Humans are able to check whether a string of parens, like ()(()()), is matched but finite state machines can't.
In any case, if you know how the regex is constructed, it's not surprising. But I found it fun to actually do the construction, instead of just being theoretically aware of the possibility.
Is this balanced or not: ((((((((((((((((((((())))))))))))))))))))? Humans can check only so many parentheses before losing track of them, so it is still an FSM in my opinion.
Also, those regexes are directly translated from the equivalent and much smaller FSM. Regexes are necessarily complex only because they have Kleene stars and nothing else; it's like representing every Boolean circuits with NAND, which is of course possible and a little fun fact but the process itself isn't exactly fun to me.
Humans can't see the balance at a glance, but we can still easily check the balance of arbitrarily complex nested parenthesis because we are not limited in the same way an FSM is. We're just way way way slower than a computer.
Yeah, I agree that humans can indeed check some non-regular languages. That doesn't however mean that humans are inherently capable for checking all non-regular languages, as they are severely limited in the working memory size. Most if not all divisibility rules are a set of least significant digits or weighted running sums because they are subject to the same constraint, so they are indeed necessarily regular.
