There are many things that are outside of space and time that we interact with all of the time.
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.
Why don't we set the math and the numbers to be defined by the golden ratio?
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.