Boris: There's a small amount of subtlety in actually doing step 1.

Douglas: Isn't it simply impossible? That doesn't interfere with your claim that such a Turing machine exists, but step 1 claims that it's computable.

It's impossible to bound BB(n) computably in n, but that leaves open the following question, on which Boris's argument depends.

Let BBB(n), the Busy Beaver Bound function, be the size of the smallest Turing machine that, starting from a blank tape, prints out an upper bound for BB(n). Boris's step (1) claims that BBB(n) is bounded by n+c for some constant c. It is not obvious to me either that this is true or that this is false.