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I'm not sure what he's 'explained'. It seems a rather long-winded way of saying 'we don't know'.
Like I said very early on, Naomi, "we don't know" covers a whole host of positions -- including, "but we have some idea of what it might be". The best current starting point for trying to understand the shape of the Universe, and the nature of what, if anything, lies beyond it, can be found in General Relativity. It doesn't provide any certainty, sure, but it does give you something to think about. I don't understand why you can't appreciate the shades of grey in "we don't know" -- a statement that covers the entire spectrum of lack of knowledge, from near-total to anything short of absolute certainty.
Also, NJ, I'm sorry to hear that latest reply. I hope that the explanations I gave helped, though. It is a difficult topic and I wouldn't dream of claiming that I understand it myself, but hopefully the more it's discussed the easier it becomes to appreciate, if not the complicated details, then certainly the necessity of them. I had to look up who said it, but it was JBS Haldane who said that the Universe is not only "queerer than we suppose, but queerer than we can suppose", and he remains correct -- although there's no harm in trying anyway.
I need to dip out, jim, because my lack of imagination simply refuses to accept what I know must have an element (if not more) of truth. Far better brains than mine have devoted their powers to developing plausible theories but I simply dismiss them because I cannot understand them. Even when OG kindly explains his “ball” theory all I do is simply say “but there are things beyond the ball” because my mind cannot accept an end to something with nothing else beyond. I perfectly understand the finite nature of the ball but cannot accept a rather larger ball surrounded by nothing.

Please don’t think your efforts have been wasted! The fault is mine for being unable to accommodate things I cannot understand. It’s been an interesting discussion.
Ok, thanks for that last post NJ -- it's reassuring to hear. I wouldn't necessarily call it your "fault", though. As I said earlie,r it's probably literally impossible to try to imagine this no matter how
gah, itchy trigger finger...

no matter how well-versed you are in the subject (and I'm not really well-versed at all).
Belated thanks, Jim, for the reply.

Because of having ecountered the idea of a two-dimensionsl "flatworld", which attempted to approach the problem of the occupants of a universe being unable to grasp the existence of a dimension which they do not (cannot) themselves inhabit (measurements rendered impossible too, presumably), I had difficulty in understanding your one (latitude *and* longitude???) but words are just too cumbersome and a pen and paper would help.

Incidentally, the one I'm referring to contains a cheat, in which the cartoon-character-like inhabitants of flatworld are permitted to be one atom thick, which prevents them passing through other inhabitants or physical obstacles but violates the 3rd dimension.

In this scenario, there is latitude (around the circular planet) and up(infinite)/down(to ground level) so maybe they can clamber over people/objects they bump into but they cannot peer out of their flat plane, to see a 3-D observer, who sees them sideways-on.

My personal conceptual limit is that I am unable to envisage how the next dimension can satisfy the condition of being mutually perpendicular to all three of the conventional dimensions, simultaneously.

The best I can manage is that, if X,Y,Z are lines then, by comparison, the next one is a sphere and the intercepts are perpendicular, if nothing else. Is that even an applicable rule, I wonder?

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