User blog comment:P進大好きbot/Analysis of 非想非非想 notation/@comment-39541634-20190827132021/@comment-32697988-20190828144949

I think there should be blog posts (or articles) that explains some ordinal notations. For example take the ordinal notation of Buchholz's OCF. The Japanese googology wiki has an explanation but it's only the technical definition, and although it's easier to understand than how Buchholz originally introduced the ordinal notation, it still feels hard to understand because there is no explanation to help understand it. It is good to have formal definitions, but without explanations only few people will be able to understand since the majority of the people that read this wiki are not mathematicians. At least, I think one blog post explaining Buchholz's OCF, the ordinal notation of it, and the fundamental sequence system will be very helpful.

I feel like the situation is getting better: a while (like a year) ago many people used UNOCF in their "analyses" of notations that aren't proved to terminate and thought it was fine. However now I think many people are starting to realize the importance of formalizations because some people have been trying to formalize the low levels of UNOCF and Syst3ms has made attempts of making pi notation and stellar OCF, which were ill-defined, into ordinal notations. However, I also feel like people are not sure how to do so. I think what people need now is knowing how to formalize OCFs, how to do analyses properly, how to prove terminations of notations, etc. (as "how" I mean the actual method, not things like "to make ordinal notations make standard form rules and comparison rules".) and an example that can be understood by non-mathematicians will be really useful here.