The study in question: [https://arxiv.org/abs/2106.13205](https://arxiv.org/abs/2106.13205)
The much friendlier Vice Motherboard article I actually read: [https://www.vice.com/en/article/3aqjkn/the-universe-is-a-giant-donut-that-we-live-inside-new-research-suggests](https://www.vice.com/en/article/3aqjkn/the-universe-is-a-giant-donut-that-we-live-inside-new-research-suggests)
The article suggests that scientists currently model the universe as a kind of infinite flat plane. First of all, I don’t even understand how our 3-D world is being understood as a plane. My main question though, is if they’re thinking of it as a plane that wraps around and touches itself, then why is a torus/donut a better model than simply a sphere?
In: Physics
It helps to think of things in terms of what would happen if you turned the surface of a donut or a sphere into a flat map. Specifically, let’s look at what happens when something goes off of the edge of the map.
You’re already familiar with how a flat map of a sphere works, because that’s what world maps are. Let’s use [this map](https://upload.wikimedia.org/wikipedia/commons/8/83/Equirectangular_projection_SW.jpg) as an example.
If we go off the western edge of that map, we would come back around on the eastern edge, since we’re actually on a sphere, and the eastern and western edges of the map are actually connected. But, it doesn’t work the same going north or south. If we go off of the northern edge, we would come back around on the northern edge but in the opposite hemisphere. This is because the northern edge all comes together at the north pole, so its connected to itself and not to the southern edge. If you go far enough north you get to the north pole and if you keep going straight you’ll start going south from the north pole.
Now let’s imagine for a moment that we lived on a doughnut shaped Earth. [Here is an animation](https://i.imgur.com/7QVgJWi.gif) showing how a flat map of a doughnut’s surface works. So what does going off of the edges of [this map](https://i.imgur.com/OLhCTrl.gif) look like? East and west are still the same – go off of one and wind up on the other. However, the north and south edges work different for a torus. Instead of being each being connected to itself at a pole, now the north and south edges are connected together! That means that if you go off of the northern edge, you come up on the southern edge, just like going east and west.
So far I’ve been talking about a flat 2D map of 3D torii and spheres, because it’s pretty easy to understand. We’re used to living on a sphere and playing video games that take place on doughnuts. Now let’s talk about a 3D projection of 4D shapes.
If the universe was completely flat, then that would mean if we started travelling in a direction we would travel forever and never come back to where we started (as long as we don’t change direction on our own). If the universe is toroidal, that would mean if we travelled far enough in one direction, we would eventually find ourselves back where we started; it would be like if we lived in a cube where going through the top would cause you to come up from the bottom, same as with the 2D maps. Travel far enough and eventually you’ll find yourself behind where you started. Similarly, if the universe is spherical, we could also travel in a straight line and find ourselves back where we started, but depending on the direction we chose, we might find our selves going past our starting point going in the opposite direction, like going over the poles on a map of Earth.
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