In our 3D universe, there are lots of options - 18 known ones, to be precise. Connect two dimensions, the top to the bottom and one side to the other, and you have a torus (aka a donut). Flip one edge over before connecting and you've made a Mobius strip. Connect one of the dimensions normally and you have a cylinder. With your 2D piece of paper, you can connect the ends a few different ways. And here's a bonus fact: not only can we not determine the topology of the universe from observations, but there are also no laws of physics that predict or restrict the topology. While the geometry of the universe is very well measured (again, it's flat), the topology is not.

There's an important distinction between geometry, the behavior of parallel lines, and topology, the way a space can get all twisted up. You heard it here first: Cylinders are flat. Carefully observe the parallel lines - they remain parallel, don't they? That's because cylinders are flat. Wrap one end around to meet the other, making a cylinder. Take out your piece of paper with two parallel lines on it. Have you ever asked yourself if there's a difference between a cylinder and a sphere? More than likely not, but it's never too late to try new things. But this article isn't over yet, which means there's more to the story. And the answer, as far as we can tell, to within an incredibly small margin of uncertainty, is that the universe is flat.

When we examine very old light - say, the cosmic microwave background - that has been traveling the universe for more than 13.8 billion years, we get a true sense of the universe's shape. So a couple light beams would naturally collide inside a wandering black hole, or bend along weird angles after encountering a galaxy or two.īut average all those small-scale effects out and look at the big picture. Any place where there's mass or energy, there's a corresponding bending of space-time - that's General Relativity 101. The universe has all sorts of deformations in space-time where it varies from the perfectly flat. In cosmology we care about the universe only at the very largest scales small-scale bumps and wiggles are not important for this question. And in cosmology, nobody cares about you. Remember that measuring the shape of the universe is a question for cosmology, the study of the entire universe. In our 3D universe, we could watch beams of light: If, say, two lasers started out perfectly parallel, then their long-term behavior would tell us important things. So there you have it: You can measure the 'flatness' of a structure just by watching how parallel lines behave. But if the actual density of the universe is equal to the critical density, as scientists think it is, then it will extend forever like a flat piece of paper. If the density is more than the critical density, the universe is closed and curves like a sphere if less, it will curve like a saddle. The shape of the universe depends on its density.

Flat space curved space