User blog comment:P進大好きbot/Relation between an OCF and an Ordinal Notation/@comment-30754445-20180810102658/@comment-80.14.89.103-20180810120956

> Nevertheless, it's the most efficient way we currently know to construct large ordinals. The only way that allows us to follow the process explicitly. This is required, for example, if we want to create a googological array notation, because we need to know the "expansion rules" at every step of the way.

> And this cannot be done with any current notation that reaches PTO(ZFC) or even PTO(Z2). Such a notation is a akin to teleporting yourself to Mt. Everest, instead of actually climbing the mountain. I suppose it still counts for breaking records, but it pretty much sucks the fun out of the game itself.

What about TON ?