🚀 go-pugleaf

> How many mutually perpendicular rulers can you affix to a single pivot?
> After you have attached three of them, you won't have room for a fourth.

This seems to amount to saying "it is easy to construct three mutually
perpendicular axes, but no one knows how to add a fourth".  This might
be taken to be pretty good evidence that there are only three
dimensions, and for some things this is about as much proof as you
get, but for something this fundamental it would be interesting to
find a proof more solid than "we don't know how to add a fourth
mutually perpendicular ruler".

>                     How do I know that time is one-dimensional?
> I'm not sure.  It certainly is a good working hypothesis until someone

This amounts to saying "we've constructed a theory that makes good
predictions on the basis of four-dimensional spacetime".  Again, good
evidence but not a proof.

Just to make this seem more plausible: consider a form of life that
might evolve on the surface of a very smooth planet with very high
gravity.  Suppose these beings were very flat, and in fact consisted
of a single layer of cells.  Their retinas for example would consist
of a single line of cells.  To them the world might seem
two-dimensional, because sensing or causing anything to happen in the
dimension perpendicular to the surface of the planet would be very
difficult.  They would have to rely on more sophisticated observations
to deduce the existence of a third dimension.

Note that I'm not saying in any way that I believe something like this
is the case, but rather that it would be interesting to see a proof
for something this fundamental.  Indeed, I have been provided by email
with a reference which I will look up:

A simple proof that the world is three-dimensional, by T. Morley,
SIAM Review 27 (1985), pp. 69-71