My confusion is around the feeling that space and time must be preconditions for numbers and operations. How can you differentiate one number or symbol (or anything) from another without dimensions?
It seems to me that you wouldn't be able to have the notion of "1" and "2" unless they can be separated, and to separate them you need dimensions. So for a number to be intelligible at all, it requires dimensions; but how do you get dimensionality in the first place, if your equation is specifying the universe?
I think the way out of the cycle here is that your equations are not specifying the universe, they are merely describing patterns in the universe. So we model the universe with numbers, which are based on set theory, which like numbers is a product of our mind, which is a structure that exists in space and time.
It is helpful, I think, to think of numbers, sets, and the like, not as anything fundamental but as tools that help us make sense of the world.
My concern is something like this: observing and modelling patterns in the universe can only take place within time. If your models derived from the observed patterns then allow you to model a universe that does not have time, then there is something fishy with the model -- you've bootstrapped a timeless universe that is only intelligible from within time.
I found it interesting, even though I don't (yet?) understand it, that Sir Roger Penrose in this talk/debate with William Lane Craig talks about that "you can have a temporal order without having a time associated with that": http://www.youtube.com/watch?v=9wLtCqm72-Y&t=58m5s
Kant had the same "confusion" which is why he considered space and time "forms of intuition", a slightly misleading translation from the German word Anschauungsformen. These Anschauungsformen in his view a part of the conditions for mathematical thinking and together with the categories make it possible.
I'm not writing that under the assumption that Kant was right, his philosophy is based on something like "inner intuitions" that are dubious and in my opinion do not match modern mathematics very well which deals with objects that go far beyond our visual imaginative capabilities and what we might check with some kind of "inner intuition" (innere Anschauung) or geometrical insights. I just wanted to point out you're not alone and if you're confused, then in an elaborate way.
You need time to differentiate, but the universe does not. The one and the one and the two of them are always here in the universe. You just need time to speak it. You need time to observe the difference between the neuronal pattern between an awareness of one and the other one and the two of them.
To have the one and the two in the first place grants spatial dimensions, to separate them. Otherwise you end up with a single point, or maybe not even that.
I can't get my head around how anyone can generate time (whether an illusion or not) just from spatial dimensions. If I have to assume spatial dimensions to get anywhere, can I also assume time?
These are just analogies, so let's just accept that first and foremost. Words are just a way for us to make sense of it, which we can't really do. Even math itself is just an approximation for reality.
But, in "this world," the one we "think about" time is the path between two simultaneously existing universes. The universe a minute ago still exists. The universe a minute from now exists already. Time is how we got here and will get there.
We aren't generating it. It's always here. It only exists when it is observed. You observing it makes it exist. That's the path. You haven't observed the universe an hour from now, so it doesn't exist yet, but that's only true in your mind. It's already here. It's there. All potential universes exist simultaneously.
Time isn't an illusion. It's a path. It's like the trail from your house to mine.
For a point to get from one point to another, it needs another dimension, a line. A line needs a plane. A plane needs a cube, a cube needs time, time needs... what? The fifth dimension. Through the fifth dimension, we can create paths from one time to another.
We just aren't there yet. We haven't observed that happening, but it's there. Always was, always will be.
1+1 is a dimensionless operation.
Do you mean how it would physically happen without time? It's possible time is just an illusion that emerges from our perception of the universe.
See https://www.nature.com/articles/d41586-018-04558-7 and https://www.quantamagazine.org/does-time-really-flow-new-clu... or https://www.npr.org/2013/05/17/184775924/resetting-the-theor... for a counter argument.