Technically speaking, at least for certain constants, our current model of the universe is that they are infinitely complicated, because we aren’t promised that all of the constants are computable real numbers, though they are almost certainly not constants we could use to perform hypercomputation, and thus the universe is infinitely complex in the sense of Kolmogorov Complexity.
That said, I’m not sure whether physicists have come to a consensus that any future theory of quantum gravity must have real numbers that are computable.
This is assuming no expression that converges to the constants exists? Which I think is an open question. (Of course, it would only be finite if there are such expressions for all constants. But even so, I think it’s an open question.)
What do you mean by no expression that converges to the constant exists? Do you just mean an Turing-computable expression that converges to the number?
Technically speaking, at least for certain constants, our current model of the universe is that they are infinitely complicated, because we aren’t promised that all of the constants are computable real numbers, though they are almost certainly not constants we could use to perform hypercomputation, and thus the universe is infinitely complex in the sense of Kolmogorov Complexity.
That said, I’m not sure whether physicists have come to a consensus that any future theory of quantum gravity must have real numbers that are computable.
This is assuming no expression that converges to the constants exists? Which I think is an open question. (Of course, it would only be finite if there are such expressions for all constants. But even so, I think it’s an open question.)
What do you mean by no expression that converges to the constant exists? Do you just mean an Turing-computable expression that converges to the number?
Yeah, e.g., any convergent series.