Applicability of Maths to the Universe

[GrandizerII]

Yeah, but you're answering a different question from what I'm pondering. Why is the answer so "messy" (irrational) rather than "clean" (rational)? Whole numbers are not the only numbers that are rational anyway.

Like Rahn, you are answering a different question: a question of how to prove some number is irrational or not a whole number or whatever. I am asking about some deep principle underlying the "messiness" of numbers that seem to be non-arbitrary in terms of its uses and practical values but nevertheless have seemingly arbitrary and random decimal digits.