I know there is a proof that it is, but I'm trying to intuitively understand it.

A human can clearly (or at least I think) compute BB(x) .....(by which I mean a function which accepts x as input and outputs the busy beaver of x).

So if a human can do it (theoretically) for any x, then does that disprove the church-turing thesis?

/e: I had no idea where else to post this.

This post was edited by Casey on Jan 9 2014 03:44am

wrong, anything above 4 is an estimate...so until you find someone with the answer you likely won't compute it

I know anything above 4 is an estimate....my question is, couldn't a human exhaustively search every possibility for BB(x)?

(You DO know that BB(5) is computable, it just hasn't been found yet....) So no, anything above 5 is only an estimate because no one has found it yet.

I'm talking about computability, not if it's realistically computable, but literal computability (does there exist an algorithm to compute it)

I know it's proven there isn't, but intuitively it bugs me. What stops a human (a hypothetical one) from computing the busy beaver function for arbitrary x given enough time? If a human could, then why can't a turing machine do it?

This post was edited by Casey on Jan 9 2014 09:42am