I'll start.
Imagine that all the lowest-level particles, whatever they may be, are in fact infinite-dimensional shapes, spacial-dimension wise, and the radius is always the same in every dimension. If any two dimensions are represented, it's a circle, three, it's a sphere, four and up we can't properly process, and if you only pick one, it's just a line. Doesn't matter what dimension you pick.
So let's think about how that would affect us if it was true.
Now imagine they're all in a perfect line. As they only move when they push or pull one another, they'll form into groups and the groups will push eachother around. Positions can be altered, but the order of particles cannot, as they cannot go around eachother. It's effectively a one-dimensional universe. As nothing can be transferred between anything but two groupings of particles, there would be no notable brown townogs to real chemical reactions.
Now here's what I'm getting to. Say we don't like this situation and have the power to affect it. Put a particle in anywhere not on the line.
Boom, you've got three points not on a line. What infinite geometrical construct can be formed with three points?
The third, new point is charged, or at least has mass. It pushes or pulls everything else, which then isn't in a line any more. It starts pushing on itself in more than one direction, all lines on that geometrical construct. The universe now occupies a plane.
Now we see things able to form, rather than just the particles moving back and forth like an abacus. Atoms form, perhaps different but still likely. Electrons begin to orbit them. We've got atoms! Gas, most likely, in space. "And it's getting closer together. And it's getting closer together. And it's getting closer toge-IT'S A STAR!" ...or a star brown townog. Nebulae form stars, stars form heavier elements, etc., etc., you have a universe similar to ours in two dimensions. Due to the dimensional restriction, electrons will likely not orbit in the same way. The periodic table's names may be applied, and even the molar masses may be close. However, reactions would likely be different because electron shells would either contain different numbers or not even be an applicable concept.
Now, put another point. Not on the plane. Now you can define... uh... Whatever we call the thing we reside on one of. A three-dimensional space like a plane. We've already got groupings. You know how this universe works, or how we think it works, at least. You're in it. Or one like it.
Every time the universe gains a dimension through another point being placed at a different coordinate in space, everything at a scale like what we know would be ripped apart. Planets would fall into themselves, like a sheet of paper being crumpled up into a ball, so for at least a little while the planetary and solar systems could potentially remain in their current positions, though the math behind the orbits would likely result in some pretty weird stuff happening.
tl;dr take a universe add a particle outside it and it will fall into another dimension also 1D universes are boring.
