What trips me up (but the article glosses over) is the concept of "the size of a dimension".
How are dimensions larger and smaller? To me, a dimension is usually something you measure in. My height is my extent in the vertical diredction (if standing up). What would it mean for that dimension to be small?
Our 3 spatial dimensions I assume are "large", meaning what? The axes extend to some apparent infinity without repeating? Does a "small" dimension behave like a longitude, that after a certain while it repeats itself? So the two dimensions of a sphere surface are "smaller" than the 2 dimensions of an infinite plane, is that how to interpret the small/large? So [the surface of] an infinitely long but finitely thick cylinder would have one large (along) and one small (around) dimension? Is "small" then always finite, but large can be large-but-finite or inifinte?
How are dimensions larger and smaller? To me, a dimension is usually something you measure in. My height is my extent in the vertical diredction (if standing up). What would it mean for that dimension to be small?
Our 3 spatial dimensions I assume are "large", meaning what? The axes extend to some apparent infinity without repeating? Does a "small" dimension behave like a longitude, that after a certain while it repeats itself? So the two dimensions of a sphere surface are "smaller" than the 2 dimensions of an infinite plane, is that how to interpret the small/large? So [the surface of] an infinitely long but finitely thick cylinder would have one large (along) and one small (around) dimension? Is "small" then always finite, but large can be large-but-finite or inifinte?