Worlds on Worlds

"What would happen if...?" has always been a staple of Science Fiction. What do you wonder about?

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Floridian Dream
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Worlds on Worlds

Post by Floridian Dream »

Stories regarding beings living in universes of only two spatial dimensions, completely oblivious to the third spatial dimension, such as Edwin A. Abbot's Flatland and A. K. Dewdney's The Planiverse have really gotten me thinking for quite some time: if a lack of third-dimensional thickness to other universes made them microscopic and virtually invisible to us, they could potentially exist right under our very noses, on the surface of any three-dimensional object in our three-dimensional universe, and a similar principle could be applied to our universe in one of four spatial dimensions. Essentially, the surfaces of entire planets, moons, asteroids, meteors, comets, stars, and all other sorts of astronomical bodies could host their own two-dimensional universes. This, however, opens a couple of questions.


Question 1: If a 2D universe existed on a sheet of paper and at least two planets existed in said universe and each one resided near opposite ends of the sheet, any technologically advanced civilization that developed on either planet could visit the other in a manner similar to what one would find if one were to google a wormhole diagram. Essentially, on the supposition that 2D universes existed on the surface of 3D objects, advanced civilizations should be able to visit relatively distant parts of their own universe by warping their universe's space in a sufficient manner, and even visit other two dimensional universes on other 3D objects by stretching their own 2D space through 3D space.

So, why don't we see a 3D object's surface inexplicably distort? Why don't we see the surfaces of said objects stretching out to touch the surface of other objects? Why do we see little evidence of astronomical bodies touching one another aside from overcontact binaries and the occasional (and often destructive) collisions?

I, myself, have arranged a list of possible answers to this conundrum.
  • If intelligent life does emerge in two-dimensional universes (and don't say that intelligent life on such a universe is impossible just because of the "overlapping neurons problem". Dewdney actually has a solution to that.), it rarely reaches the technological sophistication to create wormholes and other distortions to space of the like.
  • Warping of space is very difficult to the extent of near impossibility, so it is very seldom done — I would, however, scratch that, because warping of space is seen all the time in our own universe, mostly via the gravitational indentation of very massive objects. I don't see why it need be any different in a 2D universe.
  • At least in the case of visiting other 2D universes, it is simply much easier to visit those that are within very close proximity of each other—if not within complete contact—than those that are much farther apart, so those are visited more.
  • At least in the case of astronomical objects, we just haven't seen quite enough of our own observable universe.
  • A little something I like to call Film Theory — basically, the surface of a 3D object is not a 2D universe itself, but supports a 2D universe, which is laid over said surface as a sort of ethereal film. It is not the 3D object that gets distorted, but the ethereal film coating it that is being distorted in a manner similar to what can be seen in the topmost image of this website, if you will imagine the gridded surface as the ethereal 2D film. Essentially, a portion of that ethereal film bulges away from the surface of the 3D object it was resting on and stretches out to elsewhere in 3D space. And since this ethereal film is two-dimensional in that it holds no three-dimensional thickness, it is practically invisible to the naked human eye, and therefore, we do not see any distortions in it occurring.

Question 2: If two-dimensional universes are bound to the surface of three-dimensional objects, how do these aforementioned 2D universes continue expanding, when most three-dimensional objects that are not stars usually hold a fixed size and seldom expand continuously ?

  • There is a limit to how far 2D universes can expand. How would one explain, however, our universe, assuming that it is bound to the surface of a four-dimensional object in 4D space? A lot of evidence and observations these days seem to suggest that its expansion isn't going to stop anytime soon, if ever.
  • 2D universes are not bound to the surfaces of 3D objects, but rather compose cross sections of our 3D universe, if not the objects it contains, and thus these 2D universes expand along with our 3D universe.
  • The ethereal film which makes up 2D universes expands even when the 3D objects whose surfaces support them do not, stretching over and passing through themselves in that they form layers over themselves.
Well, that's my two cents on the subject. What are your thoughts? Please share them with me.

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