The thing is that any computable complexity measure allows one to algorithmically produce an infinite which seems to have a complexity which goes to infinite as it get longer but since it is the product of a finite length computer program has finite complexity.
On the other hand, you can prove that for "nearly all" finite sequences of symbols, the algorithmic complexity is within a constant of naive statistical measures.
How is that done? My naive approach would be "always pick the next symbol that most increases complexity" but that doesn't seem guaranteed to diverge and could easily be trapped in local Maxima...
On the other hand, you can prove that for "nearly all" finite sequences of symbols, the algorithmic complexity is within a constant of naive statistical measures.