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Message: <blockquote data-quote="Pbartender" data-source="post: 1167189" data-attributes="member: 7533">Certainly...   <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f60e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":cool:" title="Cool    :cool:"  data-smilie="6"data-shortname=":cool:" /> Consider a two-dimensional man.  He has only height and depth, no width.  He universe is a flat plane, much like a sheet of paper, but with no thickness at all.  To us, looking at him from the third dimension, he'd look like an odd cartoon person.  We'd be able to see his insides, since only a sinlge loop of line would be necessary to hold them in.  He would only need two legs (not three or four) to create a stable base.  He would need an arm (and eyes) on each side, since he cannot truly turn around with standing on his head.  His mouth would necessarily be on top of head, to be reached by both arms.  He would have no *AHEM* anus, since a digestive tract with two exits (or entrances, depending on how you look at it) would split him in two.  There's other neat effects to be explained here, but I'll get on to the universe bending stuff...Now, right now, his universe sits on a table top.  It's flat with no curvature.  If our alien travels in any direction, he will eventually reach the edge of the 'universe'.  This is a "flat" 2-dimensional universe.  In terms of the big bang, this is a stable universe, which has a perfect amount of mass and will continue on for all time.  After its creation, it expands for a finite peroid of time, before ceasing expansion and maintaining a fixed size.  Eventually, all mass and energy will be evenly distributed across the universe, which results in 'heat death'.Ok.  Next, (this is a little tricky) we take the flat universe, bend two opposite corners down, while bending the other two corners up.  This should produce an odd shape vaguely reminiscent of a saddle.  This universe has a negative curvature.  It is the "open" 2-D universe.  In terms of the big bang, this is a super-stable universe, which has too little mass to maintain its size.  After its creation, it expands, and continues to expand (essentially, all the mass of the universe is moving faster than the escape velocity of the universe).  Since our alien will never be able to travel fast enough to catach the edges of the universe, the universe is essentially infinite from his point of view.  Much like the "flat" universe, this universe will continue forever, and eventually suffer from heat death.Finally, we take the flat universe and carefully wrap it around a balloon.  The result is a universe shaped like a hollow sphere.  This universe has a positive curvature.  It is the "closed" 2-D universe.  It is an ultimately unstable that has too much mass for its own good.  The universe cannot exape its own gravitational pull.  After creation, its expansion will eventually slow down and reverse itself, to finally 'crush' the universe in upon itself in a 'Big Crunch'.  Our poor doomed alien can travel in any diretion he likes, but because of the curvature of space, he cannot escape as he eventually returns to his starting point.  To our alien, the universe looks infinite, but it eternally and regularly repeats itself.  Depressing, eh?You can vary the topologies by creating cylinders, or toroids, or ridges or whatever, but those are the three basic ideas.The favored theory varies from year to year, and is continually argued over.  It appears the latest cosmologists think that our universe is a variation on the last.Now...  You just need to imagine our 3-dimensional universe bending into the 4th dimension.Good Luck.   <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink    ;)"  data-smilie="2"data-shortname=";)" /></blockquote>

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