As though the "non-dimensional" fruit constant would be arise from a quantity of apple as measured by a unit defined as the average weight of a sample of oranges. If the orange average yields a Real number, small changes in either quantity have random effects and probably makes the comparison of apples and oranges appear chaotic, and some derivative in the relationship between them could yield an irrational constant.

Their example of R0 for viral spread and Mach2 always being twice the speed of sound are ways of enumerating a phenomenon based on some consistent physically observed measure (e.g. speed of sound in our atmosphere), and then applying an abstraction or counterfactual to the number (2x, half, etc), and you get irrational artifacts as a result. That is, you can use these non-dimensional numbers to reason effectively about physical phenomena, but not to compute precise simulations of them them in reasonable resource/timeframes.

I'd wonder if the precision of a given non-dimensional measurement and the complexity class of the algorithm required to compute it past a certain point of precision have a fast heuristic for determining it. Again, layman with language and not the tools or background, but coupled with an emerging popular interest in analog computing (optical chips, AI, fractals, synthesis, quantum etc) it just piques the imagination about what in math is signal, and what may be noise.