Ouroboros Ball: Meaning & Image

[Ginkgo]

Hey,

I'm wondering, what is an ouroboros formed as a ball instead of a circle called? That is, a ball 'eating itself', if you can visualize that. Or could anyone show me an image of such a structure?

 

[Jamma]

Heh, this is a funny question- a ouroboros is just a circle eating itself, so it's just a choice of point on a circle where it is "entering itself" and the whole circle is moving towards that point. We could start thinking about vector fields- there is an implied "motion" of the circle into this point. We probably want this vector field to be continuous, except at the point where it's eating itself where we may have a discontinuity i.e. a vector field on the circle minus a point i.e. on the line.

So I suppose for a higher dimensional version, you need to choose some subspace of the sphere, which represents the area that "eats", and have a vector field pointing into this subspace. If your subspace of the sphere is contractible, like an arc on the circle or just a point, then you effectively just need to give a vector field of the plane which points away from the origin at large distances.

This is all very vague, but that's because there is no set definition of a "higher dimensional ouroborus"!

 

[Gaia]

I'm not a physicist, but I've been having visions of this very thing. I found this post by googling ouroboros ball. I had the language to describe what I see. Maybe someone with more expertise can help out. Here goes:

It's a roiling motion. Since there is "space" between the particles, they are free to intersect without a local point of exchange. I think there is a "front" of a wave motion, but it's inside/outside rather than roundy-round. The caption read "matter/anti-matter".

It's possible I am just a flake, I suppose. Not crazy. I'd love to see an image too.

 

[Alesak]

What an interesting idea! Now that I'm thinking about it, I'm seriously surprised there is nothing called "Ouroboros theory"!

When you have ordinary Ouroboros, it has shape of circle. When you remove one point from it (mouth), you get a line segment (topologicaly speaking). Now, in this "deconstructed" Ouroboros, you need go through whole line segment to get from former mouth to the other end.

Higher dimensional analogue of this could be cylinder with empy lid and floor (mouth would be here any non-selfintersecting line connecting floor and lid), but this seems to me just trivial extension of circle.

Another possibility could be torus. I see two possibilites for mouth, one is horizontal circle and second one is vertical.

To generaly formulate this generaly, it would be probably done with manifolds using language of algebraic topology. Ouroboros could be a manifold with some submanifold designated as mouth. When you remove the mouth you get some new manifold ("deconstructed Ouroboros") that needs to satisfy some condition. For example, it should be connected.

But I don't see how to do it precisely. To recapitulate, first is Ouroboros, second is deconstructed:
circle - line segment
cylinder - disc or square
torus - cylinder

 

[meldraft]

Wouldn't that be the equivalent of a sphere with a hole inside? Pretty much like the 3D version of an annulus? Topologically speaking, I believe it is just a sphere with one discontinuity.