Math is a human language. The universe, contrary to some religious claptrap on the interwebs, is not made of math, and, in fact, math, while incredibly useful and powerful compared to, I don’t know, using your fingers, does a rather poor job at describing the universe.
The problem isn’t the math. It’s us. Our brains aren’t limited to reality. We can imagine unicorns, immovable objects, honest politicians. Bat shit crazy stuff.
The universe just is. Math is one way we try and make sense of it. But we invented it and we believe some crazy stuff and so math has some crazy stuff in it.
To the best of our knowledge the universe contains (or is) a finite amount of energy that can be transmuted, but not created or destroyed (don’t start, quantum physicists, we’ll get to that nonsense in another article). To the best of our knowledge there can’t be a negative number of hydrogen atoms or photons in the universe. To the best of our knowledge, no part of the universe (spoiler alert) is imaginary.
So how come so many cosmologists, astronomers, mathematicians, and other assorted people say things like “infinite” and “singularity” (infinitely small, or at least packed together), “imaginary numbers” and the like? No idea. But it’s complete nonsense.
I mean when comedians go around talking about different infinities (there being more even numbers than odd and even numbers). Well, they’re comedians. When physicists do it, it’s weird. I mean in our minds we can imagine an infinite set of numbers, but in the real world there aren’t any numbers, not really. There’s stuff you can either make numbers out of (shiny tape, wood, plastic) or there’s things you can count. But there’s not an infinite amount of stuff with which to do either. No line can go on forever. Lines are made of stuff. There’s not an infinite amount of stuff. We can pretend a line goes on forever. We can pretend we like oysters or scotch. There’s nothing you can’t pretend. There are limits on what you can actually do.
So. the universe can’t expand forever. It won’t exist for infinite time. Black holes don’t work that way nor the early universe (the matter doesn’t run out of space to occupy, space increasingly warps in the presence of increasing matter (or energy)). The monkeys never produce all of Shakespeare (though they get through a surprising amount of Lear).