this post was submitted on 08 Sep 2023
385 points (96.8% liked)
Asklemmy
43879 readers
1476 users here now
A loosely moderated place to ask open-ended questions
Search asklemmy ๐
If your post meets the following criteria, it's welcome here!
- Open-ended question
- Not offensive: at this point, we do not have the bandwidth to moderate overtly political discussions. Assume best intent and be excellent to each other.
- Not regarding using or support for Lemmy: context, see the list of support communities and tools for finding communities below
- Not ad nauseam inducing: please make sure it is a question that would be new to most members
- An actual topic of discussion
Looking for support?
Looking for a community?
- Lemmyverse: community search
- sub.rehab: maps old subreddits to fediverse options, marks official as such
- !lemmy411@lemmy.ca: a community for finding communities
~Icon~ ~by~ ~@Double_A@discuss.tchncs.de~
founded 5 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
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
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I'm open-source, check me out at GitHub.