I'm not arguing that you can't calculate BB numbers, in fact we've calculated some of them. What I'm arguing is that you can't calculate all the BB numbers, since this will mean that the Halting Problem is solvable. Using the results of your link I guess we can say that BB numbers can be computed if n<748 (or <20 according to Aaronson).
> In 2016, he and his graduate student Adam Yedidia specified a 7,910-rule Turing machine that would only halt if ZF set theory is inconsistent. This means BB(7,910) is a calculation that eludes the axioms of ZF set theory. Those axioms can’t be used to prove that BB(7,910) represents one number instead of another, which is like not being able to prove that 2 + 2 = 4 instead of 5.
OMG! A number that's so much big that can be contained in the ZF set theory.
I'm not arguing that you can't calculate BB numbers, in fact we've calculated some of them. What I'm arguing is that you can't calculate all the BB numbers, since this will mean that the Halting Problem is solvable. Using the results of your link I guess we can say that BB numbers can be computed if n<748 (or <20 according to Aaronson).
> In 2016, he and his graduate student Adam Yedidia specified a 7,910-rule Turing machine that would only halt if ZF set theory is inconsistent. This means BB(7,910) is a calculation that eludes the axioms of ZF set theory. Those axioms can’t be used to prove that BB(7,910) represents one number instead of another, which is like not being able to prove that 2 + 2 = 4 instead of 5.
OMG! A number that's so much big that can be contained in the ZF set theory.