User blog comment:P進大好きbot/Relation between an OCF and an Ordinal Notation/@comment-30754445-20180810102658/@comment-30754445-20180812005256

"Problems occurs when googologists misunderstood the notion of a real (set thoertic) OCF as an ordinal notation containing such a symbol. They learn "Ok, imitating the expansion rules like those, I obtain a very strong OCF". When we point out that it lacks axiomatic explanation using set theory, then thay would say "it has nothing to do with set theory, and the strength is obvious because it has a similar expansion rule as another one"."

I agree completely.

But there's no danger of falling into this trap just because people say "OCF" when they mean "an OCF-based ordinal notation". People fall into this trap because they don't understand how a typical OCF work in the first place, which is a completely different problem.

And the really funny thing is, right now people seem to be falling into the reverse trap. They seem to think that by saying "this has nothing to do with set theory so it's not an OCF at all", is somehow going to miraculously turn their notations into and OCF-clone that is somehow independent of set theory (and equally strong too).

"The point is that they could not understand "where to see" in order to observe the "similarity" respecting the strength."

Precisely.

And of-course, if you dare point that out, they accuse you of being an arrogant know-it-all.

(I'd like to think that I wasn't that insufferable when I was a beginner myself, but to be honest - I probably was...)

"> What I would mind, is if someone made a jumble of definitions and symbols, and declared he had created an OCF just because of some vague visual similarities.

Maybe this is the same as what I said above"

Yup. We are in complete agreement on this.

"Perhaps you may think that this problem is not derived from the confusion of the terminology, but I strongly think so."

Oh, I agree that the problem is (at least partially) derived from the confusion of the terminology. Just not the particular confusion you've mentioned (unless I misunderstood what you wrote).

The problem is not that people confuse an OCF with the ordinal notation that is based on it. The problem is that without a some background in set theory, they can't even understand the terminology which is used to define a typical OCF, let alone understand how it works.

And trying to mimic something without understanding how it works, tends (to put it mildly) to yield sub-optimal results.

"Ok. I understand what you mean. Although it is actually possible (because I defined expansion rules in syntax theoretic way), it is impossible for human beings to compute. Only computers can, if they have sufficient memory."

Can an actual physical computer do this in practice? Or does it have to be one of those ideal computers with near-infinite memory and near-infinite speed?