Re: Why are there 3 dimensions?
It's a question I'm asking, not answering. Not some sort of trap.
Why 3 dimensions, why the observed properties?
a) We observe 3 dimensions.
b) Those dimensions appear independent of each other, e.g. a force along X independent of Y and Z.
c) Two can interact, independent of the third, e.g. a force or motion along XY independent of Z.
d) All three can interact, i.e. forces and motion along some XYZ direction
e) They are equal in scale or are measured as equal. A force along X behaves the same as a force along Y, and as a force along Z.
f) They are arbitrary oriented. You can pick any axis and align the other two and the rules above all works regardless of the direction of your first axis.
g) They are bi-directional, a force along X could be along -X, a motion along Y can travel -Y, Z with -Z, XY forces can all be reversed, ever push can have a pull.
Time is a parameterization of motion over space, argued in a comment below. From which follows :
k) all 3 dimensions can be parameterized for motion over space the same way. i.e. time operates in *all* dimensions. You cannot have a dimension independent of time because it would violate d).
So why 3? It's easy to define the observed properties, but why are they?
If you have a model that creates property e), you might then wonder if it doesn't also need to create property b) and may also create a). So I ask.
Why would you regret asking?, the worst you'll get is someone quoting dead people as fake assumed authority. Insecurity not intellect.
Claptrap314 made some comments which caused me to google, which leads me to an awfully familiar thing. I've googled the wazoo out of twisting, topology, prime-number, knowing there will be an entire field of topology that already examined it, but that is the first time that paper has popped up.