I am a math guy. There is no way to actually do these calculations in practice that does not at some point boil down to something done on a computer to finite p

I am a math guy. There is no way to actually do these calculations in practice that does not at some point boil down to something done on a computer to finite precision. For example if you want to plot planetary orbits you should plug in your most precise available measurements, use Runge-Kutta, and produce rational approximations. There is no way to test our theories in practice that doesn't at some point involve comparing this finite precision prediction with a finite precision observation. Pontificating about the failures of a discrete approximation to be able to be computationally accurate in a continuous world may be fun armchair philosophy, but CANNOT be useful scientifically. Because we can only measure and work with finite precision approximations to that hypothesized continuous reality.