this post was submitted on 19 Jun 2023
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No problem! I was worried it might end up a bit of a word salad lol, so I'm glad you found it informative and easy to digest!
The extra dimensions in string theory are actually spatial dimensions, as far as I know, they're just "compact." So, for analogy, consider the surface of an infinitely long pencil (or straw or other cylinder). It's two dimensional. One of its dimensions is pretty large: the one along the length of the infinite pencil. It's unbounded, infinite, and flat. The other spatial dimension is the one that goes around the pencil: it's unbounded, but finite and curved (convex, like the dimensions on a sphere). That one that goes around is more like what string theorists are taking about, I think.
I also don't put that much stock in string theory, for whatever my opinion is worth (and it shouldn't be worth too much, because again I'm not a physicist). Mainly because we can't actually test it, and I think testability is important.
This I know much less about, unfortunately. I've seen this idea come up in, eg, the many worlds interpretation of quantum mechanics, but my sketchy understanding is that what they're actually talking about is something very different from the sort of multiverse as portrayed on TV and in novels. I have a bit of a suspicion that the answer might be the same (they're not contained in anything), but I really don't know for sure.