[defyonce]

I really like this answer, thank you, it gives me something to think about.

Why are we sure that mathematics is not completely a part of this time-space bubble?

Let's say there is an "outside" for the mathematics similar to warp space in wh40k.

A "something" where natural numbers, for example, cannot exist, there will be no space or time in such a case, but it may still exist in some weird sense of undivided consciousness.

In such a case for this outside you need a proper rule based bubble to say that there exists a mathematical possibility for our universe to run in according to rules defined inside that bubble.

That would be "simulation space", if we contrast it with the "outside".

I hope I've got my thought across, because I am pretty rusty in my English writing skills.

[jstanley]

My view is that pure mathematics is true because it says so. It doesn't rely on any kind of structure from the universe to hold it up (that's why the universe can be made out of mathematics). If you define mathematics the way we do, then you get the answers that we do, no other ingredients required.

There are other ways to define mathematics, sure, and if those ways allow universes that our ways don't, then those universes "exist" too.

[defyonce]

> It doesn't rely on any kind of structure from the universe to hold it up

I am not sure that this is the case, for math to be it needs a set of axioms.

Axioms have to mirror some sort of universe. I am really curious what can be done if we remove all the axioms.

I am sorry if I sound dumb, I don't know much, but it is really interesting.

[jstanley]

You can have whatever axioms you want though. There's nothing to privilege any set of axioms over any other. And all of the implied universes will equally "exist".