Why is space-time 4D? I earnestly hope the first reply will be a
succint, obvious answer.

I'm a fourth-year undergrad at the University of Toronto. I have a
technical knowledge of quantum field theory and general relativity, and
of loop quantum gravity to some small extent (largely from reading John
Baez and Carlo Rovelli). It will be a while yet before my understanding
of string theory (or whatever) has progressed much beyond jargon, though
I am trying my best to think deeply on the matter. Maybe there is some
hope people will have nice answers that I will be able to understand.

Classically, maybe we don't have to ask this question - we can say that
space- time is 4D and that's that. But then again, maybe there is some
deep answer that has occurred to someone. (I know that GR is
qualitatively different with dim 4.)

Similarly with LQG, it seems that people are happy to enforce something
like 4- dimensionality by speaking only of space-time made up of
4-simplexes, so maybe they don't have to answer that question. But
maybe they would like to. Also, my uneducated brain worries, as I
gather others' do, that LQG space-time crumples down to some effective
dimensionality between 0 and 4 at large scales. (Or, for that matter,
that it crumples down from, say, 42 to 4 dimensions.)

Other people tell me that, on some scale between M theory and real life,
space- time is definitely 11-dimensional. 7 of those dimensions are
small and compact, whereas the other 4 are large (and possibly also
compact). On the other hand, I know some people suggested that some or
all of the extra 7 dimensions are only traversed by gravity, but maybe
that is unpopular now?

So my question really is, what's so special about the number four? Is
there nothing in particular? Is 4D a distressingly random fact? If 4
is just an effective dimensionality, this doesn't seem to be an
acceptable answer.

For a while now I've been disturbed by the possibility that MATH selects
4 as the natural dimensionality, once we finally get our heads screwed
on straight about what space-time is.

Thanks,

Michael