User blog comment:Plain'N'Simple/Letter Notation Up to Z: Outline and mnemonics/@comment-36984051-20191106024302/@comment-39541634-20191106132040

"(0,0,0)(1,1,1)(2,2,2) is an important point for me, because it seems the first time when UNOCF users accepted an upperbound."

Unfortunately it's a useless upperbound, because nobody dares to attach an actual ordinal to (0,0,0)(1,1,1)(2,2,2).

Speaking of which:

I would be interested to know the percentage of UNOCF users who'd concede that UNOCF is less powerful than (say) PTO(ZFC). I think a great deal of them would accept this statement as true.

On the other side of the coin, I wonder how many UNOCF users believe that UNOCF is stronger than anything computable (which would, of-course, contradicts the notion that it is bound by (0,0,0)(1,1,1)(2,2,2), but they may not know that).

"UNOCF users regarded any other actual OCFs as weaker functions than UNOCF"

Of-course they do.

Because they think purely on the notational level. They think that if they borrow the general look of a notation, the result will automatically be just as powerful. They also think that simple extentions can put a dent in the insanely powerful notations that they borrow.

Want a Mahlo-level notation? Easy, just write down the letter M and you've conjured a demon that does Mahlo-level collapse.

Want something far stronger? No problem, just make some salady extention that uses the letter M. And just to be sure, will notate the diagonalization of this extention with the letter K, and we've magically done a collapse of Pi-3 reflections.

Who knew that ordinal analysis could be so easy? Makes you wonder why you've spent all those years learning maths in college, doesn't it?

"In my opinion, this is the main reason why googologists love to extend or simplify BMS. We do not have to care about any disappointing issue related to UNOCF."

I think that 3-row BMS is a great learning tool, as long as you realize its limits. It serves as a great visual aid for studying large ordinals (and I understand there's also a hydra analogue). I think many googologists love to play around with trio sequences, simply because they learn so much from doing so. I

UNOCF could also serve a similar purpose, if it didn't visually resemble actual OCFs so much. You could still learn tons of useful things from playing around with UNOCF, but you'll also learn a bunch of cr*p that will take a considerable effort to unlearn later.