this post was submitted on 08 Sep 2023
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Yep, just read some stuff on Quora about 4D spheres, and still don't get it ๐คทโโ๏ธ
You have an edge on the Earth, both above and below, i can't imagine the material part of the All circling upon itself, how would you visualise from outside ?
I still see an edge with an hypersphere, well, w/e, thanks for the answer anyway :) !
The problem there is you're thinking in 3d space. The surface of a sphere is two dimensional, a two dimensional creature living there would be able to travel in a straight line in any direction and they'd end up back where they started; they have no concept of "up" or "down" so wouldn't be able to move up to leave the surface of the sphere.
A 4d sphere would be similar; the surface of that sphere is three dimensional. A three dimensional creature (like a human) could travel in any direction along the surface of that sphere and end up back where they started, they would have no concept of "into" or "out of" that sphere so wouldn't be able to leave it.
A picture of a hypersphere is trying to represent a 4d object in two dimensions, you lose a lot of data every time you lose a dimension.
Thanks for the explanation, but since you, along with mathematics, agree that there's a surface, there should be a normal/perpendicular, and you can get more or less close to that surface, i guess i just can't wrap my head around it, it'd mean that the hypersphere is on both sides of its surface ?
I've read elsewhere that the universe would be this (hyper)surface, i wonder what the surface of a 5d-sphere would look like then.
There doesn't need to be a normal at all. Mathematically, the properties/content of surface of a sphere can be completely described without having to think about an embedding space. The word "surface"/"hypersurface" is a bit misleading in this context because it implies an embedding space (It just means object of dimension N-1 in an embedding space of N dimensions) (sometimes the word hypersurface is used when N โ 3). But when we say "surface of a sphere", the "sphere" and the space around it is only a visualization tool, it doesn't need to be considered as a "physical thing". If we don't want to talk about an embedding we can just say we are talking about "a space with positive curvature" or a "spherical space".
Here's a video of what it's like to live in a spherical world (a very small one with a very high curvature): https://www.youtube.com/watch?v=yY9GAyJtuJ0 Here it must be noted, they added a ground to their world to help visualize stuff but it would works without it as well. If nothing obstructed your view, you'd end up seeing yourself in all your vision, as if you were inverted like the house of the video. Trippy stuff!
Here is an alternative Piped link(s): https://piped.video/watch?v=yY9GAyJtuJ0
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