Thank you for your interest. You might not have seen the next article in the series, “Why the universe might very well be a computer simulation” — I touch on that there, even though only a little.
This is a very old problem —for example, if you could subdivide everything infinitely, the universe must be filled with infinite zero-point energy, which makes any kind of thermodynamics impossible. The solution for this in our math is quantization, ie things (dimensions, energies, masses, even times) can not get infinitely small because they consist of finite quantities. Incidentally, this is exactly how we simulate physics… Oops.
(Please note that “rational” and “irrational” in case of numbers have little to do with “ratio” as “rational mind”, but “ratio” as in “ratio between two numbers”, ie, “fraction”. “Irrational”, in that sense, does not mean “it doesn’t make sense”, but merely “it can’t be represented as a fraction”. This bit often seems to get lost.)