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<blockquote data-quote="Umbran" data-source="post: 6729986" data-attributes="member: 177">Yes, but you are still thinking from the point of view of someone used to thinking in rectangular coordinates.&nbsp; Why would we expect a rectangular coordinate join, specifically, of the universe?&nbsp; All continuous joins introduce curvature.&nbsp; Try to make a cylinder without bending the paper, dude <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile&nbsp; &nbsp; :)"&nbsp; data-smilie="1"data-shortname=":)" />Let me put it another way - as mathematicians considering topologies, we can think up all sorts of spaces, without concern for why they are shaped a given way.&nbsp; But, General Relativity tells us that the topology of our real spacetime is *not* independent of the material within the space.&nbsp; You can only have arbitrary topology if you allow arbitrary placement of material in the space.&nbsp; And, if we don't have material, then the space isn't shaped that way.It is proven, insofar as GR seems pretty good, and we've seen no evidence for other curvature of our spacetime.&nbsp; I know of no physical phenomenon currently unexplained that calls for such curvature.&nbsp; Occam's Razor, then, suggests that I not worry about the possibility too much.I wouldn't state it as you do - it isn't &quot;non-uniform axes create a substantial problem&quot;.&nbsp; I would put it as, &quot;curvature of the space that is not attributed to mass likely (if I recall correctly) equates to perpetual motion machines and/or time travel*.&quot;&nbsp; Either of those gives us serious issues with causality and the laws of thermodynamics.&nbsp; You need to have a really good reason to suggest those might exist.&nbsp; *IIRC, time travel implies perpetual motion, but perpetual motion does not necessarily imply time travel.</blockquote>

[QUOTE="Umbran, post: 6729986, member: 177"] Yes, but you are still thinking from the point of view of someone used to thinking in rectangular coordinates. Why would we expect a rectangular coordinate join, specifically, of the universe? All continuous joins introduce curvature. Try to make a cylinder without bending the paper, dude :) Let me put it another way - as mathematicians considering topologies, we can think up all sorts of spaces, without concern for why they are shaped a given way. But, General Relativity tells us that the topology of our real spacetime is *not* independent of the material within the space. You can only have arbitrary topology if you allow arbitrary placement of material in the space. And, if we don't have material, then the space isn't shaped that way. It is proven, insofar as GR seems pretty good, and we've seen no evidence for other curvature of our spacetime. I know of no physical phenomenon currently unexplained that calls for such curvature. Occam's Razor, then, suggests that I not worry about the possibility too much. I wouldn't state it as you do - it isn't "non-uniform axes create a substantial problem". I would put it as, "curvature of the space that is not attributed to mass likely (if I recall correctly) equates to perpetual motion machines and/or time travel*." Either of those gives us serious issues with causality and the laws of thermodynamics. You need to have a really good reason to suggest those might exist. *IIRC, time travel implies perpetual motion, but perpetual motion does not necessarily imply time travel. [/QUOTE]

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