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Space Science

The Universe May Be Shaped Like a Doughnut 512

Posted by michael from the krispy-kreme dept.
NewbieV writes "The NY Times (reg., etc.) is reporting that data from the Wilkinson Microwave Anisotropy Probe may suggest that the universe might be shaped like a doughnut or a cylinder: it might be possible, like in the old video game Spacewar, to drift off one 'side' of the Universe and reappear on the other."
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The Universe May Be Shaped Like a Doughnut More

The Universe May Be Shaped Like a Doughnut

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  • So I guess that makes God.. (Score:5, Funny)

    by flinxmeister ( 601654 ) on Tuesday March 11, 2003 @07:07PM (#5488748) Homepage
    ...the Cop of the Universe?

  • homer knew it (Score:2, Funny)

    by Anonymous Coward
    damn stephen hawking!

    (ps. - third?)

    • Actually Stephen Hawking predicted this already... (Score:5, Informative)

      by Omega ( 1602 ) on Tuesday March 11, 2003 @07:14PM (#5488842) Homepage
      Did anyone here actually *read* A Brief History of Time [amazon.com]? Hawking described how the gravity of the universe may be so intense that it causes the universe to wrap around into a spherical shape. Of course this was just a theory back when he wrote the book.

      • Re:Actually Stephen Hawking predicted this already (Score:5, Informative)

        by Xeriar ( 456730 ) on Tuesday March 11, 2003 @07:21PM (#5488914) Homepage
        We're talking about a Torus, not a spherical universe. If true, the universe is still 'flat', there's no 'wrapping' as you put it, it just repeats in all directions.
        • On learning of this news Ford Motor Company immediately sent the universe a "cease and desist" letter, claiming violation of their trademark "Taurus."

          While someone was trying to explain to a Ford executive that "Taurus" was a different word, and only applied to to an abstract portion of space, not the universe, and the word "Torus" refered to a donut shaped object, said executive got a blank look in his eye, muttered the words, "Hmmmmmmmmmmm, Donut," and wandered off.

          KFG
      • Yep; great book; I loved one of his analogies (referring to a finite universe with no boundaries) that went something like this:

        Imagine you're a 2-D dude wandering the earth (which is really a 3-D globe like you'd find in a classroom). You can walk and walk and never hit a wall but there's a finite amount of 2-D space. Now imagine you're a 3-D dude... This is where my feeble brain says 'help!'.

        The analogy would seem to back up the article; whatever direction you take if you walk long enough you end up where you started.

      • Re:Actually Stephen Hawking predicted this already (Score:2, Informative)

        by Anonymous Coward
        Hawking described how the gravity of the universe may be so intense that it causes the universe to wrap around into a spherical shape.

        IIRC, Hawking was talking about the shape of spacetime in that section. And in fact, the results from WMAP indicate that the universe will expand forever, contradicting that particular model of spacetime.

        When these people say that the universe may be shaped like a donut or like a cylinder, they are supposing that spacetime can be expressed as the product of a space part and a time part, and that the space part is shaped like a donut (or whatever).

        In this model the space part would be the 3-torus T^3, the time part would be an open interval I, and spacetime would be IxT^3. Good luck on visualising that!
      • And er Stephen Hawking was hardly the first to suggest this.

  • oh no (Score:2, Funny)

    by odyrithm ( 461343 )
    homer was right!

  • Mmmmm... (Score:2, Funny)

    by joncraft ( 237454 )
    Mmmm... Universe... (knew someone would do this, thought I'd try to get in first)

  • Coming up... (Score:5, Funny)

    by Lemmy Caution ( 8378 ) on Tuesday March 11, 2003 @07:08PM (#5488768) Homepage
    The Krispy Kreme Endowment for Excellence in Cosmology.

  • Silly students (Score:5, Funny)

    by ObviousGuy ( 578567 ) <ObviousGuy@hotmail.com> on Tuesday March 11, 2003 @07:08PM (#5488769) Homepage Journal
    2 dimensional universes are shaped like donuts. 3 dimensional ones like ours are shaped like hyperspheres.

