[JadeNB]

> I believe the digits of pi can be calculated algorithmically, no? That program is a bound on the information content of pi.

Yes, good point. I was using the term informally, and probably incorrectly, to mean that π (conjecturally) contains any finite string of digits (in any base)—what is formally called 'normality' (https://en.wikipedia.org/wiki/Normal_number). Apropos of your correct belief, there's a lovely so called 'spigot algorithm' due to Bailey–Borwein–Plouffe that can generate any hexadecimal digit of π that you please without having to generate intermediate digits: https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula .