> But BB is an uncomputable function. You've not escaped undecidability at all. You cannot write a program that will compute BB(n) given n as an input.

I think you're going down the wrong path re "uncomputable". BB(n) is easily computable, just write a little program that enumerates (generates) and runs all n-state BB machines. BB(n) is the largest lifetime of any those n-state machines. BB(n) is known and easily computable for small n.

The problem is that the number of machines increases very quickly with n, and the time taken to evaluate each machine often increases quickly with n. So for even moderate n, it is completely impractical to brute-force compute BB(n). But impractical is not uncomputable.

Just because you don't wait to wait past the heat-death of the universe, doesn't mean that you wouldn't have got an answer eventually. And eventually = computable.