    I guess they forgot to carry the 1.

    • Re:Silly students (Score:5, Informative)

      by YU Nicks NE Way ( 129084 ) on Tuesday March 11, 2003 @07:20PM (#5488903)
      Actually, no, they didn't. n-dimensional universes -- if they are compact -- are shaped like n-tori, not n-spheres. The question is quether they have genus one (and are thus flat) or have genus 2+ (are have negative curvature.)
    • You mean 3-uncurled non time dimensional ones like ours are hyperspheres.......
      :)

  • Okay... (Score:2, Insightful)

    by Flarelocke ( 321028 )
    In this case, the obligatory Simpson's references really *are* obligatory.

  • Old hat (Score:4, Funny)

    by Anonymous Coward on Tuesday March 11, 2003 @07:09PM (#5488781)
    Those of us who have played games like Space Wars, Asteroids and Star Castle were already well aware of the toroidal truth.

  • Obligatory free link (Score:3, Informative)

    by Anonymous Coward on Tuesday March 11, 2003 @07:09PM (#5488785)
    no registration required link in printer friendly format [nytimes.com] (otherwise it's five pages)

    More images from probe homepage [nasa.gov]

  • Mmmmm.... (Score:4, Funny)

    by n3rd ( 111397 ) on Tuesday March 11, 2003 @07:10PM (#5488796)
    ....cosmic size donut with solar sprinkles.

    /me drools

  • Observations (Score:5, Interesting)

    by TWX_the_Linux_Zealot ( 227666 ) on Tuesday March 11, 2003 @07:11PM (#5488813) Journal
    Then in theory, we'd be able to see the same part of space from two vantage points, assuming that they're not farther away from us than the distance that light could have travelled since the universe came into being, assuming that one believes in the big bang theory.

    So, would this mean that if we can't see one point from two directions now, that if we suddenly can, we've reached the halfway point of the life of the universe? Would we lose the redshift in favour of a green shift?

    • Re:Observations (Score:3, Informative)

      by fredrikj ( 629833 )
      Though I could be wrong, I think the opposite of redshift is blueshift, not greenshift.

    • Re:Observations (Score:3, Informative)

      by The_K4 ( 627653 )
      Yes we could see "the half way" point, however there red shift would NOT become green shift (there is no such thing) or blue shift (which does exist) because each point of view would still see things in that direction as getting further away. Think of the donught getting larger....just becuase you know where the oppisites side is doesn't mean taht things getting further from the right get closer to the left. In fact it wouldn't even effect the amount of redshift.
      • How does this 'torus getting larger' (I'm eschewing the 'donut') idea relate to the space in the middle of the torus?

        -Zipwow
        • Think of all the weakly interacting objects in space (that which interacts via gravity over a long distance, Ex. galaxies) as being linked by straws. As the overall volume of the universe increases the straws must get longer to maintain the same relative spacing. AKA everything is moving away from us.

          In the three versions of cosmic doom, the universe can end up colapsing, expanding quickly at first and then slowing down, or expanding faster and faster until it basically falls apart. In the first case Einstein's Equations (General relativity) lead to a concave universe, the second leads to a flat universe, and the last leads to a convex universe. The only one of these forms that is really easy to picture is the flat universe since it is pretty much what we live in. The concavity or convexity of the universe has mainly to do with how to find the shortest distance between two points. Basically math becomes a pain in the a** because the derivative becomes location dependant.

        • the universe isn't the space in the middle, it's the surface area, (remember this is a 3-d representation of a 4-d problem. In this "flat world" (as it's been called before) has only X and Y axies. There in no height....so it would be impossible to get off the surface of the donught into the middle....

