User blog comment:Eners49/The secret 0th hyper-operator?/@comment-35470197-20180726231426/@comment-35532815-20180727161004

Yes, I know the slow-growing hierarchy and how it works, and it really is super slow-growing considering the amount of work you need to go to just to get relatively large googolisms; for example, you can't reach Graham's Number until the Feferman-Schutte ordinal and you can't reach numbers like a tethrathoth until reaching the Bachmann-Howard ordinal. However, it intrigued me to know that you can use the slow-growing hierarchy and Veblen ordinals to create googolisms as large as a GODSGODGULUS or even larger!

I've heard that it's theorized the slow-growing hierarchy eventually exceeds the fast-growing one. Is this true? Has it been proven? That brings to another interesting question i wanted to make a blog on too - do down-arrows eventually catch up to up-arrows? With smaller numbers of arrows, the down-arrows lag about one or two arrows behind the up-arrows. So: Do the down-arrows always lag an arrow or two behind the up-arrows, continually get weaker than them, or at some point catch up? It would help so much if I found out the answer