russ_watters said:
Latitude and longitude have an arbitrary reference at the prime meridian and equator, but that's not a center: Finite surface, no center.
[late edit]
And no edge either.
phinds said:
It is a trivial claim, as Russ has shown.
Loren said:
I agree, but a cube is a different story, so, the statement doesn't hold for all geometries.
with all due respect i believe you are too quick to shoot these things down and that you haven't paid close attention to the detail of what i said.
at the risk of coming off with a similar poor tone to these comments, allow me to explain in more detail so that it is not so easy to make the mistakes.
i quite explicitly defined what i imagine a laymen means by 'finite' - bounded in the dimensions of the coordinate system under consideration. in his ideals the surface of a sphere like you describe is an /infinite/ surface because in the local coordinate spaces there are no bounds unless you are choosing a chart that has a seam (singularity) on it rather than multiply wrapping around the sphere (e.g. a cylindrical projection) - in which case we now have a finite area /with well defined bounds in all coordinates/ and so we can use the layman's understanding of what a centre is and there very much is one at 0 latitude and longitude (assuming we go from -pi to pi, -1/2 pi to 1/2 pi).
with regards the cube you can map a cube to a sphere and a sphere to a cube (any convex geometry to a sphere) so using a cube makes no difference to the nature of this, nor a dodecahedron or a cylinder. it just introduces a deformed version of the same coordinate system.
the other point that people try to make is that with the balloon analogy it has volume, and the volume has a centre. comparing this to volume in the universe completely missing the abstraction the balloon analogy makes to simplify things - specifically using 2D as a substitute for 3D because people struggle with visualising and understanding 4D representations. in that sense, if the universe was an unbounded 3-sphere then we have a 'hypervolume' inside of it which also very much has a centre in that 'fictional' 4-space - note, that this 4-space is not a minkowski style space-time but a 'fictional' euclidean 4-space, in the same sense that the 3-space the balloon is embedded is not a 2,1 space-time, but euclidean 3-space - or alternatively an extension of the sphere's local coordinate system that replaces intrinsic curvature with extrinsic curvature by embedding the system in a space with higher dimensionality.
now, if i am wrong, and you can construct a reasoned argument for why instead of a flat statement asserting that these things are wrong and that i simply do not understand, then i will consider it and hope that i have the good graces adjust my stance accordingly if it is a convincing argument.
again i apologise if my tone is poor. its very frustrating to see these kinds of comments, they paint a poor picture of the scientific community to laypeople and they are not uncommon - i have been guilty of this my self plenty too. its a natural way to behave when you are confident in your knowledge and weary of trying to explain the same things repeatedly.