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Cosmological topology is nothing new--in fact, Poincaré brought forth a conjecture that lasted for a hundred years (the only solved Millennium problem so far) that involved viewing the universe curved into four-space, without being able to freely allow the Ricci Flow to proceed without a topological singularity forming (proven by Perelman in 2003), although I digress. Let's pretend we have a ball, on which a two-dimensional creature lives. Light always travels parallel to this surface. Given enough time, the creature can see itself from the back, as it were that time ago. The light can keep wrapping around and around and around the ball, and make it look to the creature as if its world is infinite and flat. We don't perceive the universe's curvature because of how big it is, as well as because we are curved along with it (think of the creature and how light travels parallel to the surface. However, if we had theoretical "beacons" throughout the universe that remain exactly the same and
MathematicallyMindedFractal MathematicallyMindedFractal 16-17, F 3 Answers Jun 27 in Hobbies

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But don't we already know the curvature? Given that we could calculate the size. Although we don't know it's constant...

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No we don't. We know that it is most likely that it's curved. But we don't know its topology, nor do we know if it's positively or negatively curved.

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Oh, ok then. Too bad, although you could get 3 points and determine the curvature between them of course

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placed at a known distance away, given an amount of time, we could see where the light from the beacon appears after it wraps around the universe and get a rough model of the universe. It's kind of like how the creature could place a known dot on the ball, and watch for where it next appears, and also kind of like how Kinect senses the shapes of ob<x>jects, though with a slightly different principle here.

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Exactly the same and......and what? AND WHAT? D:

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I continued it as a comment.

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It's an interesting idea. I wish we were capable of such things.

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Oh, but in a way, we are. I wish I had my bookmarked page with me to show you. It's very interesting and talks about a potential method for measuring this.

We could theoretically use supernovae, but we would need a huuuuge amount of time to actually calculate the exact shape of the universe.

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Oh, wait, I thought you meant if humankind could physically place those beacons. Space is truly the final frontier.

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That's why I said hypothetical.
And no it isn't. It's the penultimate frontier. The ultimate frontier is the multiverse :D

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That's true. (Also I love it that you used the word 'penultimate'. Hardly anyone uses it anymore, and it's such a good word.)

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