I think this more or less has to do with formal languages for specifying numbers. If you have a formal language in which any string might (or might not) be inte

I think this more or less has to do with formal languages for specifying numbers. If you have a formal language in which any string might (or might not) be interpreted to mean a single integer, then by the pigeonhole principle, half the integers of a given string-length will require strings of greater information length expression to be referred to. So relative to this given formal language, you can have a smaller integer that doesn't have a compact representation, doesn't have representation "smaller" than itself (and so might be labeled "boring"). And you can refer to the smallest of these integers in some meta-language but you can't refer to this smallest integer within the given formal language (and still have the language be consistent). Related to: Kolmogorov complexity, Godel's Second Incompleteness Theorem, Chaitin's Number Omega