>In the most basic sense, to believe the mind a box that can output things not based on input is inherently to believe it "irrational" in the truest sense of the word.
No, it believes that the mind has an internal state. We have many physical cases of state which is in practice undecidable. Moreover, in many formulation of quantum physics one can have a state which is unreachable even in theory - not just hidden variable style QM theory, there are ways to get unreachable state even in 'regular' QM[0].
>And if that's the case, the question is where does that irrationality come from?
The universe itself. The linked PDF - you might be familiar with the author, he features often on HN - provides one method this is possible. Though, I'm not saying this is true, I suspect it may not be.
[0]
https://arxiv.org/abs/1306.0159