    • Re:Observations (Score:5, Informative)

      by wurp ( 51446 ) on Tuesday March 11, 2003 @07:29PM (#5488989) Homepage
      Well, firstly, it has long been thought that the universe was closed. This is just suggesting that the universe might be topologically equivalent to the equivalent of the hypersurface of a hypertoroid, rather than the hypersurface of a hypersphere, as previously assumed.

      Secondly, the opposite of a red-shift is a blue-shift. The complementary nature of red and green is a property of human eyes, not of the light itself. Red light is lower in energy; blue light is higher. Things rushing away from us as space expands would leave light from distant objects moving more slowly relative to us if not for special relativistic effects. With the effects, the energy of the light is reduced. However, you're right... when an object is approaching you, light from it is blue-shifted, and that would be what we should expect when the universe starts collapsing.
    • Greenshift? What the fuck is that?

      I think you mean Blueshift.
    • I don't think this changes anything in regard to whether or not we should be able to see something half-way around. As I always heard before the assumption was that its like being on the surface of a balloon. (I have no idea the manifold differences between a balloon and a donut other than how it maps onto a 2d plane.) But the reason for the explanation of the balloon was that as you blow up a balloon all points move away from each other. Even those half-way around (where you could potentially see 4 copies from left right up and down. (Oh, hmm, I guess if it were on a donut you'd see only two copies as opposed to 4) Anyway if we do see a greenshift then it means the universe is collapsing again and you should panic... or at least reserve your seats at the Restaurant.

    • Re:Observations (Score:5, Funny)

      by Tablizer ( 95088 ) on Tuesday March 11, 2003 @07:57PM (#5489232) Journal
      Then in theory, we'd be able to see the same part of space from two vantage points

      SETI: "We found a signal! Yipeee! Wait, Is that a Toyota commercial? Damn! It is just us."

  • Re: (Score:2, Funny)

    by account_deleted ( 4530225 )
    Comment removed based on user account deletion
  • That is kinda vague. What kind of donut, as we all know the jelly filled ones take on a different shape than a fritter.
  • Not the doughnut shaped part, because I wasn't sure if it would be render-able in a three dimension shape, but rather just connected at the ends, if that makes sense. I always though it would be interesting to take a light speed trip around the universe and see how humans end up doing in a bzillion years. (that's the scientific term for a lot, I think).

  • mmm....donuts... (Score:2, Interesting)

    by bravehamster ( 44836 )
    I had a math teacher at the Naval Academy that specialized in donut-shaped mathematics. I bet he's calling up all his math friends right now and yelling at them "See! I told you I wasn't wasting my time!" He did have a really cool poster of the earth if it were shaped like a donut and he spent several class periods describing what the gravity and climate would be like on such a world.
  • ... since the longest distance possible in the universe is going forward to what one is having behind, I think that not all will be so nice.
  • I found the story very interesting but skipping over the details to keep it lively. I would be interested in reading something of the level of Scientific American on this elsewhere on the web.

    The article made it seem like this idea is far from proven. If it IS so wacky then why such attention paid to it?
  • At BASF, we don't make the Universe, we make it, more doughnut like.

  • dimensions (Score:4, Interesting)

    by planckscale ( 579258 ) on Tuesday March 11, 2003 @07:15PM (#5488855) Journal
    A popular theory is that our universe is but a bubble (or doughnut) in a sea of other universe bubbles (or doughnuts); contained and wrapped up into about 10 dimensions. But looking at our universe from another dimension, it may have the appearance of an O or just some contorted blob of goo. This is depending on the relative point and dimension of the observer.

  • What is outside of the donut? (Score:3, Interesting)

    by CresentCityRon ( 2570 ) on Tuesday March 11, 2003 @07:17PM (#5488871)
    Coffee? Void? Dark Matter? Does that question even make sense? I'm not up on this and would be most interested in getting a better understanding of this.

