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Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons).

One such of course is string theory; but I wondered if there might be others, and perhaps even a survey of this topic along the lines of those expository articles one often sees in the ArXiV.

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possible duplicate of Is 3+1 spacetime as privileged as is claimed? – Qmechanic Dec 22 '11 at 21:59
The dimensionality of spacetime is a historical accident in string theory, like the number of planets in the solar system, although it can't be too big. The problem with the question is that I think it is too restrictive. You can ask more generally, Why does space appear as a smooth locally symmetric structure at all? In other words, why are we not living on a 4d version of a Sierpinsky gasket? Any scale-invariant object can emerge as the domain of a low-energy effective field theory, it doesn't have to look like a manifold at all. – Ron Maimon Dec 23 '11 at 5:04
Great to see you here, John! I hope you are, with smile and USD 500 in an envelope, celebrating the arrival of the Higgs to be discovered in Spring. My $500 is ready for you! ;-) – Luboš Motl Dec 23 '11 at 6:34

JFYI yesterday released a story titled with "The mechanism that explains why our universe was born with 3 dimensions: a 40-year-old puzzle of superstring theory solved by supercomputer". Where Japanese scientist using a supercomputer found out that three out of nine spatial directions start to expand at some “critical time”, after which the space has SO(3) symmetry instead of SO(9). Here is the link to arxiv.

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+1 The paper looks interesting . – centralcharge Aug 10 '13 at 8:17

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