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re: Around and around and back and somewhere else

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What does it mean that the space was only locally euclidean?

Would a Torus space (like in pacman) be euclidean?

[A torus space is not Euclidean because it loops back on itself. However, it is locally Euclidean, because if you look at a small piece at a time (the space immediately surrounding the pacman's current location), that small piece looks Euclidean. It is only when you look at large pieces that you notice that the space is warped funny. Another example of a locally Euclidean space is a spiral ramp. To an ant walking on the ramp, it looks like a regular flat space, but if the ant has a good memory, he may realize, "Wait a second, I walked a complete circle but I did not come back to my starting point." That was the sort of behavior I was experiencing in my dream. -Raymond]

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