    • Re:What is outside of the donut? (Score:5, Informative)

      by wurp ( 51446 ) on Tuesday March 11, 2003 @07:33PM (#5489023) Homepage
      The question is assumed to not make sense. The surface of a torus has topological properties similar to that of the universe (according to the article). It's just a statement about what happens when you move a long way in one direction and how points in the universe can be reached from one another, not an assertion that the universe is sitting in some hyperdimensional 'space' outside the universe.

  • that's interesting (Score:4, Funny)

    by Joe the Lesser ( 533425 ) on Tuesday March 11, 2003 @07:18PM (#5488878) Homepage Journal
    But then what the hell is the jelly?

  • So does this mean.... (Score:5, Funny)

    by kaoshin ( 110328 ) on Tuesday March 11, 2003 @07:18PM (#5488879)
    Voyager could also become the first device of our civilization to sail around the entire universe?
  • So what is the radius?
  • The universe is going to end in a few minutes, as soon as Homer Simpson hears about this!!
  • During the meeting down at Dunkin' Donuts, I explained how the torus is a great shape for confining stuff with fields (think cyclotrons, eg). This suggests that we are just part of some big experiment. When the experimenter's funding runs out, our donut is toast.
  • Just aslong enough souls believe something it becomes our reality since more and more start believing. Its like a sort of Matrix...

    One person thinks its a donut, then he convince's person two etc, etc, until the universe is what we think it is. Isnt this why science keeps coming with new improved idea's ?

    its all in our mind...happy dreaming
  • The Space War anlaogy for a curved universe doesn't really fit. The behavior in Spae War is discontinuous. You start out on one edge of the screen and after going past the edge of the screen, you are magically transported to the other side.

    In certain types curved universe the behavior would be quite different. If you start out going in one direction and continue going long enough, you may end up where you started. There would be nothing discontinuous about this motion though. A "straight" path in a curved universe isn't really what we would think of as straight. As you go along your "straight" path the stars that appear to be ahead of you would impercibly change as time wore on. Eventually you could end up back where you started, but considering the likely size of the Universe, it might take you longer than the age of the Universe to do it.

    Anyway, curved space is weird to think about, but not as weird as Space War.

    • Actually it is very good analogy (Score:5, Insightful)

      by efuseekay ( 138418 ) on Tuesday March 11, 2003 @07:34PM (#5489031)
      -Begin Jargon-

      A torus (dougnut) is topologically equivalent to a square with sides identified (like the Space War).

      -End Jargon-

      Discontinuous or stuff like that is not really important concept. Whether you are "magically" transported or not when you reached the end is just a matter of choosing the right coordinates.

      Also, curved universes do not enter the argument. Curvature is a statement on Geometry of the Universe, while being a Dougnut is a Topological Statement.Both of completely independent of each other. A Toroidal Universe can be flat (like, hey , a square with sides identified!). A curved universe can be a plain sphere.

    • Actually, the analogy is fine*, it's just that your point of reference is off. If you fixed the position of the ship in Space War so that it's always in the center of the screen, and moved everything else instead, then Space War would, topologically, fit the same way the theory proposes (except in 2D, of course - but it is an analogy).


      To put it another way, if you fixed a camera outside the universe (just pretend like there can be an outside of the universe), and watched the ship, it would have to warp around the other side from the proper camera angle.


      =Brian


      * - Um, well, I'm guessing the analogy's fine. I didn't really read the article. But presuming the parent post is correct aside from what I'm mentioning, then my post is also correct.

    • How is the SpaceWar behaviour discontinuous? It only looks that way to us as observers because our view is stationary. It could be easily reprogramed so that the view stayed centered on the ship and you would see the star and other ship disapearing into the distance behind you and reapearing in front of you.

      If the universe does work in the way proposed in the article, and you had a ship capable of traveling many _many_ times the speed of light, observers who stayed behind on earth would see the same behavior (ignoring relativity for the moment of course.) "Oh look, it disapeared off in some direction to galactic north. Oh look, it 'magically' reapeared to the galactic south!"

