The thing that frustrates me about this argument is that there is no shortest program that produces pi. You need a computer to run it, which is massive non compressed data, or a human to calculate stuff, an uncountable amount of entropy.

I see that the irrational pi has a smooth distribution of digits and a file full of zeroes is compressible, but they are both sort of magically part of a world that does not run programs and thus not quite different in a practical sense.

Just my thoughts and sorry for the confusion.

I think that does not hold, Kolmogorov complexity is measured relative to a pre-defined universal machine for everything. The machine is not counted in the description of π, for the same reason a book's length isn't measured by including the size of the reader. You fix one interpreter, then ask "how long is the shortest input that makes something?" The interpreter is a constant — the same constant for π, for the random file, for every string in the post