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If you can not come to an edge, then there is no edge, and thus there is no shape.
If you take the shape as a dodecahedron and you start at the center of this shap and move outward, you come to a face. Now this mathematician is saying that when you hit that face you instantly come back into the dodecahedron through the opposite face.
Now, let us assume that the universe is two light years across (it isn't but go with me on this), if the above theory is correct then when you exit one face you would be instantly transported two light years across to the other side of the universe, thus making the journey at a speed greatly in excess of the speed of light.
The only way this could happen without breaking the light-speed barrier would be for the opposite face to actually abut the face you exit, meaning that it would be pulled around in a innertube like shape. but the same would have to be said for every face, forming an incredibly complex system of tubes.
But then the problem arises: what about the sides of the tubes? What if instead of travelling through the tube, i cut acroos to the side and try to get out there? Then every side of every tube would have to abut every other side of every other tube!
In other words, if there is a SINGLE face of any kind, you would be able to leave the universe, or would have to break the lightspeed barrier by intersecting one of these faces.
Basically, what I am saying is, according to this theory, the universe either has NO shape, or the light-speed barrier is not absolute.
What does this mean? This means that claiming the universe is shaped like a football (or soccer ball) or ANY shape is totally wrong.
Another effect of what he is claiming is that a star on one side of the universe would shine directly on the other side, without the light travelling the entire distance across the universe. This would mean that that light would travel at speeds in excess of C, thus making the speed of light variable, not absolute.
Also, imagine we are sitting on one side of the universe looking at one of these faces. In front of us would be the entire universe seen fron the opposite face looking back towards ourselves. Could we actually know we were at the edge under such circumstances? For all intents and purposes we would actually be sitting on the other side of the universe looking inwards, rather than on this side looking outwards. Thus we would essentially be in two places at once. If we look forward we are on the right side, for example, but if we look backwards we are on the left.
In fact could we ever know where the edges were, and if not can we really say there are edges?
So how can we prove that this is not happening? Because we would be seeing an infinite universe! If we looked out at the universe, we would see all the stars in it multiple times, in fact an infinite number of times, because as we look further and further out, we would approach one of these magical faces and see the whole universe before us again, as we continued looking further out, we would see it all over again, and so on.
So our entire sky would be filled with multiple images of the same star transmitted over and over again through the edges of the universe like a hallway lined with mirrors. If you have ever been in such a halway, you would know what I mean, as standing there, you see your reflection repeated off into infinity as each mirror reflects what the opposite mirrors sees and that mirror reflects that image again and so on.
Basically, I think this mathematician has talked himself into a corner. If the universe is the way he says it is, then why can't we see it that way? If it is not the way he says it is, it calls into question his interpretation of the data.
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