# Some questions regarding $n+m$-dimensional spacetime [duplicate]

The following image:

serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime. It is however, incomplete, as the wikipedia sub-article also mentions String Theory, which also considers having 10 or even 26 spatial dimensions. My first question is: are these the only notable exceptions to all the "unstable" versions of spacetime in the second row?

Furthermore, I would like to know if the concept of having a negative amount of dimensions has been considered, or even adequately mathematically described.

Lastly, I am wondering whether or not (mathematical) physicists have considered the possibility of having a non-integer amount of time and/or space dimensions. The notion of having a non-integer amount of dimensions is at least mathematically defined by concepts such as the "Hausdorff Dimension" and the "Minkowski Dimension".

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## marked as duplicate by Qmechanic♦Dec 18 '12 at 10:52

–  Qmechanic Jan 20 '12 at 23:48
I have a big problem with the "unstable" and other labels. Whether a spacetime is stable depends on the dynamics in it. And be sure that supersymmetric $n+1$ dimensional spacetimes are always stable, and there are lots of them in string theory and outside string theory, too. The label "too simple" may have a point but one would have to discuss what it exactly means, much like the "ultrahyperbolic/unpredictive" label. Those things are for a long discussion with many aspects and it's not clear which of them you're really interested in, especially if you add fractional and negative dims (WTF?). –  Luboš Motl Jan 21 '12 at 6:48
Could you say where the image comes from ? Maybe some background on the classifications is provided there –  twistor59 Jan 21 '12 at 13:06
–  Qmechanic Jan 21 '12 at 19:34
For a mathematical discussion see mathoverflow.net/questions/47569/… –  jjcale Oct 18 '12 at 23:19