    • Actually it's not that bad (Score:3, Insightful)

      by oGMo ( 379 )
      The Space War anlaogy for a curved universe doesn't really fit. The behavior in Spae War is discontinuous. You start out on one edge of the screen and after going past the edge of the screen, you are magically transported to the other side.

      Actually it's a fine analogy. The problem is the display screen, not the Space War universe. If you were to map a torus onto a flat display, it would seem that you're magically transported. In reality, the discontinuity is the display, not the universe. (In similar games, I'm not sure about this one in particular, you can be "right on the border" and see your ship halfway on either edge. Perhaps Space War lacks this "sophistication".)

      Anyway, this is like saying "that is not a picture of something 3D, because the picture is 2D". Just because it's 2D doesn't mean it can't represent something 3D.

      Besides, if you want to be really pedantic, the real problem would be the dimensions of the toroid universe in question... it wouldn't really map exactly to a rectangular screen unless you changed a few "universal constants". ;-) (Not that I have a problem with this. ;-))

  • Dr. Seuss? (Score:2, Interesting)

    by earthforce_1 ( 454968 )
    There was a Dr. Seuss book I remember about three animals who bragged of their senses. The bear was showing off how far he could smell, the rabbit bragged about how much further than that he could hear. The winner was a worm that could see so far that it could look all the way around the world, and see the back of his own head.

    Who would have thought....

  • mmmmmmm...Universe

  • Somewhere in the code running the universe... (Score:5, Funny)

    by product byproduct ( 628318 ) on Tuesday March 11, 2003 @07:25PM (#5488958)
    /* comment this out to get an infinite universe */
    if (particle->position.x < LEFT_LIMIT)
    particle->position.x += RIGHT_LIMIT - LEFT_LIMIT;
    else if (particle->position.x >= RIGHT_LIMIT)
    particle->position.x -= RIGHT_LIMIT - LEFT_LIMIT;

  • Not Sound Waves...Gravity Waves (Score:3, Informative)

    by codeonezero ( 540302 ) on Tuesday March 11, 2003 @07:26PM (#5488960)
    From the article:
    As the COBE satellite first confirmed in 1992, the microwave cloud is laced with ripples and splotches -- lumps in the cosmic gravy -- from which galaxies and other cosmic structures would ultimately form. According to theory, these lumps are born as microscopic fluctuations during the first instant of time and then
    amplified into sound waves as the universe expands and matter and energy slosh around.
    That should be "amplified into gravity waves" i think... I seem to remember reading this description in Scientific American...and yeah its gravity not sound waves.

    • They are "sound waves" (Score:5, Insightful)

      by efuseekay ( 138418 ) on Tuesday March 11, 2003 @07:49PM (#5489170)
      They are sound waves in the looses sense of the word.In the sense that you have stuff (the photon-baryon fluid) and a wave is travelling through it (like sound waves travelling through air).

      Gravity waves exist of course, but we have no way of detecting them yet since their signature is much much much harder to detect.

  • Dr. Tegmark's original paper on the web (Score:5, Interesting)

    by LinuxParanoid ( 64467 ) on Tuesday March 11, 2003 @07:29PM (#5489000) Homepage Journal
    There's also a BBC story [bbc.co.uk] on the same topic, or you can go straight to Dr. Tegmark's webpage version of his paper (with cool pics). [upenn.edu]

    I've admired Dr. Tegmark's home page [upenn.edu] since he was a grad student, not so much for the design skills (ha!) but as an exemplar of mixing serious and non-serious publications for other colleauges and onlookers to enjoy, explore, and learn from. Tegmark gets the web. As for the science, some of it I can actually understand.

    I would also commend to the curious Slashdot reader a couple items I found facinating from the 'non-serious' section of his website:

    a very cool diagram of "Relationships between various basic mathematical structures" [upenn.edu] from his Theory of Everything [upenn.edu] paper

    and another paper addressing the question: Why does the universe have 3 spatial and 1 time dimension? [upenn.edu]

    --LP

  • ... is our perception of the universe warped along with the toroid shape? If so, couldn't we eventually look so far that we see ourselves?

