User blog comment:Boboris02/MBOT/@comment-30167082-20161218101337/@comment-30754445-20161218155820

I second Mush9's question.

How does one get form this definition to Turing Machines? A string of 1's and 0's can mean tons of other things.

How does "⇔0=∞" get you to "give machines that don't halt a score of zero"? (At least, I assume that what it means, given that the end result should be "The Busy Beaver Function")

How does "⇔k⇔m" gets you to "the largest m for the set k"? I don't recall seeing such a definition or even implication anywhere in the actual post.

And where does the definition tell us that "set k" is the set of all TM's with n states?

Where does it tell us that the number m is the total number 1's the machines output upon halting (rather than the maximum number of 1's a given machine outputs anytime during its run? or the distance between the first 1 and the last 1 even if there are 0's in between? or the maximum number of consecutive 1's, even though they may be 1's elsewhere? Or a score of m for machines that output only consecutive 1's and a score of 0 to those who also produce spaces?)

To summarize:

Would it be possible to extract the "Busy Beaver" meaning of this definition, without the explicit "spoiler" in the text saying it refers to Busy Beavers? If so, how?