Ah, I should clarify that point, it is confusing as I wrote it.
I meant that there is no physical domain over which some point wise property varies discontinuously as a function of whether the point, in some measure, has a rational or irrational distance from some reference, and that the only physical systems that in any sense represent the function do so indirectly, by representing propositions about it (such as the examples you gave).
Ah, I should clarify that point, it is confusing as I wrote it.
I meant that there is no physical domain over which some point wise property varies discontinuously as a function of whether the point, in some measure, has a rational or irrational distance from some reference, and that the only physical systems that in any sense represent the function do so indirectly, by representing propositions about it (such as the examples you gave).