    I'm curious how we'd test that, given that the distances involved would mean that we'd see events so long ago that we wouldn't recognize them. It would explain how the universe would seem infinite, though...
  • After having initially said it was more like a pancake [slashdot.org], their only comment about the donut was

    Doh!
  • Dougie as General Disarray: "Simpsons did it! [spscriptorium.com]"

  • In related news... (Score:4, Funny)

    by BlackjackGuy ( 631964 ) on Tuesday March 11, 2003 @07:38PM (#5489065)
    It was discovered that the internet is shaped like a pringle.

  • In the Flintstone's Universe (Score:3, Funny)

    by zephc ( 225327 ) on Tuesday March 11, 2003 @07:38PM (#5489066)
    I think the Flintstone's house is it's own tightly bounded universe with high curvature... notice when they run in a straight line, they nevertheless keep passing the same circular window and pelican ash tray? Perhaps they have floating bubble universes they get trapped in from time to time.
  • Doughnuts, is there anything they can't do? -Homer, in the monorail episode.

  • Interesting... (Score:3, Funny)

    by raehl ( 609729 ) <(moc.oohay) (ta) (113lhear)> on Tuesday March 11, 2003 @07:43PM (#5489120) Homepage
    I wonder what color our sprinkles are.

  • A Thought... (Score:2, Interesting)

    by solarlux ( 610904 )
    Interesting... let's assume for a moment that the universe's expansion was frozen.

    Now, if I threw a baseball in a straight line from point x,y,z in the universe, at some point, that baseball would again pass through one of the planes of its starting location? (I'm neglecting all interferences, including gravity)

    3-d space curving ... hmmmmm... I'm having trouble picturing what this 3-d curvature would look like. Anyone have a helpful mental image of this?
  • Most of this is based on the low quadrupole in the Cosmic Microwave Background (CMB) power spectrum.

    But... it's not really that much lower than in the concordence model, and is more likely just a result of cosmic variance - you can only measure 2 quadrupoles over the entire sky. The quadrupole power in our observable universe happens to be slightly below average - if you did the same experiment at many random points in the universe (esp. if you include points outside our horizon), you'd get a distribution of values whose mean was the concordence model value, with our observation slightly on the low side of the distribution.

    [TMB]

  • Infinite universe is philosophically unattractive (Score:3, Funny)

    by scotay ( 195240 ) on Tuesday March 11, 2003 @07:53PM (#5489203)
    In an infinite volume, he pointed out, anything that can happen will happen.

    "Somewhere there are two guys having this same conversation," Dr. Starkman said in a telephone interview, "except that one of them has a purple phone."

    Whoa!
  • And that, my liege, is how we know the Earth to be banana shaped.

    Someone had to say it. ;-)

  • Black hole from the inside. (Score:5, Interesting)

    by Ungrounded Lightning ( 62228 ) on Tuesday March 11, 2003 @08:03PM (#5489272) Journal
    Remember the rubber-sheet/morning glory shaped deformation model of gravity? Some time back I recall a description of a black hole as dropping such a BIG marble on the rubber sheet that it keeps going down, stretching the "rubber sheet" forever, at least as fast as the speed of light. Think a "taffy sheet", or a "stem" of the "morning glory" stretching like a stream of honey.

    It's easy to see why enough gravity keeps light ORBITING the gravity from spiraling out and away. But this also explains why light going STRAIGHT AWAY from the center of the hole never gets out - space is being stretched at least as fast as it moves (or maybe even faster), so it never makes it out of the hole.

    Well, this got me thinking: "What does a black hole look like from the INSIDE? What would one see from the viewpoint of the matter that was already there when the event horizon formed?"

