User blog comment:Mh314159/The psycholog of large numbers/@comment-35470197-20190708222539/@comment-39585023-20190708231819

Wow, that's as good an explanation for someone like me of the large uncomputable numbers. A function that grows faster than all functions provably finite in a given mathematical system. I don't know what ACA0+Π12−BIACA0+Π21−BI is but I assume from what you said that you can't use it to prove that TREE(n) terminates, but that there are other systems that can prove it. But I don't understand how you can talk about the output of a function if it grows faster than all functions that are provably finite in "the usual math". How do you know it has an output? So I can't follow you all the way to the joy of the LTIs and how they can be classified as "computable". Do the LTIs grow faster than the fastest growing versions of the busy beaver?

And I'm still not getting a lot closer to understanding WHY I find these things compelling!