Space and time are things themselves and do exist independent of our perception. As evidence: all the solutions to general relativity that have no matter content but nonetheless are not flat, because the curvature of spacetime itself has energy that gravitates (the Schwarzschild solution comes to mind). Spacetime has its own real, physical, dynamics.
All you did there was prove your assumption. You assumed spacetime, then you assumed it to be a thing-in-itself (which, by the way, is an IDEA) and then noticed it has certain properties as described by various theories (such as from Schwarzild). None of this is evidence that space or time - which, by the way, I DARE you to define - are properties of some world independent of consciousness (the witness/observer), your just merely asserting them. You can say they are empirical (or phenomenological) facts, but that is much different than saying they are things-in-themselves
Kant agrees that empirically, space and time are things themselves and exist independent of our perception. In fact, for Kant, anything that can come to us or be reasoned by us, and the relations of those things, must comply with space, time, and, therefore, mathematics.
I wasn't trying to say that space, time, and mathematics do not exist independent of our perception. Rather, I was refuting the idea that mathematics is either a Platonic form or something we made up. The Kantian idea is: anything we come into contact with or understand must come to us in a way that conforms with mathematics, or else we wouldn't be able to experience it. Therefore, everything we know complies with mathematics--it's not some Platonic form outside us or our creation, but the very structure of our understanding. There might be a superset of laws that things in themselves comply with that we don't have access to. We are, however, limited to the understanding we can achieve through space, time, and mathematics (which do describe everything we can encounter).
My initial response wasn't terribly well written and was rambling, so I tried to clean it up a bit. It started to address your point but veered off-topic. There's also an important difference between perception and intuition that I originally didn't express very well.
Getting back to what I was originally trying to say, I don't think the nature of mathematics has much to do with whether or not we live in a computer simulation. We could be bound to mathematics for any number of reasons that are beyond our capability for understanding. What I was commenting on was the article's introduction to the question. I suppose, though, that the article itself admits the relation between the introduction and the topic may not be strong ("But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics"). I just don't think "Mathematics applies to everything we can experience, therefore we live in a computer" is a particularly interesting approach.
> I don't think the nature of mathematics has much to do with whether or not we live in a computer simulation.
Yes, I don't understand the logic behind this idea. If our universe is only orderly because it is inside a simulation, what is the universe in which the simulating computer like? Totally non-mathematical, and yet rich enough to have computers in it? Seems farfetched.
