Okay, let's go back to the example of the sphere. Geodesics in the time direction are lines of longitude. Our experience of time passing means that we are all moving down lines of longitude. Hence, latitude is our measure of time, while longitude is a measure of spatial location. A person on this world sees her universe as having one spatial dimension (she thinks she lives on a line) and one time dimension.
Now imaging three galaxies, one, where our protaganist is located, at longitude 0, which we will call O, galaxy A at 30 degrees longitude, and galaxy B at 60 degrees longitude.
Now, as observed by our scientists at O, both A and B seem to be moving a way from her since the lines of longitude are diverging. (Unless they have already passed the equator, in which case they will seem to be coming together). What is more, as the galaxies move down the lines of longitude, the further galaxy, B, seems to be receding at a faster rate than A.
In fact, it could be that the rate at which O and B are moving apart seems to be faster than the speed of light. Now, in this case, the scientist at O cannot actually see galaxy B. However, she may be familiar with General Relativity, and can hypothesize that her universe is a curved 2-manifold, and may even theorize that it is a sphere. She may not be able to physically construct this model of a 2-sphere existing in a 3-d universe in her 1-d space, but if she knows differential geometry she can do all the math.
In this case, she can then put a coordinate system on the sphere, perhaps based on lines of latitude and longitude. She can then figure out how to calculate actual distances in her standard system of units on this sphere based on their coordinates, much like we can calculate the distances between any two cities on the surface of the earth if we only know their coordinates.
Now she can deduce that even if she cannot see it, there exists a geodesic along the 60 degree longitude line. Furthermore, she can now calculate the distance along a line of latitude between 0 and the hypothetical galaxy B (distance along a line of latitude being an actual distance in
space), and she will notice that this distance is increasing at a rate faster than the speed of light.
I'll leave it to cavediver or Son Goku to critique the accuracy of this analogy.
Edited by Chiroptera, : construct -> physically construct
Edited by Chiroptera, : criticize -> critique
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