There's an argument to be made, if reality isn't discrete (can be represented exactly by rational numbers) but continuous (can be represented by real numbers) y

There's an argument to be made, if reality isn't discrete (can be represented exactly by rational numbers) but continuous (can be represented by real numbers) you can represent programs that cannot be represented in a discrete way like a Turing machine. For instance the typical proof that the halting problem is unsolvable relies on there being just a discrete infinite amount of programs.