Cat: I would just like to add that, if different people have different insights, and, perhaps see more in an analogy, then that is fine by me.
Well, that's very kind but can I also repeat that the analogy is just a step to a more revealing picture of a Hypersphere?
Gibsense, I do not seem to be able to get myself understood.
I appreciate that you are extending the flatlander idea, beyond my original conception, but my original purpose, and
still my only interest here, is to help
myself understand the concept of 'extending into itself'. My only hold on this requires, based only on my analogy, that a 'higher dimensional empowered observer' sees the 'expansion' of a flatlander (observed) universe in a way unavailable to the flatlander.
For the purposes of
my objective, I do not, nor do I see any need to, introduce hypersphere. Indeed, I would go further, and suggest that
any introduction of hypersphere into
my analogy is
not only useless, but actually
causes totally unnecessary confusion.
Nothing of this, of course, contradicts the rights of yourself, or anyone else, to pursue different objects, generalisations or investigations into hyperspheres.
They are just not in mine.
Am I making myself clear? Please continue to mention hyperspheres if you wish, but please do not suggest that they have anything to do with my objective.
At the risk of repeating myself, My only objective here is to try to
help myself understand how any (observable)) universe can be seen as
expanding into anything, when a universe is supposed to be '
all there is'.
I am helped by this analogy, and
my objective is satisfied.
That is all I care about in this matter. You can widen your thoughts on this as you please, but that has
absolutely no effect on helping me in my objective. They are simply superfluous to my understanding.
I acknowledge your right to think as you please, but please do not try to force me into your way of thinking, when I am absolutely happy with my results
Cat
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