Sean, (01)
> In the context of this thread, I might observe that with this
> background
> knowledge, I look at the 3D/4D discussion as involving a lot of unstated
> assumptions, and that therefore the answer is not 3D or 4D, but depends on
> quite a number of other purely mathematical considerations, such as
whether
> one uses a homogenious co-ordinate system. (02)
Could you being mislead by the names? The ontological distinction between 3D
and 4D is really about one's position on change (whether it exists - hence
ontology) and the 'D' name is used as this can be a helpful way of thinking
about the problem. See, for example,
http://plato.stanford.edu/entries/change/ and
http://plato.stanford.edu/entries/temporal-parts/ . This might relate to
your 'lot of unstated assumptions'. (03)
It is claimed this is a metaphysical choice rather than an empirical
question, so if there are empirical results that might influence the choice,
this is interesting. (04)
So if space turns out to have 16 or 28.5 dimensions and is quantised, there
will still be a 3D/4D question, though it will be clear that it not about
counting the number of dimensions. (05)
This is not to take anything away from your points about needing to consider
metric spaces, co-ordinate systems, etc. when working out the details. (06)
Regards,
Chris (07)
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