[achierius]

Concretely we know that there exist irreducible structures, at least in mathematics: https://en.wikipedia.org/wiki/Classification_of_finite_simpl...

The largest of the finite simple groups (themselves objects of study as a means of classifying other, finite but non-simple groups, which can always be broken down into simple groups) is the Monster Group -- it has order 808017424794512875886459904961710757005754368000000000, and cannot be reduced to simpler "factors". It has a whole bunch of very interesting properties which thus can only be understood by analyzing the whole object in itself.

Now whether this applies to biology, I doubt, but it's good to know that limits do exist, even if we don't know exactly where they'll show up in practice.

[whatshisface]

That's not really true, otherwise every paper about it would be that many words long. The monster group can be "reduced" into its definition and its properties which can only be considered a few at a time. A person has a working memory of three to seven items.