Seems weird to think that some of the possible configurations of bits on my 1.5TB hard drive don't exist. Which ones? I hope none of the really good collections of pr0n are logically unreachable.

If that number does exist, then what about really big busy beaver numbers, like bb(2^10^13 )? They're just a series of computations on hard drive contents. And that number is so close to infinity that we might as well just step from ultrafinitism to plain old finitism.