User blog comment:Boboris02/Algorithm for Generating LUCOs From TON Expressions + Intuitive Analysis/@comment-2607:FB90:D90:ACA8:DCB6:A3F6:47D:84D1-20180602235655/@comment-32697988-20180603010713

1) G(65) is so much larger than G(64) that G(64) seems like nothing compared to G(65). For exmample G(64)↑^(G(64)-1)G(64), or G(64)-1 up arrows between G(64) ang G(64), is still much smaller than G(65). 2) 3) The Church-Kleene Ordinal is the growth rate of the Busy Beaver function. It is impossible to make a turing machine that calculates BB(n) because of the halting problem, which says that there is no algorithm that can compute whether a turing machine halts given an input. The Church-Kleene ordinal is the supremum of all recursive ordinals. Recursive ordinals are the ordinals whose fundametal sequence can be computed with an algorithm. This means f_α(n) in FGH is computable if and only if α is recursive, making f_{ω_1^CK}(n) the first uncomputable function in the hierarchy.