    And the answer seemed to be: "An expanding universe, starting from a very small but finite volume and expanding indefinitely, containing a large-but-finite amount of matter, which was initially compressed into an EXTREMELY dense lump - perhaps a quark fluid or denser."

    In other words, something like the current universe. Perhaps with the moment of the formation of the event horizon corresponding to the end of the big-bang model's "inflationary period", but eliminating the need for a faster-than-light inflationary period.

    Cosmic background becomes the layer of matter and energy just below the event horizon, which is just getting here now. Cosmic background structure represents the matter distribution at that level at that time - a fossil of the orbital dynamics of the accretion cloud. (I don't think you get to see an "inside view" of the infalling half of the Hawking radiation.)

    You can go in any direction at up to the speed of light and never reach "the edge", which is (from your viewpoint) receeding at lightspeed.

    Not being a professional physicist, at this point I haven't attempted any mathematical models or resolutions with any of the current cosmological models. So I have no idea if I'm just spinning a yarn or if this can be pounded int shape for testing against the real universe. But it might be interesting to try some time.

    (The concept of gravity indefinitely stretching the coordinate system also leads to another possibility: Can gravity be modeled as masses constantly "sucking up" the coordinate system, which stretches between them meanwhile?)
    • First, let me just start with the qualfier "I Am Not A Physicst."

      "Think a "taffy sheet", or a "stem" of the "morning glory" stretching like a stream of honey."

      Except it can only get stretched so far until you run into the brick wall that is quantum mechanics. Space-time isn't infinitely smooth, and the finer a view of it you get, the less uniform it is.

      This is why physics gets all weird at the infinitessimal center of a black hole, because "infinitessimal" shouldn't be possible.

      "space is being stretched at least as fast as it moves (or maybe even faster), so it never makes it out of the hole."

      Except that relativity tells us that light is always moving 3E8 m/s faster than that. Even an observer in that space that's getting stretched to the breaking point would measure light as going 3E8 m/s away from him.

      "What does a black hole look like from the INSIDE? What would one see from the viewpoint of the matter that was already there when the event horizon formed?"

      As you pass through the event horizon, the entire sky would shrink until all you saw was a single point of light in the direction directly away from the center. All light that passes through the event horizon gets pulled towards the center, and unless its journey from its source to the center of the black hole is intercepted by your head, you'd never see it. It would get deflected towards the center of the black hole before it had a chance to reach your retinae.

      "An expanding universe, starting from a very small but finite volume and expanding indefinitely, containing a large-but-finite amount of matter, which was initially compressed into an EXTREMELY dense lump"

      You're forgetting about the space being taken up by you. As the space you occupy gets stretched out, so do you. And you can only get stretched out so far before you're torn apart (the old quantum mechanics bit again). That finite mass being smeared out into a seemingly infinite volume is you.

      "In other words, something like the current universe."

      Our universe looks uniform in any direction we look. The view inside a black hole would be a whole lot of nothing in the sky except for that point directly away from the center of the black hole.

      I'm pretty sure we'd know if we were inside one.

  • Curvature vs Topology (Score:3, Informative)

    by GryMor ( 88799 ) on Tuesday March 11, 2003 @08:27PM (#5489514)
    Even if the hypertori topology of the universe is correct it doesn't imply that the universe has any particular curvature, it's still possible that it has positive, negative or flat intrinsic curvature.

    You have to remember that the curvature of a torus embeded in 'flat' 3 space is purely an artifact of that embeding and not intrinsic in the topology of the torus. More specifically, there exist mappings from the embeded (intrinsicly curved) surface of the three dimensionally embeded torus to topologically identicle spaces that have everywhere flat intrinsic curvature.

    As a thought experiment, consider a cube where the faces are portals to their oposites. Internally, this construct has the topology of a hypertorus but an everywhere flat topology.

    For some nice diagrams and comentary that explain curvature (of the important, intrinisic kind) rather well, take a look at this [caltech.edu], just skip over any of the math thats beyond your abilities, it's not really needed to understand the concepts.

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