User blog comment:Vel!/Googology and well-defined-ness/@comment-83.237.170.16-20141017233503/@comment-83.237.175.41-20141018165849

In that particular case, the author couldn't have used the formula because the relevant notation hadn't existed yet (though apparently a different one did); it was a very old article. (For what it's worth, the formulas involved do eventually veer into typical grade B descriptions of the "then we repeat the last dozen steps using the function we just got" sort; and as far as I can figure out, by the end of the article the poor guy is well into grade C territory, almost hitting the grade D boundary.)

I don't entirely agree with the statement, by the way; but it's very debatable what exactly counts as an unambiguous definition (the infamous proof of x+y=y+x - which in printed form is three meters wide - comes to mind in particular). I won't be surprised if, this side of Conway (and the occasional Ramsey-style problem), there had in fact been no true grade A definitions beating Graham's number. (And most of the known descriptions of Graham's number gloss over a lot of details anyway; only mentioning examples of the up-arrow system where the right-hand number is equal to 3 - thus mystifying readers such as me as to why exactly does 3^^^3=3^^(3^^3) evaluate to a power tower of height 3^27 - is a common problem in particular.) In light of that, the statement basically means that "we're all amateurs, sure, occasional precision is useful, but unless you're going to feed that into a computer we're fine as long as we can figure out how it's supposed to work approximately". Which I can almost agree with, sure (and the "almost" is because we do get the occasional "let's write a computer program to handle stupidly huge numbers" Munafo or "I'm a serious mathematician, I'd better write it down in serious mathematics" Conway).