[ravi-delia]

Oh absolutely, you could never actually use BB(n) even with an oracle on hand. I simplify to cheating on math mostly because it's sort of crazy to think about coming at a problem from that angle (if the Goldbach conjecture is false there's obviously some N where it stops holding, but it's bizarre that you can formulate an N which is independent of the question), but really BB is hard because it's such a slight relaxation of the halting problem. It is a little more interesting (to me at least) than SAT because you expect SAT to be as hard as math. I mean, it's basically just a proof done the long hard way. But even though BB(n) doesn't provide an especially useful upper bound, it does let you expand the halting problem out large enough to use as a bludgeon, since even having information about BB(n) would still let you cheat. It's fun that way!