The author is talking about toroidal space which is confusing because a normal torus is a three dimensional thing with normal Euclidean geometry.
If I lived on a small sphere and saw a pole in the ground, tied a rope to it, and walked all the way around the sphere I would see the same pole and I could tie the other end of the rope to it. I wouldn't see dozens of poles floating in the sky.
So why would I see duplicate copies of the same pole if I lived on a donut-shaped planet instead?
Pacman lives on the surface of an actual 2D donut, when he goes to the left side of the screen, he pops out on the right side, and when he goes to the topmost part of the screen, he comes out from the bottom. (Not convinced this is the same as a donut? Imagine the surface was made of a stretchy film and bend the lefthand side to meet the righthand side, forming a cylinder. Now, to make the topmost side meet the bottom side, you fold the cylinder into a donut shape!)
This is the 3D version of the "Pacman universe", where if you go up enough, you come back around the bottom, and the same for all the cardinal directions.
As a side note, if you lived in a small three-dimensional sphere, you would be able to see an object located at the antipodal point smeared out in every direction, because following a geodesic in each direction leads to the antipode. I've seen this visualised in the video game Hyperbolica.
Or am I just not smart enough to understand this?
As explained in the article, the torus in question is locally three-dimensional, and you might mistake it for ordinary 3d space at first. The specific geometry we're visualizing is the 3d analogue of the square from above: it's a cube where going off an face brings you to the opposite face.
https://twitter.com/lproven/status/1564613978155802631
For a post that claims to be explaining something, I have to say, I think it's really quite stunningly poor at explaining itself.
This is not about living on a torus. As others have said, a torus is a perfectly possible 3D object in our universe, and SF has many toroidal habitats, including the original Larry Niven Ringworld and Iain M Banks' "Orbitals" as used in several Culture novels, and as also used in the videogame Halo (I believe -- not played it; not a gamer).
Since the article is called:
> Living on a Torus
Note: on
And begins:
> life in a three-dimensional torus that measured only several metres in each dimension
That to me implies inside an object. A toroidal habitat is an absolutely standard part of SF and has been since before 2001: A Space Odyssey in 1969.
The article is in fact about living inside a spacetime continuum, a universe, which is toroidally shaped, and strangely small. (What you are on is unspecified.) It doesn't say so but it seems to be.
Since I have never really wondered about the shape of spacetime, I could not even begin to parse the essay.
About a paragraph of explanation setting out your axioms and explaining that you are discussing the shape of the universe, of a finite bounded spacetime continuum, was needed.
And ideally, several paragraphs of explanation, building up slowly, was what you really needed. Starting with examples of a linear 1D continuum where you can only move in 1 dimension, and how it would look, then of a 2D one where it's possible to go round the axis, then a planar one, then illustrations of how the planar one's edges could be connected. It also needed explanations of the notions of flatness and curvature, of connectivity, and some basic explanations of the topology involved.
As it was, nothing was explained: just a cryptic title that contradicted the misleading first line. :-(
Sorry to be a harsh critic, but as an educated layman who's read entire books on topology, spacetime, definitions of connectivity and dimension and so on, this was totally opaque and mystifying.
If you'd at least given it that 1-para context, it might have worked. Even a sentence of context. But just jumping into a complex thought experiment? Impenetrable.
I can't help but hear this in Bon Jovi's voice.
