Assumptions that such things as chemical molecules and black holes are
radically different in the 4th dimension, are equivalent to the idea that only in
a mirror is my face exactly reversed.
If dimensions, geometrically speaking, are inherent in space rather than
superimposed on it, then - for a domain of n dimensions - any domain of n-1
dimensions is a shadow world, with no more substantiality than reflections in
a mirror. We can see them, but they don’t exist. And if there are an infinity of
dimensions, reality is an unreachable illusion always beyond the visible. A
reality defined by boundaries, so that the infinite cannot exist, as a manifest
at least.
A guided tour of the universe - “here we have a 1-space, and over here a 4-
space” - would be absurd. In 4-space, our realm wouldhave to be an
infinitely thin cross-section of something; otherwise its chemistry would fail.
Personally, I think space can exist without dimensions, just as a line can be
without points. Insofar as either are real. And that it becomes, say, 4-space
only after 4-space geometry is ‘put into it’, and disappears when empty.
An infinity of points can be assigned to a finite line only because there is no
space between them. In spite of which they all occupy different positions. In
the same way, isn’t our realm merely an infinity of planes (‘flat’, or curved
like onion-skins), each having no thickness whatever, packed on top of each
other?
Or maybe I should stay off the liquor.
Simeon