With 1D, energy would never dissipate. It's only a matter of when you'll be hit by a force, but it‘ll be at full strength.
In a 2D universe, energy doesn't dissipate quickly enough; it would be a inverse law; that is twice as far away means half the strength. Gravity would reach out much further before weakening, and everything would quickly collapse in a massive singularity again. Explosions would push harder. So everything would be continuously pulled in until an explosions shockwave hits it. Does this balance out? Well, maybe....
In a 4D or higher universe, energy would dissipate too quickly with an inverse-cubed law. Gravity would become too weak too quickly to hold it all together. But then explosions would also become weaker sooner. (Maybe it would all balance out too.) Higher n dimensions also dissipate energy too quickly with their own inverse x(n-1) law.
I guess it comes to acceleration, if the forces are too strong or too weak, the system is unstable. I guessing here, but it gives me a warm fuzzy, and that's why I call this a religion instead of science.
You might think that the other 2D Inverse, 4D Inverse-Cubed, or Inverse
higher-dimension laws are in
balance too, right? Well, maybe they are. However, I have been
educated in why 3D Inverse-Square is important, though I do not have the
expertise to test/verify this. In an uniform inverse-square spherical
universe, you can not tell how far you are from the edge. The only forces felt,
such as gravitational attraction, comes from the material closer to the center. Here's
why. Although you have more material influencing you on the far side,
it is further away and is exactly balanced by the less but
closer material on your side. That is a consequence of the 3D
Inverse-Square universe. (Does 2D and 4D have that? It’s plain
to see that 1D certainly does not!)
I know I'm not articulating this very well. Think up a uniform sphere and pick a point some place inside. (No, the center or any where on the edge; Stop being difficult.) Now, divide the sphere into two regions: one region that contains everything closer to the center and the other that contains everything further away. The argument goes that everything in the second/outer region will be gravitationally inert. That's because even though there is more to one side, it's balanced by the stuff on the near side. This only works in an Inverse-Square universe. In a lower dimension universe, the forces from the material on the far side is too strong; while in a higher dimension universe, it is too weak. The math is hard, so I'll leave that to the experts.
Incidentally, I finally heard a good analogy that helped me understand what Cosmic String theorist mean by small, spatially closed dimensions. It came in a movie called What The Bleep Do We Know?. Before, it was boring and uninformative explanations: “They’re small and closed. We are large and expanded. Therefore we can’t see them.” (End of argument.) Well, this movie explained it like this: “When you look out this window, you’ll see a telephone wire across the street. Think of that as a 1-dimenional wire. You can move forward or backward along the wire. Now imagine you are an ant on that wire. You can still move forward and backward, but you can also move around the wire clockwise and counter-clockwise. The wire is now 2D, that is 1D that is large and expanded plus 1D that is small and closed.”