In the open universe, you are constantly veering off - no matter which direction you choose to travel, you are always, ultimately or relatively, going away from everything else.
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In the closed universe it is just the opposite - just as an ant would take a straight path around the earth, eventually reaching the place where it started off and not knowing how such a thing was ever possible, so the traveller will make endless loops, constantly revisiting places. Soon enough, he will memorize the order of celestial bodies as they appear to him - one after the other in time, sphere upon sphere in geometry. He has been here before - he knows this from his past.+-+-+-+-+
In the flat universe, Euclid may be God. The traveller finds flat sheets of paper, any which way he looks. In the flat universe, a line will, more or less, be a line.+-+-+-+-+
Saddles, spheres or sheets of paper? The saddles becomes the sphere in reverse time and so the sphere becomes the saddle. The space and time curves and uncurves, curves and unnerves. Where is the edge? is a question. The universe seems to be beyond geometry. It builds itself somewhere in our collective mind now, instead.
“beyond geometry” is a lovely thought. Especially when you think of geometry as precision – and if I may be so bold, perfection.
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