Comment by qmalxp

This kind of thing happens in math a lot. Any time you use the axiom of choice to prove something exists, it's non-constructive. It exists, but you can't get your hands on it.

I wrote a comment down below about how one could in principle determine a number which is probably BB(n), but you could never be sure. But I just had the crazy thought that if a human brain is really just an N-state Turing machine for some giant N, then any human would either wait forever or give up before finding the true BB(n) for some n. Time for bed!