I have been reading a lot about string theory and the necessity of extra dimensions (particularly as visualized in Calabi-Yau spaces), as "curling-ups" in our apparently 3-dimensional (or 4-dimensional, including time) world. I do not understand, though, how all these "extra dimensions" are actually adding dimensions to our world.
Even if these little multi-dimensional curls are everywhere and too tiny for us to see, how is it still adding extra dimensions? I mean, if our eyes were sharp enough, couldn't one still specify their location according to an $x,y,z$ axis? They will be a certain amount to the "left," a certain amount "high," and a certain amount front or backward (etc). It's still length, width and depth.
What am I missing here?
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