# Where do our 4 macroscopic spacetime dimensions reside in multidimensional models of the universe?

In models such as M-theory with 7 'higher dimensions' plus the 4 macroscopic spacetime dimensions, where do our 4 macroscopic spacetime dimensions reside ordinally? My reason for asking is TV shows such as the 'Fabric of the Cosmos' that alludes to 'lower' dimensions in string theory. I can understand if our 4 are, say the 7th, 8th, 9th and 10th so there are dimensions lower than us but that we cannot readily detect.

• I am way out of may region of expertise here, but my first reaction is that this is equivalent to asking which of the three spacial dimension we live in is "first", which is ill-defined. They all come into the interval in either a space-like or a time-like way $(\Delta s)^2 = \sum_{i \in \text{spacelike}}(\Delta x_i)^2 - \sum_{j \in \text{timelike}}(c \Delta x_j)^2$ (or the other sign convention if you prefer, of course) so they are all equivalent. – dmckee --- ex-moderator kitten Mar 20 '14 at 23:59
• @dmckee. Aren't there specific mathematical definitions of (orthogonal) dimensions that tie dimensions N and N+1 together by things like projection? So, some sort of ordering should be possible, no? And in matrix math the spaces of "points, lines, plane" are based on tensors of 1st, 2nd and 3rd order etc. – PlaysDice Mar 21 '14 at 0:26
• I think what dmckee is saying is that we can't really say that $x$ is the 1st ordinal dimension or 3rd ordinal dimensions when considering 3D only, how could we possibly say anything at higher dimensions? – Kyle Kanos Mar 21 '14 at 0:28
• @KyleKanos Thanks. (I was a bit slow in the uptake, thanks dmkee.) So is the answer that M-theory does not (and does not need to) place our macroscopic universe in a particular ordinal range of possible dimensions? – PlaysDice Mar 21 '14 at 0:39
• My pre-post search missed this answer re compactification that looks useful – PlaysDice Mar 21 '14 at 0:43