User blog comment:PsiCubed2/For Newbies (and Veterans too): The Great Scale of Googology/@comment-24725252-20171219225952/@comment-30754445-20171220041310

(1) The scale is discontinous anyway, because it isn't a generally defined function. It's just a ruler or a guide that may (or may not) help beginners find their way through the large number (and ordinal) landscape.? So "level 490" is meaningless unless we manually define it. And we can't define it unless we reach it. Right now, the only thing we can say about "level 490" is that the numbers there are way bigger than anything any human has ever concieved to date.

(2)  Remember that this is a scale of large numbers and not a scale of ordinals. The two don't directly correspont to one-another. It is only when we decide on specific fundamental sequences (or some other similar criteria), that the two can be linked. And this, obviously, cannot be done for all countable ordinals.

So unless we're dealing with a realm that googologists have already travelled, the question of "which ordinal corresponds to large number X" is meaningless.

(3) Ordinals are becoming less and less useful as we get to the extreme top of the scale, anyway. Case in point: Do you know what's the ordinal corresponding to Rayo's number? I don't either, and it doesn't matter. We don't need ordinals to understand how big Rayo is. It isn't defined by a recursive process, so who cares? I strongly doubt that the size of a "level 490" number, if we ever define one, would correspond to a specific ordinal.

(4) The limit of human understanding will always be strictly less then level 500. If there's anything that googology has taught us, is that the infinite is forever unreachable. The faster we chase it, the faster it runs away. In the words of Richard Schwartz: "Infinity is bigger than you think".