User blog comment:Syst3ms/YAUD/@comment-35470197-20180810233326/@comment-32697988-20180810234452

He is not talking about ordinals. At least he does not say so.

What he did is just defined the binary function α[β] (α and β are strings). (α[β] is not defined for some α and β.) To make large numbers, just put these strings in the FGH and pretend you don't know about fundamental sequences.