect the shape of the universe is mass. I think that near a mass, the curvature is negative (saddle-shaped), but my memory could be failing me on that point. I don’t think there is any known way of having a positive curvature. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 29, 2012, 2:35pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/16 "2012-09-29T14:35:55Z")
Saying something is a torus isn’t actually a statement about its curvature at all, but a statement about its topology. The surface of a donut is a torus because it has one hole. The surface of a coffee cup is also a torus, even though it has a radically different shape than a donut, because it also has one hole. A torus will always have an _average_ curvature of zero, but that doesn’t necessarily mean that it’s zero everywhere on it: The surface of a donut, for instance, is negatively curved toward the hole, but positively curved on the outer edge. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [September 29, 2012, 5:11pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/17 "2012-09-29T17:11:39Z")
Does knowing that there’s more universe out there than what we can see or detect make determining the curvature of the universe next to impossible, or are there other more subtle, non-direct ways that might help resolve it? ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [September 30, 2012, 1:47pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/18 "2012-09-30T13:47:55Z")
> [@Really\_Not\_All\_That\_Bright](#): > > My personal theory (which I came up with when I was about seven) is that the universe is shaped like a ring, only in a demension we can’t perceive - so yeah, you end up back where you started. Dimension, even. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 30, 2012, 4:59pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/19 "2012-09-30T16:59:06Z")
> [@](#): > > Does knowing that there’s more universe out there than what we can see or detect make determining the curvature of the universe next to impossible, or are there other more subtle, non-direct ways that might help resolve it? Well, you do have to assume that on the largest scales, the Universe is more-or-less uniform, so that the curvature we measure in our observable region of space is about the same as that beyond what we can observe. This is probably a decent assumption, though, since there’s no known phenomenon that could cause irregularities on such large scales. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [September 30, 2012, 6:20pm UTC](https://boards.straightdope.com/t/is-the-universe-curved/636127/20 "2012-09-30T18:20:45Z")
> [@Chronos](#): > > Well, you do have to assume that on the largest scales, the Universe is more-or-less uniform, so that the curvature we measure in our observable region of space is about the same as that beyond what we can observe. This is probably a decent assumption, though, since **there’s no known phenomenon that could cause irregularities on such large scales.** On the other hand, if there were such a phenomenon, it wouldn’t be surprising that we wouldn’t know about it.