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Thanks that was super helpful

A 3D obj stretched everywhere equally -- I suppose this is the same as the 2D balloon -- as it is also stretched everywhere equally

One says everywhere is equi-distant from the origin in a 4th dimension. The other also says everywhere equi-distant but from zero, but adds a topolgy with no edges

A 3D topology with no edges ofcourse requires a 4th dimension though

So I think these are really two ways of saying the same thing?

--

In any case, it really helped answer some other Qs for me

In a simplistic sense the differences in the Hubble constant, are of course a dimension. So adding dimensions as in string theory is a fancy way of explaining nothing. But I wondered... Is there a correlation between Hubble constant differences and 3D space?

If so, it would (in my unremmitingly small brain) show an interaction with dark energy a.k.a. this 4th dimension

A clearer way to say that: the skin of the balloon has a thickness, and differences in the Hubble constant are measuring that thickness

-- Your answer was awesome and super helpful -- Can you do it a second time? :)



Your questions are answered at:

1. https://www.youtube.com/watch?v=aPStj2ZuXug&t

2. https://www.youtube.com/watch?v=blSTTFS8Uco

And more such videos at PBS SpaceTime. A fair warning though that that is a rabbit hole and likely to consume a lot of your hours/days to get through.




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