Really good thought on the subject
However, I have to disagree with most of it.
There are many things that are outside of space and time that we interact with all of the time. Time and space are constructs. And some of the more higher level constructs at that.
π is actually a rational number. But, the way we have defined mathematics has really big problems and holes in it. A basic premise of modern mathematics is that you can always add 1 to a number. And thus, we add infinity and asymptotic to the mix. Further, we cannot divide by zero.
All of these will change when man learns to tune mathematics.
Like, 1,1,2,3,5,8,13,... approximates the golden ratio. Why does it approximate? Why don't we set the math and the numbers to be defined by the golden ratio? Then math would be a better tool for describing the world we are in.
By that very definition the things you talk about cannot be outside space and time if we're interacting with them. Perhaps many people believe they are doing so, however since they can only prove it to themselves it doesn't really warrant discussion.
That's the point, because we can't. In the late 19th century, an American mathematician claimed to have solved the old Greek problem of squaring a circle. Problem was, pi had to have a value of 3.2 for it to work, he even got as far as getting a bill passed, before having it rejected by the Senate.
You can't change numbers that approximate to other numbers, because they have very real statistical implications with each other. The values of these things aren't arbitrary, they are very real in that sense, hence not only their usefulness, but their objectively constant behaviour.
Still though, it's interesting to ponder such abstract things.
Cg