I asked this over on the Phyisics part of StackExchange, and they suggested I move my question here.
And said question is:
Can something contain itself?
The question is simple enough, and I can think of two ways it could happen:
1: The object contains a portal to itself
This is a kind of a loophole, but still may be impossible, so I'm including it.
Let's start with Box A. Inside of Box A, we have Box B, which is a portal to Box A: Portals on the outer sides of Box B correspond to the respective inner sides of Box A. Note that I said portals, when really the idea is of one, continuous portal.
For extra interesting-ness, What if the sides on Box B didn't correspond to Box A's sides? What if it was random? Could the portal still be continuous or would it have to be 6 differing portals, one for each side?
Are either of the above ideas Mathematically or Physically possible?
2: The object literally contains itself
Box A doesn't contain Box B anymore. Now, instead of them being two different boxes, they're both the same. Let's calle them Box A$_0$ instead of Box A and, inside of Box A$_0$, there is Box A$_1$. This raises a few questions:
- Is this possible?
- Would this go on forever, where Box A$_1$ contains a Box A$_2$, which contains a Box A$_3$
- If this is so, would Box A$_0$ be inside of a Box A$_-1$, which would, again, go on forever?
I tagged this as topology as I wasn't totally sure as to what it should belong in. Suggestions?