Does the mathematics of string theory require extra dimensions to be "higher" than our own? Is it possible that extra dimensions are lower that that the four we currently know? Could our four be placed somewhere in the middle of a proposed scheme of dimensions?
closed as unclear what you're asking by ACuriousMind♦, Brandon Enright, Danu, user10851, Kyle Kanos Aug 24 '14 at 23:28
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There is no significance to the numbering of the dimensions.
When we refer to a vector it's common to write is as $x^\alpha$, where $\alpha$ runs from zero to the number of spacetime dimensions minus one. $x^0$ is frequently used to refer to the timelike dimension, so $x^1$ to $x^n$ refer to the $n$ spatial dimensions. However there is no signficance as to which of the spatial dimensions is referred to by which index. The three dimensions we are familiar with from everyday experience don't have to be $x^1$ to $x^3$, though they often are.
To explicate what we mean by no significance, I would suggest that you understand the indexing as a convenient type of naming. We need some way to say which dimension we are referring to and using numbers lets us use convenient notation, but we could just as well have named the dimensions. The ones we experinece might be Tim, Alice, Bob, and Carol. Any new ones found would then (obviously) be named Dave, Eve, Frank, Gloria and so on.
Now, would you describe the names as having a ranking (not an ordering, a hierarchy of value)?