I think the point is that McLoone is using two different notations and measuring an artifact of this. There's nothing special about base-10 denominators.
Perhaps we could say he's comparing Shannon entropy per symbol for the two systems.
It seems that what's special about rationals with power-of-10 (with power > 1) denominators is that we have a readily available shorthand, uh notation, for them.
Notation can be very significant. The transition from Roman numberals to positional notation with 0 took a thousand or so years. But boy did it ever make long division easier!
Strictly speaking it is not Kolmogorov complexity (That has an upper bound, namely the constant size of a program that can output arbitrarily many digits of Pi.)
Kolmogorov complexity requires a standard Turing machine to measure -- switching notations isn't allowed. Rational approximations to Pi (or any other irrational number) vary substantially in terms of accuracy/size, which is why many standard libraries include functions for computing convergents.
Yes, isn't saying that rational approximations of pi are useless the same as saying that all approximations of pi are useless? Or is there some meaningful irrational approximation of pi that can be made?
