User blog comment:Boboris02/MBOT/@comment-30167082-20161218151736/@comment-1605058-20161219215647

What I wanted to emphasize, but I didn't in the last comment, is that taking "the largest number describable in n symbols in array notation" is not that far off from creating \(\{\underbrace{n,n,\dots,n}_n\}\). In both cases, we are taking a notation which has already been created and has its strength, and we are just turning it into a single, fast-growing function. This might be more akin to what Bird has done e.g. with his S function, where \(S\) is actually defined by taking the notation and diagonalizing one more time.

I don't really want to keep this argument going here, but if you want, feel free to join our IRC channel, where we can talk about it more (everyone else is invited as well!).