There is no PRACTICAL difference between a theory that treats e and pi as “rational but not yet perfectly determined” and “irrational.” And by practical I mean as used by practitioners, people who build stuff, people who survey, even people who need to know the parallax to the most distant object in the universe between two relatively closely spaced telescopes on earth.
“infinite” broken down to its roots means “not finite.” The practical value of “not finite” is probably “so large that we need to be sure we always get the same answer when we assume it is a million times larger,” that is, we verify that we have a PRACTICAL solution that has converged as we make x larger and larger, and whether x is > 1 km (when designing a microcircuit) or x > 1 quadrillion light-years, we never need to know, PRACTICALLY, what happens when x finally reaches infinity.
Engineering principles which are WRONG when quantum and relativistic considerations are taken in to account stand firmly and valuably behind quadrillions of dollars worth of human infrastructure.
Philosophical theories which are limited in validity only to these principles are possibly not useless.
There is no PRACTICAL difference between a theory that treats e and pi as “rational but not yet perfectly determined” and “irrational.” And by practical I mean as used by practitioners, people who build stuff, people who survey, even people who need to know the parallax to the most distant object in the universe between two relatively closely spaced telescopes on earth.
“infinite” broken down to its roots means “not finite.” The practical value of “not finite” is probably “so large that we need to be sure we always get the same answer when we assume it is a million times larger,” that is, we verify that we have a PRACTICAL solution that has converged as we make x larger and larger, and whether x is > 1 km (when designing a microcircuit) or x > 1 quadrillion light-years, we never need to know, PRACTICALLY, what happens when x finally reaches infinity.
Engineering principles which are WRONG when quantum and relativistic considerations are taken in to account stand firmly and valuably behind quadrillions of dollars worth of human infrastructure.
Philosophical theories which are limited in validity only to these principles are possibly not useless.