I think the models involving the tiny extra dimensions are pure mathematical ones to give mathematical meaningful solutions to overcome discrepancies with the current models. It doesn´t mean those extra dimensions do really exist. But if, there would be no way for us to detect them. In a higher dimensional universe (no proof of its existence however) we indeed would appear like flatlanders in our universe. By the way, we don´t have to apply the flatlander´s analogy. Already the 4th dimension, the time, is not reachable for us, we can see time only as going by, but we cannot influence it. A truely 4 dimensional being could travel through time like we through 3 dimensions.
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