"Interesting. I see this as some kind of anti-thesis to rationality; being in some sense exactly what rationalists deny. Sure, we may believe in chaos and unpredictability, but we still believe that rationality is the best way to deal with it."

Yes, I suppose you could characterize it as an anti-thesis to rationality. Mostly, I think that rationality is an excellent way to deal with many things. But it is not the solution to every single problem (love is probably the best example of this I can give).

As for things beyond rational, well, your second paragraph, you might agree, is beyond rational. It's not irrational, but it's a value judgment about the fact that the theory of rationality can always be expanded. You can't justify it within the theory itself.

So I'm not advocating for irrationality as a better means to rationality, simply that they both exist and both have their uses. To believe that you can and should increase your rationality is both rational and great. But to believe that you will always be able to achieve perfect rationality strikes me as a bit irrational.